**Meet the editor**

Prof Dr Eng Dan Constantin Dumitras graduated at the Faculty of Electronics, University Politehnica Bucharest in 1970. He obtained his PhD at the Institute of Atomic Physics, Bucharest in 1978. Since 1970 he has been involved in research on laser physics and applications (frequency stabilization of lasers, photoacoustic spectroscopy, laser applications in medicine and biology,

material processing and ultrashort pulse, high intensity lasers - extreme light) at the Department of Lasers, Institute of Atomic Physics and at the National Institute for Laser, Plasma and Radiation Physics, Bucharest. He works as a professor and a PhD supervisor at the Faculty of Applied Sciences, University Politehnica Bucharest. He is the author and/or editor of 15 books and has published more than 120 papers in scientific journals. He held more than 200 presentations at the international conferences (30 invited lectures).

Contents

**Preface IX** 

**Part 1 Basic Processes 1** 

**Part 2 New Systems 137** 

Chapter 4 **Ultrashort Pulses 139** 

Akira Endo

Rakesh Kumar Soni

**I. Principles 3** 

Chapter 1 **CO2 Laser Photoacoustic Spectroscopy:** 

Chapter 2 **CO2 Laser Photoacoustic Spectroscopy:** 

Chapter 3 **CO2 Lasing on Non-Traditional Bands 103**  Vladimir Petukhov and Vadim Gorobets

Chapter 5 **High Average Power Pulsed CO2 Laser** 

Chapter 6 **Diffusion Cooled V-Fold CO2 Laser 179** 

Chapter 7 **Heterodyne Interferometer for Measurement** 

Chapter 8 **Transmission of CO2 Laser Radiation Through** 

A. D. Pryamikov, A. F. Kosolapov, V. G. Plotnichenko and E. M. Dianov

Keiichiro Urabe and Kunihide Tachibana

Dan C. Dumitras, Ana Maria Bratu and Cristina Popa

**II. Instrumentation and Applications 43**  Dan C. Dumitras, Ana Maria Bratu and Cristina Popa

Mikhail N. Polyanskiy and Marcus Babzien

**for Short Wavelength Light Sources 163** 

**of Electron Density in High-Pressure Plasmas 209** 

**Glass Hollow Core Microstructured Fibers 227** 

### Contents

#### **Preface XI**

### **Part 1 Basic Processes 1**  Chapter 1 **CO2 Laser Photoacoustic Spectroscopy: I. Principles 3** Dan C. Dumitras, Ana Maria Bratu and Cristina Popa Chapter 2 **CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 43** Dan C. Dumitras, Ana Maria Bratu and Cristina Popa Chapter 3 **CO2 Lasing on Non-Traditional Bands 103**  Vladimir Petukhov and Vadim Gorobets **Part 2 New Systems 137**  Chapter 4 **Ultrashort Pulses 139**  Mikhail N. Polyanskiy and Marcus Babzien Chapter 5 **High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 163**  Akira Endo Chapter 6 **Diffusion Cooled V-Fold CO2 Laser 179**  Rakesh Kumar Soni Chapter 7 **Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 209**  Keiichiro Urabe and Kunihide Tachibana Chapter 8 **Transmission of CO2 Laser Radiation Through Glass Hollow Core Microstructured Fibers 227**  A. D. Pryamikov, A. F. Kosolapov, V. G. Plotnichenko and E. M. Dianov

#### **Part 3 Material Processing 249**

Chapter 9 **Application of Laser-Burnishing Treatment for Improvement of Surface Layer Properties 251**  Joanna Radziejewska

#### Chapter 10 **Covering with Carbon Black and Thermal Treatment by CO2 Laser Surfaces of AISI 4340 Steel 275**  G. Vasconcelos, D. C. Chagas and A. N. Dias


#### **Part 4 Medical Applications 355**


### Preface

The molecular carbon dioxide laser was invented in 1964 by C. K. N. Patel at Bell Labs. Immediately, it proved to be a high-power, continuous wave (CW) laser and a relatively high-efficiency gas laser (20-25% conversion of electrical energy into laser radiation), both in CW or pulsed operation. As a matter of fact, the CO2 lasers are the highest-power CW lasers (more than 100 kW) and one of the highest-energy pulsed gas laser (100 kJ) that are currently available. It demonstrated the utility in different device concepts and found a wide range of applications, from basic sciences till material processing and medicine, because it has a well established technology, it is versatile, simple to operate and relatively cheap on investment and maintenance.

The present book includes several contributions aiming a deeper understanding of the basic processes in the operation of CO2 lasers (lasing on non-traditional bands, frequency stabilization, photoacoustic spectroscopy) and achievement of new systems (CO2 lasers generating ultrashort pulses or high average power, lasers based on diffusion cooled V-fold geometry, transmission of IR radiation through hollow core microstructured fibers). The second part of the book is dedicated to applications in material processing (heat treatment, welding, synthesis of new materials, micro fluidics) and in medicine (clinical applications, dentistry, non-ablative therapy, acceleration of protons for cancer treatment).

The editor would like to thank all the chapter authors for their effort in completion of this book.

> **Dan C. Dumitras** National Institute for Laser, Plasma and Radiation Physics (INFLPR) Romania

**Part 1** 

**Basic Processes**

**Part 1** 

**Basic Processes**

**1** 

**I. Principles** 

 *Romania* 

**CO2 Laser Photoacoustic Spectroscopy:** 

*Department of Lasers, National Institute for Laser, Plasma, and Radiation Physics, Bucharest* 

Laser photoacoustic spectroscopy (LPAS) has emerged over the last decade as a very powerful investigation technique, capable of measuring trace gas concentrations at ppmV (parts per million by volume), or even sub-ppbV (parts per billion by volume) level. Recent achievements in this field have made it possible to fully characterize the method and improve the design of instrument components in view of the task they are expected to

The photoacoustic (PA) (formerly also known as optoacoustic) effect consisting in sound generation from the interaction of light and matter was discovered by Alexander Graham Bell (Bell, 1880). He noticed that focused intensity-modulated light (chopped sunlight) falling on an optically absorbing solid substance produced an audible sound. In the next year, light absorption was detected through its accompanying acoustic effect not only in solids, but also in liquids and gases by Bell (Bell, 1881), Tyndall (Tyndall, 1881), Röntgen (Röntgen, 1881), and Preece (Preece, 1881). They found the sound was stronger when the substance was placed in a sample cell (then called "photophone" and later "spectrophone"). It was Bell again that first described the resonant amplification of the PA signal (Bell, 1881). The PA effect was also investigated at different light wavelengths. Bell and Preece were among the first to notice a PA signal for an aerosol when they experimented with cigar smoke. The advances of photoacoustic spectroscopy up to the invention of the laser were

Over the last five decades, technological developments in the field of lasers and highsensitivity pressure detection systems (microphones and electronics) have contributed to the substantial progress of photoacoustic spectroscopy. The introduction of laser light sources emitting highly monochromatic and collimated intense beams have opened up new areas of research. Lasers provide the advantage of high spectral power density owing to their intrinsic narrow linewidth. This laser linewidth is usually much smaller than the molecular absorption linewidth (GHz region at atmospheric pressure), and therefore it is not an important issue in most measurements. A true revival of PA spectroscopy was due to Kerr and Atwood (Kerr & Atwood, 1968), who made the earliest experiments with a laser illuminated PA detector in 1968, and Kreuzer (Kreuzer, 1971), who first measured gas

**1. Introduction** 

**1.1 Historical remarks** 

reviewed by Kaiser in 1959 (Kaiser, 1959).

fulfill.

Dan C. Dumitras, Ana Maria Bratu and Cristina Popa

### **CO2 Laser Photoacoustic Spectroscopy: I. Principles**

Dan C. Dumitras, Ana Maria Bratu and Cristina Popa *Department of Lasers, National Institute for Laser, Plasma, and Radiation Physics, Bucharest Romania* 

#### **1. Introduction**

Laser photoacoustic spectroscopy (LPAS) has emerged over the last decade as a very powerful investigation technique, capable of measuring trace gas concentrations at ppmV (parts per million by volume), or even sub-ppbV (parts per billion by volume) level. Recent achievements in this field have made it possible to fully characterize the method and improve the design of instrument components in view of the task they are expected to fulfill.

#### **1.1 Historical remarks**

The photoacoustic (PA) (formerly also known as optoacoustic) effect consisting in sound generation from the interaction of light and matter was discovered by Alexander Graham Bell (Bell, 1880). He noticed that focused intensity-modulated light (chopped sunlight) falling on an optically absorbing solid substance produced an audible sound. In the next year, light absorption was detected through its accompanying acoustic effect not only in solids, but also in liquids and gases by Bell (Bell, 1881), Tyndall (Tyndall, 1881), Röntgen (Röntgen, 1881), and Preece (Preece, 1881). They found the sound was stronger when the substance was placed in a sample cell (then called "photophone" and later "spectrophone"). It was Bell again that first described the resonant amplification of the PA signal (Bell, 1881). The PA effect was also investigated at different light wavelengths. Bell and Preece were among the first to notice a PA signal for an aerosol when they experimented with cigar smoke. The advances of photoacoustic spectroscopy up to the invention of the laser were reviewed by Kaiser in 1959 (Kaiser, 1959).

Over the last five decades, technological developments in the field of lasers and highsensitivity pressure detection systems (microphones and electronics) have contributed to the substantial progress of photoacoustic spectroscopy. The introduction of laser light sources emitting highly monochromatic and collimated intense beams have opened up new areas of research. Lasers provide the advantage of high spectral power density owing to their intrinsic narrow linewidth. This laser linewidth is usually much smaller than the molecular absorption linewidth (GHz region at atmospheric pressure), and therefore it is not an important issue in most measurements. A true revival of PA spectroscopy was due to Kerr and Atwood (Kerr & Atwood, 1968), who made the earliest experiments with a laser illuminated PA detector in 1968, and Kreuzer (Kreuzer, 1971), who first measured gas

CO2 Laser Photoacoustic Spectroscopy: I. Principles 5

At present many research groups are actively involved in the development of LPAS systems for various applications in different disciplines, including nondestructive evaluation of materials, environmental analysis, agricultural, biological, and medical applications, investigation of physical processes (phase transitions, heat and mass transfer, kinetic studies), and many others. Our facility, which was originally designed for ethylene (C2H4) analysis at the low ppb level, is adaptable with minor modifications to a broad range of

A gaseous molecule that absorbs electromagnetic radiation is excited to a higher electronic, vibrational or rotational quantum state. The excited state loses its energy by radiation processes, such as spontaneous (fluorescence) or stimulated emission, and/or by collisional relaxation, in which energy is converted into translational energy. Radiative emission and chemical reactions do not play an important role in the case of vibrational excitation, because the radiative lifetimes of the vibrational levels are long compared with the time needed for collisional deactivation at pressures used in photoacoustics (∼1 bar), and the photon energy is too small to induce chemical reactions. Thus, in practice the absorbed energy is completely released via either fluorescence (at low pressures) or collisions. The latter give rise to a gas temperature increase due to energy transfer to translation as heat, appearing as translational (kinetic) energy of the gas molecules. The deposited heat power density is proportional to the absorption coefficient and incident light intensity. The nonradiative relaxation process occurs when the relaxation time can compete with the radiative lifetime of the excited energy levels. Radiative decay has a characteristic lifetime of 10-7 s at visible wavelengths as compared with 10-2 s in IR at 10 μm. For nonradiative decay these values depend on pressure (the decay time

is inversely proportional to pressure) and may vary strongly at atmospheric pressures (10-3-10-

There are three techniques of linear laser spectroscopy, based on measurement of different

The most important optical process, as far as spectroscopic trace gas detection is concerned, is based on the extinction of radiation by molecular absorption. The absorption features and strengths specific of each molecule make it possible to identify trace gases and determine their concentrations. Absorption coefficients are typically on the order of 1 cm-1 (one wave number). The absorption of trace gas molecules in a gas mixture may be monitored by detecting the attenuation of the laser beam over a fixed absorption path length *L*. According to the Beer-Lambert law, the transmitted laser power in the absence of saturation is given by:

where *P*(0) and *P*(*L*) are the laser powers before and after the absorption cell, respectively;

(cm-1) is the absorption coefficient at a given pressure of the gas at a specific laser

*P L P L P cL* () () = α= α 0 exp( ) 0 exp *<sup>p</sup>* () ( ) , (1)



τ

α*p*

gases and vapors having absorption spectra in the infrared (IR).

8 s) depending on the gas nature and the involved energy level.


**2. Basic principles** 

physical quantities:

**2.1 Linear laser spectroscopy methods** 

concentrations using a PA detector and a laser in 1971. Later experiments by Kreuzer and collaborators (Kreuzer & Patel, 1971; Kreuzer et. al., 1972) effectively demonstrated the extremely high sensitivity attainable by this method. To improve the detection of atmospheric pollutants, Dewey et al. (Dewey et. al., 1973) have used in 1973 an acoustic resonance chamber and have reached amplification factors higher than 100. In 1977, the feasibility of *in situ* aerosol measurements, which were important for atmospheric applications, was first reported by Bruce and Pinnick (Bruce & Pinnick, 1977) and Terhune and Anderson (Terhune & Anderson, 1977). Subsequently, many experimental and theoretical works have been reported in the literature, proving the applicability of the method not only in spectroscopy, but also in various fields of physics, chemistry, biology, medicine, and engineering. The potential of laser photoacoustic spectroscopy has been discussed in several review articles (Patel & Tam, 1981; West, 1983; Hess, 1983; Tam, 1986; Sigrist, 1986, 2003; Meyer & Sigrist, 1990; Harren & Reuss, 1997; Harren et al., 2000; Miklos et al., 2001; Schmid, 2006) and books (Pao, 1977; Rosencwaig, 1980; Zharov & Letokhov, 1986; Hess, 1989; Mandelis, 1992, 1994; Bicanic, 1992; Gusev & Karabutov, 1993; Sigrist, 1994; Mandelis & Hess, 1997).

#### **1.2 Features of a gas sensor**

The most important features of a gas sensor include high sensitivity and selectivity, large dynamic range, high accuracy and precision, good temporal resolution, ease of use, versatility, reliability, robustness, and multicomponent capability. Gas chromatographs are neither sensitive nor fast enough. Although there is no ideal instrument that would fulfill all the requirements mentioned above, a spectroscopic method and particularly the simple setup of LPAS provide several unique advantages, notably the multicomponent capability, high sensitivity and selectivity, wide dynamic range, immunity to electromagnetic interferences, convenient real time data analysis, operational simplicity, relative portability, relatively low cost per unit, easy calibration, and generally no need for sample preparation. LPAS is primarily a calorimetric technique and, as such, differs completely from other previous techniques, as the absorbed energy can be determined directly, instead of via measurement of the intensity of the transmitted or backscattered radiation. In conjunction with tunable lasers, *in situ* monitoring of many substances occurring at ppbV or even pptV (parts per trillion by volume) concentrations is a routine task today. PA detection provides not only high sensitivity but also the necessary selectivity for analyzing multicomponent mixtures by the use of line-tunable IR lasers, e.g., CO lasers (Sigrist et al., 1989) or CO2 lasers (Meyer & Sigrist, 1990).

CO2 laser photoacoustic spectroscopy offers a sensitive technique for detection and monitoring of trace gases at low concentrations. The CO2 laser is of special interest, as it ensures high output power in a wavelength region (9-11 μm) where more than 250 molecular gases/vapors of environmental concern for atmospheric, industrial, medical, military, and scientific spheres exhibit strong absorption bands (Hubert, 1983). This laser, however, can be only stepwise tuned when operated in cw (continuous wave). Nevertheless, it is an ideal source to push the sensitivity of PA gas detection into the concentration range of ppbV or even lower. Instruments based on LPAS have nearly attained the theoretical noise equivalent absorption detectivity of 10-10 cm-1 in controlled laboratory conditions (Harren et al., 1990). This high sensitivity cannot be achieved in real detection conditions due to the coherent photoacoustical background signal and interfering background absorption of normal atmospheric constituents.

At present many research groups are actively involved in the development of LPAS systems for various applications in different disciplines, including nondestructive evaluation of materials, environmental analysis, agricultural, biological, and medical applications, investigation of physical processes (phase transitions, heat and mass transfer, kinetic studies), and many others. Our facility, which was originally designed for ethylene (C2H4) analysis at the low ppb level, is adaptable with minor modifications to a broad range of gases and vapors having absorption spectra in the infrared (IR).

#### **2. Basic principles**

4 CO2 Laser – Optimisation and Application

concentrations using a PA detector and a laser in 1971. Later experiments by Kreuzer and collaborators (Kreuzer & Patel, 1971; Kreuzer et. al., 1972) effectively demonstrated the extremely high sensitivity attainable by this method. To improve the detection of atmospheric pollutants, Dewey et al. (Dewey et. al., 1973) have used in 1973 an acoustic resonance chamber and have reached amplification factors higher than 100. In 1977, the feasibility of *in situ* aerosol measurements, which were important for atmospheric applications, was first reported by Bruce and Pinnick (Bruce & Pinnick, 1977) and Terhune and Anderson (Terhune & Anderson, 1977). Subsequently, many experimental and theoretical works have been reported in the literature, proving the applicability of the method not only in spectroscopy, but also in various fields of physics, chemistry, biology, medicine, and engineering. The potential of laser photoacoustic spectroscopy has been discussed in several review articles (Patel & Tam, 1981; West, 1983; Hess, 1983; Tam, 1986; Sigrist, 1986, 2003; Meyer & Sigrist, 1990; Harren & Reuss, 1997; Harren et al., 2000; Miklos et al., 2001; Schmid, 2006) and books (Pao, 1977; Rosencwaig, 1980; Zharov & Letokhov, 1986; Hess, 1989; Mandelis, 1992, 1994; Bicanic, 1992; Gusev &

The most important features of a gas sensor include high sensitivity and selectivity, large dynamic range, high accuracy and precision, good temporal resolution, ease of use, versatility, reliability, robustness, and multicomponent capability. Gas chromatographs are neither sensitive nor fast enough. Although there is no ideal instrument that would fulfill all the requirements mentioned above, a spectroscopic method and particularly the simple setup of LPAS provide several unique advantages, notably the multicomponent capability, high sensitivity and selectivity, wide dynamic range, immunity to electromagnetic interferences, convenient real time data analysis, operational simplicity, relative portability, relatively low cost per unit, easy calibration, and generally no need for sample preparation. LPAS is primarily a calorimetric technique and, as such, differs completely from other previous techniques, as the absorbed energy can be determined directly, instead of via measurement of the intensity of the transmitted or backscattered radiation. In conjunction with tunable lasers, *in situ* monitoring of many substances occurring at ppbV or even pptV (parts per trillion by volume) concentrations is a routine task today. PA detection provides not only high sensitivity but also the necessary selectivity for analyzing multicomponent mixtures by the use of line-tunable IR lasers, e.g., CO lasers (Sigrist et al., 1989) or CO2 lasers

CO2 laser photoacoustic spectroscopy offers a sensitive technique for detection and monitoring of trace gases at low concentrations. The CO2 laser is of special interest, as it ensures high output power in a wavelength region (9-11 μm) where more than 250 molecular gases/vapors of environmental concern for atmospheric, industrial, medical, military, and scientific spheres exhibit strong absorption bands (Hubert, 1983). This laser, however, can be only stepwise tuned when operated in cw (continuous wave). Nevertheless, it is an ideal source to push the sensitivity of PA gas detection into the concentration range of ppbV or even lower. Instruments based on LPAS have nearly attained the theoretical noise equivalent absorption detectivity of 10-10 cm-1 in controlled laboratory conditions (Harren et al., 1990). This high sensitivity cannot be achieved in real detection conditions due to the coherent photoacoustical background signal and interfering background

Karabutov, 1993; Sigrist, 1994; Mandelis & Hess, 1997).

**1.2 Features of a gas sensor** 

(Meyer & Sigrist, 1990).

absorption of normal atmospheric constituents.

#### **2.1 Linear laser spectroscopy methods**

A gaseous molecule that absorbs electromagnetic radiation is excited to a higher electronic, vibrational or rotational quantum state. The excited state loses its energy by radiation processes, such as spontaneous (fluorescence) or stimulated emission, and/or by collisional relaxation, in which energy is converted into translational energy. Radiative emission and chemical reactions do not play an important role in the case of vibrational excitation, because the radiative lifetimes of the vibrational levels are long compared with the time needed for collisional deactivation at pressures used in photoacoustics (∼1 bar), and the photon energy is too small to induce chemical reactions. Thus, in practice the absorbed energy is completely released via either fluorescence (at low pressures) or collisions. The latter give rise to a gas temperature increase due to energy transfer to translation as heat, appearing as translational (kinetic) energy of the gas molecules. The deposited heat power density is proportional to the absorption coefficient and incident light intensity. The nonradiative relaxation process occurs when the relaxation time can compete with the radiative lifetime of the excited energy levels. Radiative decay has a characteristic lifetime of 10-7 s at visible wavelengths as compared with 10-2 s in IR at 10 μm. For nonradiative decay these values depend on pressure (the decay time τ is inversely proportional to pressure) and may vary strongly at atmospheric pressures (10-3-10- 8 s) depending on the gas nature and the involved energy level.

There are three techniques of linear laser spectroscopy, based on measurement of different physical quantities:


The most important optical process, as far as spectroscopic trace gas detection is concerned, is based on the extinction of radiation by molecular absorption. The absorption features and strengths specific of each molecule make it possible to identify trace gases and determine their concentrations. Absorption coefficients are typically on the order of 1 cm-1 (one wave number). The absorption of trace gas molecules in a gas mixture may be monitored by detecting the attenuation of the laser beam over a fixed absorption path length *L*. According to the Beer-Lambert law, the transmitted laser power in the absence of saturation is given by:

$$P(L) = P(0) \exp(\alpha\_p L) = P(0) \exp(\alpha x L) \, , \tag{1}$$

where *P*(0) and *P*(*L*) are the laser powers before and after the absorption cell, respectively; α*p* (cm-1) is the absorption coefficient at a given pressure of the gas at a specific laser

CO2 Laser Photoacoustic Spectroscopy: I. Principles 7

The fluorescence method requires that a certain part of the excitation should relax through radiative channels. This condition is fulfilled by detecting atoms and molecules in the UV, visible, and near-IR spectral regions. As a principal advantage of the fluorescence techniques, the observed signal is proportional to the concentration of the measured species and the accuracy, therefore, depends on the magnitude of the signal relative to detector noise. The sensitivity is so high, that it makes it possible to detect single atoms in the laser

The basic principle of all photothermal (PT) techniques is the absorption of light in a sample leading to a change in its thermal state. This may be a change in temperature or another thermodynamic parameter of the sample that is related to temperature. Measurement of either the temperature, pressure or density change that occurs due to optical absorption is ultimately the basis for all PT spectroscopic methods. PT analysis can be considered as an indirect absorption measurement, since the measured quantity is not an optical signal. (It should be noted here that the classical absorption measurement is not a direct measurement either. Though the measured value in this case is an optical one, namely the transmitted light, the absorbed light quantity is derived from the difference of the incident energy and the transmitted one). The sample heating which produces the PT signal is directly correlated to the absorbed electromagnetic energy. Unlike in conventional transmission spectroscopy, neither scattered nor reflected light contributes to the signal. Although a PT effect can be induced by any light source, lasers are nowadays the preferred source of excitation for two reasons: (i) To a first approximation, the PT signal is proportional to the temperature rise in the sample and thus proportional to the absorbed energy. (ii) For many applications, the selectivity of a PT analysis, as with any other absorption method, depends on the tunability

PA spectroscopy is an indirect technique in that an effect of absorption is measured rather than absorption itself. Hence the name of photoacoustic: light absorption is detected through its accompanying acoustic effect. The advantage of photoacoustics is that the absorption of light is measured on a zero background; this is in contrast with direct absorption techniques, where a decrease of the source light intensity has to be observed. The spectral dependence of absorption makes it possible to determine the nature of the trace components. The PA method is primarily a calorimetric technique, which measures the precise number of absorbent molecules by simply measuring the amplitude of an acoustic signal. In LPAS the nonradiative relaxation which generates heat is of primary importance.

In the IR spectral region, nonradiative relaxation is much faster than radiative decay.

spectroscopy methods is presented in Table 1 (Zharov & Letokhov, 1986).

PA spectroscopy relies on the PA effect for the detection of absorbing analytes. The sample gas is in a confined (resonant or nonresonant) chamber, where modulated (e.g., chopped) radiation enters via an IR-transparent window and is locally absorbed by IR-active molecular species. The temperature of the gas thereby increases, leading to a periodic expansion and contraction of the gas volume synchronous with the modulation frequency of the radiation. This generates a pressure wave that can be acoustically detected by a suitable sensor, e.g., by a microphone. The advantages of the PA method are high sensitivity and small sample volume; besides, the acoustic measurement makes optical detection unnecessary. The main drawback is caused by the sensitivity to acoustic noise, because the measurements are based on an acoustic signal. A comparison of the linear laser

beam.

of the excitation wavelength.

wavelength: α*p* = α*c*; α (cm-1 atm-1) is the gas absorption coefficient (the absorption coefficient normalized to unit concentration), and *c* (atm) is the trace gas concentration. Also, α*p* = *Ntot*σ, where σ (cm2) is the absorption cross section per molecule and *Ntot* = 2.5x1019 molecules cm-3 is the number of absorbing molecules per cubic centimeters at 1013 mbar and 20oC. It results:

$$\varepsilon = -\frac{1}{\alpha L} \ln \frac{P(L)}{P(0)} = -\frac{1}{\alpha L} \ln \left( 1 - \frac{\Delta P}{P(0)} \right) \equiv \frac{1}{\alpha L} \frac{\Delta P}{P(0)},\tag{2}$$

which is valid for Δ*P*/*P*(0) << 1 (optically thin sample), where Δ*P* = *P*(0) – *P*(*L*). For a given *L*, the detection limit is given by the smallest relative change Δ*Pmin*/*P*(0) that can be measured in the transmitted signal. For dilute mixtures and modest absorption path lengths, the desired signal is the small difference between two large values so that high quantitative accuracies in signal intensities are required. The most sensitive method employs frequency modulation and harmonic detection. The sensitivity depends on the linewidth, and for atmospherically broadened lines, Reid et al. (Reid et al., 1978) have reached Δ*Pmin*/*P*(0) ≅ 10-5 in a diode laser spectrometer (1050-1150 cm-1). With a path length of 100 m, the result is a sensitivity of 10-9 cm-1, which corresponds to concentrations of 3 ppbV of a weakly absorbing molecule such as SO2 (ν1 band), or 0.01 ppbV of a strongly absorbing molecule such as CO. Assuming the same detectable attenuation Δ*Pmin*/*P*(0) ≅ 10-5, a path length *L* = 1 m, and an absorption coefficient α = 30.4 cm-1atm-1 (typical of fundamental absorption in the mid-IR), one obtains a minimum detectable absorption coefficient α*<sup>p</sup>* = 10-7 cm-1. This number corresponds to a concentration of 3.3 ppbV at atmospheric pressure. Conventional absorption techniques, which require precise measurements of the difference between two nearly equal signals are, however, unable to realize the full potential of the higher power levels now attainable. Improvement may be obtained by: increasing the path length *L* in a multipass or intracavity arrangement, or using wavelength modulation, i.e., by modulating the wavelength of the incident intensity across a molecular absorption line. In multipass transmission absorption spectroscopy, a multipass transmission cell (White cell) filled with analyte gas with mirrors at each end is used. The beam is folded back and forth through the cell, creating an extended yet defined optical path length within a confined space.

Cavity ringdown spectroscopy confines gas in an optically reflective cavity where laser radiation is introduced. Radiation amplitude decays at a certain rate in the absence of absorption. An absorbing sample gas in the cavity increases the rate of decay, thus indicating the presence of an absorbing species. The advantages of the method are high sensitivity and a small sample volume, while indirect measurement is an important drawback: as the measured parameter is the rate of light intensity decay, decay caused by absorption by the analyte of interest has to be distinguished from the one caused by the mirrors and other cavity-dependent losses.

In linear detection, sensitivity is limited by laser power fluctuations, and a considerable improvement can be obtained by the dark background methods, in which one measures a quantity that is directly proportional to absorption, rather than that part of the laser beam which is absorbed. In the visible, this can be done by monitoring the fluorescence from the upper level of the transition. In the IR, however, the spontaneous emission rate is too low, and most of the excess vibrational energy is converted to heat through inelastic collisions.

coefficient normalized to unit concentration), and *c* (atm) is the trace gas concentration.

2.5x1019 molecules cm-3 is the number of absorbing molecules per cubic centimeters at 1013

11 1 ln ln 1

=− =− − ≅ αα α

*L P L P LP*

which is valid for Δ*P*/*P*(0) << 1 (optically thin sample), where Δ*P* = *P*(0) – *P*(*L*). For a given *L*, the detection limit is given by the smallest relative change Δ*Pmin*/*P*(0) that can be measured in the transmitted signal. For dilute mixtures and modest absorption path lengths, the desired signal is the small difference between two large values so that high quantitative accuracies in signal intensities are required. The most sensitive method employs frequency modulation and harmonic detection. The sensitivity depends on the linewidth, and for atmospherically broadened lines, Reid et al. (Reid et al., 1978) have reached Δ*Pmin*/*P*(0) ≅ 10-5 in a diode laser spectrometer (1050-1150 cm-1). With a path length of 100 m, the result is a sensitivity of 10-9 cm-1, which corresponds to concentrations of 3 ppbV of a weakly

such as CO. Assuming the same detectable attenuation Δ*Pmin*/*P*(0) ≅ 10-5, a path length *L* = 1

number corresponds to a concentration of 3.3 ppbV at atmospheric pressure. Conventional absorption techniques, which require precise measurements of the difference between two nearly equal signals are, however, unable to realize the full potential of the higher power levels now attainable. Improvement may be obtained by: increasing the path length *L* in a multipass or intracavity arrangement, or using wavelength modulation, i.e., by modulating the wavelength of the incident intensity across a molecular absorption line. In multipass transmission absorption spectroscopy, a multipass transmission cell (White cell) filled with analyte gas with mirrors at each end is used. The beam is folded back and forth through the

Cavity ringdown spectroscopy confines gas in an optically reflective cavity where laser radiation is introduced. Radiation amplitude decays at a certain rate in the absence of absorption. An absorbing sample gas in the cavity increases the rate of decay, thus indicating the presence of an absorbing species. The advantages of the method are high sensitivity and a small sample volume, while indirect measurement is an important drawback: as the measured parameter is the rate of light intensity decay, decay caused by absorption by the analyte of interest has to be distinguished from the one caused by the

In linear detection, sensitivity is limited by laser power fluctuations, and a considerable improvement can be obtained by the dark background methods, in which one measures a quantity that is directly proportional to absorption, rather than that part of the laser beam which is absorbed. In the visible, this can be done by monitoring the fluorescence from the upper level of the transition. In the IR, however, the spontaneous emission rate is too low, and most of the excess vibrational energy is converted to heat through inelastic collisions.

cell, creating an extended yet defined optical path length within a confined space.

( ) ( ) ( )

0 00 *P L P P*

( )

ν

mid-IR), one obtains a minimum detectable absorption coefficient

α

(cm-1 atm-1) is the gas absorption coefficient (the absorption

(cm2) is the absorption cross section per molecule and *Ntot* =

1 band), or 0.01 ppbV of a strongly absorbing molecule

= 30.4 cm-1atm-1 (typical of fundamental absorption in the

α

, (2)

*<sup>p</sup>* = 10-7 cm-1. This

Δ Δ

wavelength:

Also, α*p* = *Ntot*σ, where

α*p* = α*c*; α

mbar and 20oC. It results:

absorbing molecule such as SO2 (

m, and an absorption coefficient

mirrors and other cavity-dependent losses.

σ

*c*

The fluorescence method requires that a certain part of the excitation should relax through radiative channels. This condition is fulfilled by detecting atoms and molecules in the UV, visible, and near-IR spectral regions. As a principal advantage of the fluorescence techniques, the observed signal is proportional to the concentration of the measured species and the accuracy, therefore, depends on the magnitude of the signal relative to detector noise. The sensitivity is so high, that it makes it possible to detect single atoms in the laser beam.

The basic principle of all photothermal (PT) techniques is the absorption of light in a sample leading to a change in its thermal state. This may be a change in temperature or another thermodynamic parameter of the sample that is related to temperature. Measurement of either the temperature, pressure or density change that occurs due to optical absorption is ultimately the basis for all PT spectroscopic methods. PT analysis can be considered as an indirect absorption measurement, since the measured quantity is not an optical signal. (It should be noted here that the classical absorption measurement is not a direct measurement either. Though the measured value in this case is an optical one, namely the transmitted light, the absorbed light quantity is derived from the difference of the incident energy and the transmitted one). The sample heating which produces the PT signal is directly correlated to the absorbed electromagnetic energy. Unlike in conventional transmission spectroscopy, neither scattered nor reflected light contributes to the signal. Although a PT effect can be induced by any light source, lasers are nowadays the preferred source of excitation for two reasons: (i) To a first approximation, the PT signal is proportional to the temperature rise in the sample and thus proportional to the absorbed energy. (ii) For many applications, the selectivity of a PT analysis, as with any other absorption method, depends on the tunability of the excitation wavelength.

PA spectroscopy is an indirect technique in that an effect of absorption is measured rather than absorption itself. Hence the name of photoacoustic: light absorption is detected through its accompanying acoustic effect. The advantage of photoacoustics is that the absorption of light is measured on a zero background; this is in contrast with direct absorption techniques, where a decrease of the source light intensity has to be observed. The spectral dependence of absorption makes it possible to determine the nature of the trace components. The PA method is primarily a calorimetric technique, which measures the precise number of absorbent molecules by simply measuring the amplitude of an acoustic signal. In LPAS the nonradiative relaxation which generates heat is of primary importance. In the IR spectral region, nonradiative relaxation is much faster than radiative decay.

PA spectroscopy relies on the PA effect for the detection of absorbing analytes. The sample gas is in a confined (resonant or nonresonant) chamber, where modulated (e.g., chopped) radiation enters via an IR-transparent window and is locally absorbed by IR-active molecular species. The temperature of the gas thereby increases, leading to a periodic expansion and contraction of the gas volume synchronous with the modulation frequency of the radiation. This generates a pressure wave that can be acoustically detected by a suitable sensor, e.g., by a microphone. The advantages of the PA method are high sensitivity and small sample volume; besides, the acoustic measurement makes optical detection unnecessary. The main drawback is caused by the sensitivity to acoustic noise, because the measurements are based on an acoustic signal. A comparison of the linear laser spectroscopy methods is presented in Table 1 (Zharov & Letokhov, 1986).

CO2 Laser Photoacoustic Spectroscopy: I. Principles 9

τ

2. Excitation of a fraction of the ground-state molecular population of the target molecule by absorption of the incident laser radiation that is stored as vibrational-rotational energy; the amount of energy absorbed from the laser beam depends on the absorption

3. Energy exchange processes between vibrational levels (V-V: vibration to vibration transfer) and from vibrational states to rotational and translational degrees of freedom (V-R, T transfer); the energy which is absorbed by a vibrational-rotational transition is almost completely converted to the kinetic energy of the gas molecules by collisional de-excitation of the excited state; the efficiency of this conversion from deposited to translational energy depends on the pressure and internal energy level structure of the molecule; vibrational relaxation is usually so fast that it does not limit the sensitivity; however, notable anomalies occur in the case of diatomic molecules, such as CO, where vibrational relaxation is slow in the absence of a suitable collision partner, and of the dilute mixtures of CO2 in N2, where the vibrational energy is trapped in slowly relaxing vibrational states of N2; the kinetic energy is then converted into periodic local heating

4. Expansion and contraction of the gas in a closed volume that give rise to pressure variation which is an acoustic wave; the input of photon energy with correct timing

5. Monitoring the resulting acoustic waves with a microphone; the efficiency at which sound is transmitted to the microphone depends on the geometry of the cell and the

Fig. 1. Schematic of the physical processes occurring during optical excitation of molecules

From kinetic gas theory it can be estimated that a molecule performs 109-1010 collisions per second at 1 bar pressure. This means that at atmospheric pressure the photon energy is transformed into an acoustical signal in about 10-5-10-6 s. For most polyatomic molecules signal production is even faster. The time needed by the pressure wave to travel from the laser beam area to the microphone in the acoustic cell is therefore in most cases longer than the vibrational relaxation time. For a distance of a few centimeters this transit time is about 10-4 s. The time delay between excitation and detection of the pressure wave, however, is influenced not only by energy transfer processes and the transit time, but also by the response time of the gas-microphone system, being about 10-4 s or longer (Hess, 1983).

leads to the formation of a standing acoustic wave in the resonator.

the range

τ

at the modulation frequency.

in photoacoustic spectroscopy.

thermodynamic properties of the buffer gas.

*th* >> 1/*f* >>

coefficient, which is a function of pressure.

τ

*nr*, where

nonradiative lifetime of the excited energy state of the molecule.

device may also be employed, or the laser beam is modulated directly by modulation of its power supply; the extremely narrowband emission of the laser allows the specific excitation of molecular states; the laser power should be modulated with a frequency in

*th* is the thermal relaxation time, and

τ*nr* the


Table 1. Comparison of linear laser spectroscopy methods.

The favorable properties of LPAS are essentially determined by the characteristics of the laser. The kind and number of detectable substances are related to the spectral overlapping of the laser emission with the absorption bands of the trace gas molecules. Thus, the accessible wavelength range, tunability, and spectral resolution of the laser are of prime importance. With respect to minimum detectable concentrations (LPAS sensitivity), a laser with high output power *PL* is a benefit, because the PA signal is proportional to *PL*. The broad dynamic range is an inherent feature of LPAS and therefore is not affected by the choice of the radiation source. In contrast to remote-sensing methods, LPAS is a detection technique applied locally to samples enclosed in a PA cell. In order to still obtain some spatial resolution, either the samples have to be transported to the system, or the system has to be portable. The temporal resolution of LPAS is determined by the time needed for laser tuning and the gas exchange within the cell. Thus, a small volume PA cell and a fast tunable laser are a plus.

The availability of suitable laser sources plays a key role, as they control the sensitivity (laser power), selectivity (tuning range), and practicability (ease of use, size, cost, and reliability) that can be achieved with the photoacoustic technique. The CO2 laser perfectly fits the bill for a trace gas monitoring system based on LPAS. This IR laser combines simple operation and high output powers. The frequency spacing between two adjacent CO2-laser transitions range from 1 to 2 cm-1. By contrast, the typical width of a molecular absorption line is approximately 0.05 to 0.1 cm-1 for atmospheric conditions. Since this is not a continuously tunable source, coincidences between laser transitions and trace gas absorption lines are mandatory. Fortunately, this does not hamper its applicability to trace gas detection, as numerous gases exhibit characteristic absorption bands within the wavelength range of the CO2 laser which extends from 9 to 12 μm when different CO2 isotopes are used. The CO2 laser spectral output occurs in the wavelength region where a large number of compounds (including many industrial substances whose adverse health effects are a growing concern) possess strong characteristic absorption features and where absorptive interferences from water vapors, carbon dioxide, and other major atmospheric gaseous components may influence the measurements.

#### **2.2 PA effect in gases**

The PA effect in gases can be divided into five main steps (Fig. 1):

1. Modulation of the laser radiation (either in amplitude or frequency) at a wavelength that overlaps with a spectral feature of the target species; an electrooptical modulation

UV – far IR 10-5 – 10-9

1 -

Table 1. Comparison of linear laser spectroscopy methods.

**Absorption Fluorescence PA** 

1 – 10-12

The favorable properties of LPAS are essentially determined by the characteristics of the laser. The kind and number of detectable substances are related to the spectral overlapping of the laser emission with the absorption bands of the trace gas molecules. Thus, the accessible wavelength range, tunability, and spectral resolution of the laser are of prime importance. With respect to minimum detectable concentrations (LPAS sensitivity), a laser with high output power *PL* is a benefit, because the PA signal is proportional to *PL*. The broad dynamic range is an inherent feature of LPAS and therefore is not affected by the choice of the radiation source. In contrast to remote-sensing methods, LPAS is a detection technique applied locally to samples enclosed in a PA cell. In order to still obtain some spatial resolution, either the samples have to be transported to the system, or the system has to be portable. The temporal resolution of LPAS is determined by the time needed for laser tuning and the gas exchange within the cell. Thus, a small volume PA cell and a fast tunable

The availability of suitable laser sources plays a key role, as they control the sensitivity (laser power), selectivity (tuning range), and practicability (ease of use, size, cost, and reliability) that can be achieved with the photoacoustic technique. The CO2 laser perfectly fits the bill for a trace gas monitoring system based on LPAS. This IR laser combines simple operation and high output powers. The frequency spacing between two adjacent CO2-laser transitions range from 1 to 2 cm-1. By contrast, the typical width of a molecular absorption line is approximately 0.05 to 0.1 cm-1 for atmospheric conditions. Since this is not a continuously tunable source, coincidences between laser transitions and trace gas absorption lines are mandatory. Fortunately, this does not hamper its applicability to trace gas detection, as numerous gases exhibit characteristic absorption bands within the wavelength range of the CO2 laser which extends from 9 to 12 μm when different CO2 isotopes are used. The CO2 laser spectral output occurs in the wavelength region where a large number of compounds (including many industrial substances whose adverse health effects are a growing concern) possess strong characteristic absorption features and where absorptive interferences from water vapors, carbon dioxide, and other major atmospheric gaseous components may

1. Modulation of the laser radiation (either in amplitude or frequency) at a wavelength that overlaps with a spectral feature of the target species; an electrooptical modulation

UV and visible Up to single atoms

Radiative channels of relaxation

UV – far IR 10-7 – 10-10 1 – 10-3 Nonradiative

channels of relaxation

 **Method Characteristics** 

Spectral range Sensitivity (cm-1) Time resolution (s) Necessary conditions

laser are a plus.

influence the measurements.

The PA effect in gases can be divided into five main steps (Fig. 1):

**2.2 PA effect in gases** 

device may also be employed, or the laser beam is modulated directly by modulation of its power supply; the extremely narrowband emission of the laser allows the specific excitation of molecular states; the laser power should be modulated with a frequency in the range τ*th* >> 1/*f* >> τ*nr*, where τ*th* is the thermal relaxation time, and τ*nr* the nonradiative lifetime of the excited energy state of the molecule.


Fig. 1. Schematic of the physical processes occurring during optical excitation of molecules in photoacoustic spectroscopy.

From kinetic gas theory it can be estimated that a molecule performs 109-1010 collisions per second at 1 bar pressure. This means that at atmospheric pressure the photon energy is transformed into an acoustical signal in about 10-5-10-6 s. For most polyatomic molecules signal production is even faster. The time needed by the pressure wave to travel from the laser beam area to the microphone in the acoustic cell is therefore in most cases longer than the vibrational relaxation time. For a distance of a few centimeters this transit time is about 10-4 s. The time delay between excitation and detection of the pressure wave, however, is influenced not only by energy transfer processes and the transit time, but also by the response time of the gas-microphone system, being about 10-4 s or longer (Hess, 1983).

CO2 Laser Photoacoustic Spectroscopy: I. Principles 11

usual lengths of the PA cells (∼30 cm), the fractional absorption is very small (10-6-10-2), which means that in the worst case less than 1% of the incident laser power is absorbed in the sample gas inside the PA cell. It follows that the powermeter measures the real value of

Another advantage of photoacoustic spectroscopy as a tool for trace gas analysis is that very few photons are absorbed as the laser beam passes through the sample cell. As a result, notwithstanding the losses from absorption in the windows, the transmitted beam typically has sufficient power for analyzing samples in successive cells, via a multiplexing arrangement. A multiplexed photoacoustic sensor can be used to monitor many different samples simultaneously so that one instrument can be deployed to monitor up to 20 different locations within a clean room, industrial plant or other facility (Pushkarsky et al.,

Following the terminology introduced by Miklos et al. (Miklos et al., 2001), the name 'PA resonator' will be used for the cavity in which the resonant amplification of the PA signal takes place. The term PA cell (or PA detector; both terms are used in the literature to describe the device in which the PA signal is generated and monitored) is reserved for the entire acoustic unit, including the resonator, acoustic baffles and filters, windows, gas inlets and outlets, and microphone(s). Finally, PA instrument (PA sensor) stands for a complete setup, including the PA cell, light source, gas handling system, and electronics used for

It is interesting to mention that the *reverse* PA effect, called "sonoluminiscence", consists in the generation of optical radiation by acoustic waves, while the *inverse* PA effect is the generation of sound due to optical energy being lost from a sample, instead of being

A PA cell can be operated either in nonresonant mode or at an acoustic resonance frequency specific to the PA resonator. In the so-called nonresonant mode, the modulation frequency is much lower than the first acoustic resonance frequency of the PA resonator. In this case, the wavelength of the generated acoustic wave is larger than the cell dimensions. Thus, the generation of standing acoustic waves is not possible. A nonresonant PA cell lacks any means of energy accumulation in the acoustic wave, i.e., the induced pressure fluctuations are a function of the energy absorbed on that cycle alone and, in fact, any acoustic energy remaining from previous cycles tends only to produce noise on the desired signal. The main drawbacks of the nonresonant scheme are the low modulation frequency, which makes the system susceptible to 1/*f* noise, and the relatively large background signal generated by absorption in the windows of the cell and by radiation scattered to the walls. Nevertheless, the acoustically nonresonant cell has an advantage in low-pressure operation, as the signal, and hence the SNR, remains constant as pressure is decreased, whereas for the resonant cell, it drops almost linearly with decreasing pressure (Fig. 3) (Dumitras et al., 2007b). Also, the background signal, which limits the sensitivity of the nonresonant cell at atmospheric pressure, has been found to depend approximately linearly on pressure and would be less

the laser power inside the PA cell (we have "transparent" gases).

deposited in a sample as in the usual PA effect (Tam, 1986).

troublesome in low-pressure operation (Gerlach & Amer, 1978).

2002).

signal processing.

**3. Photoacoustic signal** 

**3.1 Resonant cells** 

#### **2.3 Typical laser photoacoustic setup**

A typical setup of a resonant LPAS, as used in the authors' laboratory for gas studies, is shown in Fig. 2. The continuous wave laser radiation is amplitude-modulated by a mechanical chopper operating at an acoustic resonance frequency of the PA cell. It is then focused by a lens and directed through the resonant PA cell. The transmitted laser power is monitored with a powermeter (signal *PL* in Fig. 2). Inside the cell the radiation produces pressure modulation recorded by microphone as an acoustical signal *V*, which is processed by a lock-in amplifier locked to the chopper frequency. The normalized absorption can then be deduced as being proportional to *V*/*PL* ratio (Cristescu et al., 1997, Dumitras et al., 2007a).

Fig. 2. Typical laser photoacoustic setup for trace gas measurements.

The power reading after beam passage through the PA cell can only be used for "transparent" gas samples. Let us evaluate if this condition is fulfilled. If the absorption is assumed to follow the Beer-Lambert law (Eq. 1), in the case of small absorption, the fractional absorption of the laser beam in the PA cell is given as Δ*P*/*P*(0) ≅ α*Lc* (Eq. 2). The quantity α*Lc* is known as the optical density of the gas in the resonator tube (this quantity is also called absorbance). Therefore, the PA signal proportional to Δ*P* depends linearly on the absorption coefficient, and its dependence on gas concentration is also linear. At α*Lc* = 0.06, a deviation of ~3% results from the linear behavior (~10% for α*Lc* = 0.07). An optical density of 0.06 (an ethylene concentration of 65 ppmV for *L* = 30 cm, the length of our cell) may thus be regarded as the upper limit of the linear range of a PA detector. Consequently, the PA signal can be modeled as a linear function of concentration in the full range from a few tens of pptV to 65 ppmV ethylene, so that the range spans over 6 orders of magnitude! Taking into account typical values for the absorption coefficients of the species to be measured (e.g., for ethylene at concentrations in the range 1 ppbV-10 ppmV, α*c* ≅ 3x10-8-3x10-4 cm-1) and

A typical setup of a resonant LPAS, as used in the authors' laboratory for gas studies, is shown in Fig. 2. The continuous wave laser radiation is amplitude-modulated by a mechanical chopper operating at an acoustic resonance frequency of the PA cell. It is then focused by a lens and directed through the resonant PA cell. The transmitted laser power is monitored with a powermeter (signal *PL* in Fig. 2). Inside the cell the radiation produces pressure modulation recorded by microphone as an acoustical signal *V*, which is processed by a lock-in amplifier locked to the chopper frequency. The normalized absorption can then be deduced as being proportional to *V*/*PL* ratio (Cristescu et al., 1997, Dumitras et al.,

Fig. 2. Typical laser photoacoustic setup for trace gas measurements.

a deviation of ~3% results from the linear behavior (~10% for

for ethylene at concentrations in the range 1 ppbV-10 ppmV,

fractional absorption of the laser beam in the PA cell is given as Δ*P*/*P*(0) ≅

absorption coefficient, and its dependence on gas concentration is also linear. At

The power reading after beam passage through the PA cell can only be used for "transparent" gas samples. Let us evaluate if this condition is fulfilled. If the absorption is assumed to follow the Beer-Lambert law (Eq. 1), in the case of small absorption, the

also called absorbance). Therefore, the PA signal proportional to Δ*P* depends linearly on the

of 0.06 (an ethylene concentration of 65 ppmV for *L* = 30 cm, the length of our cell) may thus be regarded as the upper limit of the linear range of a PA detector. Consequently, the PA signal can be modeled as a linear function of concentration in the full range from a few tens of pptV to 65 ppmV ethylene, so that the range spans over 6 orders of magnitude! Taking into account typical values for the absorption coefficients of the species to be measured (e.g.,

*Lc* is known as the optical density of the gas in the resonator tube (this quantity is

α

α

α

*Lc* = 0.07). An optical density

*c* ≅ 3x10-8-3x10-4 cm-1) and

*Lc* (Eq. 2). The

*Lc* = 0.06,

α

**2.3 Typical laser photoacoustic setup** 

2007a).

quantity

α

usual lengths of the PA cells (∼30 cm), the fractional absorption is very small (10-6-10-2), which means that in the worst case less than 1% of the incident laser power is absorbed in the sample gas inside the PA cell. It follows that the powermeter measures the real value of the laser power inside the PA cell (we have "transparent" gases).

Another advantage of photoacoustic spectroscopy as a tool for trace gas analysis is that very few photons are absorbed as the laser beam passes through the sample cell. As a result, notwithstanding the losses from absorption in the windows, the transmitted beam typically has sufficient power for analyzing samples in successive cells, via a multiplexing arrangement. A multiplexed photoacoustic sensor can be used to monitor many different samples simultaneously so that one instrument can be deployed to monitor up to 20 different locations within a clean room, industrial plant or other facility (Pushkarsky et al., 2002).

Following the terminology introduced by Miklos et al. (Miklos et al., 2001), the name 'PA resonator' will be used for the cavity in which the resonant amplification of the PA signal takes place. The term PA cell (or PA detector; both terms are used in the literature to describe the device in which the PA signal is generated and monitored) is reserved for the entire acoustic unit, including the resonator, acoustic baffles and filters, windows, gas inlets and outlets, and microphone(s). Finally, PA instrument (PA sensor) stands for a complete setup, including the PA cell, light source, gas handling system, and electronics used for signal processing.

It is interesting to mention that the *reverse* PA effect, called "sonoluminiscence", consists in the generation of optical radiation by acoustic waves, while the *inverse* PA effect is the generation of sound due to optical energy being lost from a sample, instead of being deposited in a sample as in the usual PA effect (Tam, 1986).

#### **3. Photoacoustic signal**

#### **3.1 Resonant cells**

A PA cell can be operated either in nonresonant mode or at an acoustic resonance frequency specific to the PA resonator. In the so-called nonresonant mode, the modulation frequency is much lower than the first acoustic resonance frequency of the PA resonator. In this case, the wavelength of the generated acoustic wave is larger than the cell dimensions. Thus, the generation of standing acoustic waves is not possible. A nonresonant PA cell lacks any means of energy accumulation in the acoustic wave, i.e., the induced pressure fluctuations are a function of the energy absorbed on that cycle alone and, in fact, any acoustic energy remaining from previous cycles tends only to produce noise on the desired signal. The main drawbacks of the nonresonant scheme are the low modulation frequency, which makes the system susceptible to 1/*f* noise, and the relatively large background signal generated by absorption in the windows of the cell and by radiation scattered to the walls. Nevertheless, the acoustically nonresonant cell has an advantage in low-pressure operation, as the signal, and hence the SNR, remains constant as pressure is decreased, whereas for the resonant cell, it drops almost linearly with decreasing pressure (Fig. 3) (Dumitras et al., 2007b). Also, the background signal, which limits the sensitivity of the nonresonant cell at atmospheric pressure, has been found to depend approximately linearly on pressure and would be less troublesome in low-pressure operation (Gerlach & Amer, 1978).

CO2 Laser Photoacoustic Spectroscopy: I. Principles 13

govern the loss mechanisms that determine the quality factors of the resonances and also

A comparison of the microphone signals for nonresonant operation at 100 Hz and resonant operation at 564 Hz is depicted in Fig. 4 (a) and (b), respectively, together with the chopper waveforms. For nonresonant operation, the laser beam was amplitude-modulated with a duty cycle (pulse duration divided by the pulse period) of 25%, and the PA signal exhibits ringing at the resonant frequency on top of the 100-Hz square wave. For resonant operation, the laser beam was amplitude-modulated with a duty cycle of 50% and the microphone output was simply a coherent sine wave. In Fig. 4 (b), the data were recorded with a

The resonant cells can be adequatelly characterized by a model based on an acoustic

(a)

(b) Fig. 4. Microphone signals for: (a) nonresonant operation of the PA cell (Pushkarsky et al., 2002); (b) resonant operation of the PA cell (our cell), recorded with a Tektronix DPO 7104 Digital Oscilloscope, horizontal scale 1 ms/div, vertical scales 1 V/div. (rectangle wave) and

Several distinct resonances can be generated if the dimensions of a cavity are comparable with the acoustic wavelength. The standing wave patterns and resonance frequencies depend on the shape and size of the PA resonator. The most frequently used resonator is the cylinder, the symmetry of which coincides well with that of a laser beam propagating along the cylinder axis. The natural acoustic resonance frequencies of a lossless cylindrical resonator (fully reflecting walls) are determined as a solution of the wave equation in

cause small shifts in the resonant frequencies.

concentration of 1 ppmV of ethylene in the PA cell.

transmission line (Cristescu et al., 2000).

0.5 V/div. (sine wave amplified x 100).

cylindrical coordinates (Hess, 1983):

**3.2 Resonance frequencies** 

Fig. 3. Dependence of the PA cell responsivity on the total gas pressure in the cell (measured with 1 ppmV ethylene in nitrogen).

Nonresonant operation can compete with enhanced resonant operation only at much lower frequencies and smaller cell volumes; however, a number of practical difficulties have been cited. At low frequencies, gas inlet-outlet ports act as pneumatic short circuits for the induced pressure (Kritchman et al., 1978). Excess acoustic energy in previous cycles of the modulated light can produce noise in the nonresonant signal, while in resonant operation this type of noise is avoided because the energy in each cycle contributes to a standing wave (Kamm, 1976). For the small, nonresonant cell, attachment of the microphone can lead to difficulties in extracting the optimum pressure response signal (Dewey, 1977).

With increasing modulation frequency, the acoustic wavelength equals the cell dimensions at a certain point, and the resonant modes of the cell can be excited, leading to an amplification of the signal. The signal can be boosted manifold by: a) designing the sample cell as an acoustic resonance chamber, so that the pressure fluctuations produced by spatially and temporally nonuniform excitation contribute to standing acoustic waves within the chamber, and b) minimizing dissipation of the acoustic energy and modulating the laser beam spatially and temporally at a frequency which coincides with one of the natural resonant acoustic frequencies of the chamber. The system becomes an acoustic amplifier in the sense that the energy existing in the standing wave is many times higher than the energy input per cycle, and the signal is amplified by a quality factor *Q*. The final signal amplification obtainable depends on the resonator losses. After an initial transient state, during which energy is accumulated in the standing acoustic wave, a steady state is reached in which the energy lost per cycle by various dissipation processes is equal to the energy gained per cycle by absorption of IR laser photons. Resonance properties mainly depend on the geometry and size of the cavity. For an acoustically resonant PA cell, important parameters will include gas characteristics such as heat capacity, thermal conductivity, viscosity, energies and relaxation times of the molecular vibrations and the sound velocity which determines the resonant frequencies of the cavity. Other parameters

Fig. 3. Dependence of the PA cell responsivity on the total gas pressure in the cell (measured

0 200 400 600 800 1000

p (mbar)

Nonresonant operation can compete with enhanced resonant operation only at much lower frequencies and smaller cell volumes; however, a number of practical difficulties have been cited. At low frequencies, gas inlet-outlet ports act as pneumatic short circuits for the induced pressure (Kritchman et al., 1978). Excess acoustic energy in previous cycles of the modulated light can produce noise in the nonresonant signal, while in resonant operation this type of noise is avoided because the energy in each cycle contributes to a standing wave (Kamm, 1976). For the small, nonresonant cell, attachment of the microphone can lead to

With increasing modulation frequency, the acoustic wavelength equals the cell dimensions at a certain point, and the resonant modes of the cell can be excited, leading to an amplification of the signal. The signal can be boosted manifold by: a) designing the sample cell as an acoustic resonance chamber, so that the pressure fluctuations produced by spatially and temporally nonuniform excitation contribute to standing acoustic waves within the chamber, and b) minimizing dissipation of the acoustic energy and modulating the laser beam spatially and temporally at a frequency which coincides with one of the natural resonant acoustic frequencies of the chamber. The system becomes an acoustic amplifier in the sense that the energy existing in the standing wave is many times higher than the energy input per cycle, and the signal is amplified by a quality factor *Q*. The final signal amplification obtainable depends on the resonator losses. After an initial transient state, during which energy is accumulated in the standing acoustic wave, a steady state is reached in which the energy lost per cycle by various dissipation processes is equal to the energy gained per cycle by absorption of IR laser photons. Resonance properties mainly depend on the geometry and size of the cavity. For an acoustically resonant PA cell, important parameters will include gas characteristics such as heat capacity, thermal conductivity, viscosity, energies and relaxation times of the molecular vibrations and the sound velocity which determines the resonant frequencies of the cavity. Other parameters

difficulties in extracting the optimum pressure response signal (Dewey, 1977).

with 1 ppmV ethylene in nitrogen).

0

50

100

150

R (cmV/W)

200

250

300

govern the loss mechanisms that determine the quality factors of the resonances and also cause small shifts in the resonant frequencies.

A comparison of the microphone signals for nonresonant operation at 100 Hz and resonant operation at 564 Hz is depicted in Fig. 4 (a) and (b), respectively, together with the chopper waveforms. For nonresonant operation, the laser beam was amplitude-modulated with a duty cycle (pulse duration divided by the pulse period) of 25%, and the PA signal exhibits ringing at the resonant frequency on top of the 100-Hz square wave. For resonant operation, the laser beam was amplitude-modulated with a duty cycle of 50% and the microphone output was simply a coherent sine wave. In Fig. 4 (b), the data were recorded with a concentration of 1 ppmV of ethylene in the PA cell.

The resonant cells can be adequatelly characterized by a model based on an acoustic transmission line (Cristescu et al., 2000).

Fig. 4. Microphone signals for: (a) nonresonant operation of the PA cell (Pushkarsky et al., 2002); (b) resonant operation of the PA cell (our cell), recorded with a Tektronix DPO 7104 Digital Oscilloscope, horizontal scale 1 ms/div, vertical scales 1 V/div. (rectangle wave) and 0.5 V/div. (sine wave amplified x 100).

#### **3.2 Resonance frequencies**

Several distinct resonances can be generated if the dimensions of a cavity are comparable with the acoustic wavelength. The standing wave patterns and resonance frequencies depend on the shape and size of the PA resonator. The most frequently used resonator is the cylinder, the symmetry of which coincides well with that of a laser beam propagating along the cylinder axis. The natural acoustic resonance frequencies of a lossless cylindrical resonator (fully reflecting walls) are determined as a solution of the wave equation in cylindrical coordinates (Hess, 1983):

CO2 Laser Photoacoustic Spectroscopy: I. Principles 15

For nonideal gases, the sound velocity can be approximately calculated by the following

Little attention has been given to the role of the buffer gas (defined as the optically nonabsorbing gaseous component in photoacoustic detectors). In principle, the molecular weight and the thermodynamic and transport properties of the buffer gas should have a significant impact on the photoacoustic signal. One would also expect the energy transfer between the absorbing species and the buffer gas to play an important role in PA detection (Thomas III et al., 1978; Gondal, 1997). In a mixture of ideal gases, the sound velocity *<sup>s</sup> v* and consequently the resonant frequencies of a PA resonator depend on the effective specific

( )1/2

( ) ( ) 1 1 *b a p p b a v v*

*xC x C xC x C* + −

+ −

Here *<sup>b</sup> Cp* , *<sup>b</sup> Cv* , *<sup>a</sup> Cp* and *<sup>a</sup> Cv* are the heat capacities of the buffer and absorbing gases, respectively; *M<sup>b</sup>* and *M<sup>a</sup>* are their molecular weights; and *x* is the fractional concentration of the buffer gas. When the molecular weight of the buffer gas is increased, the resonance frequency of the PA resonator shifts to lower values. In conclusion, the resonance frequency is a sensitive function of temperature and gas composition, both of which influence the

At a fixed temperature, *vs* also depends on the water content in the air (Rooth et al., 1990):

*p* <sup>γ</sup> =− − <sup>γ</sup>

pressures of water and air are denoted as *pw* and *pair*. The sound velocity in dry air is written

*<sup>s</sup>*<sup>0</sup> *v* . The increase of the resonance frequency of a 30-cm long longitudinal resonator at ambient temperature is 0.90 Hz for 1% of water vapors added to the gas. For all practical purposes, the variation of the resonance frequency with the CO2 concentration is negligible: -0.15 Hz per 1000 ppmV. For a given water vapor concentration, the resonance frequency provides information about the gas temperature inside the resonator. In most cases, the PA

<sup>5</sup> <sup>1</sup>

*w w*

*air air*

8

*air* are the ratios of the specific heats of water vapor and air. The partial

'

*s s*

cell resonance frequency has to be determined experimentally.

0

*<sup>p</sup> v v*

where the specific heat ratio γ and the average molecular weight *M* are:

γ =

where *B* is the second virial coefficient and *p* is the pressure*.* 

heat ratio and the average mass of the mixture:

( ) 1/2 *v RT Bp M <sup>s</sup>* =γ + 2 / , (7)

*v RT M <sup>s</sup>* = γ / , (8)

( ) 1 *M b a* = +− *xM x M* . (10)

, (9)

. (11)

formula:

speed of sound.

Here γ*w* and γ

as '

$$f\_{kun} = \frac{\upsilon\_s}{2} \left[ \left( \frac{k}{L} \right)^2 + \left( \frac{\alpha\_{mu}}{\pi r} \right)^2 \right]^{1/2},\tag{3}$$

where *vs* is the sound velocity, *L* and *r* are the length and radius of the cylinder, the *k, m, n* indices (non-negative integers) refer to the values of the longitudinal, azimuthal, and radial modes, respectively, and α*mn* is the *n*-th root of the derivative of the *m*-th Bessel function:

$$\frac{\text{dJ}\_m(z)}{\text{d}z} = 0\tag{4}$$

(α<sup>00</sup> = 0, α<sup>01</sup> = 3.8317, α<sup>02</sup> = 7.0153, α<sup>10</sup> = 1.8412, α<sup>11</sup> = 5.3311, α<sup>12</sup> = 8.5360, etc.). For the first longitudinal mode, *k* = 1, *m* = 0, *n* = 0 and *f*100 = *f*0 = *vs*/2*L*.

In deducing Eq. (3), it was assumed that there was no phase shift on reflection of the pressure wave from the cavity walls caused either by wall compliance or boundary layer effects. If we depart from the assumption of complete wall rigidity, the boundary layer can be seen to cause significant frequency deviations from the above formula. To evaluate the frequency from Eq. (3), we must know the sound velocity, which may vary with frequency and pressure due to molecular relaxation effects and the nonideal behavior of the gas.

In reality, frequencies at the resonances are somewhat smaller. The corresponding resonance frequencies for PA resonators with open-open ends can be obtained from the following expression (Morse & Ingard, 1986):

$$f\_0 = \frac{\upsilon\_s}{2\left(L + \Delta L\right)} \,\,\,\tag{5}$$

where the quantity Δ*L* is the so-called end correction, which should be added to the length of the pipe for each open end. Physically, the end correction can be understood as an effect of the mismatch between the one-dimensional acoustic field inside the pipe and the threedimensional field outside that is radiated by the open end. The end correction can be approximated by the following expression: Δ*L* ≅ 0.6*r*, where *r* is the radius of the pipe (Miklos et al., 2001). More precisely, the end correction slightly decreases with frequency; therefore the resonance frequencies of an open pipe are not harmonically related but slightly stretched. In our experimental setup, the resonance frequency for 0.96 ppmV of ethylene in pure nitrogen is 564 Hz at *L* = 30 cm. By taking *vs* = 343 m/s in nitrogen at 22oC (the sound velocity in nitrogen of 330 m/s at 0oC was corrected for the room temperature), we have Δ*L* ≅ 0.2 cm for the two open ends of our PA resonator and Δ*L* ≅ 0.6*r* (*r* = 0.35 cm).

In an ideal gas, the sound velocity is given by:

$$w\_s = \left(\gamma RT \;/\; M\right)^{1/2},\tag{6}$$

where γ = *Cp*/*Cv* is the ratio of specific heats at constant pressure and volume, *R* is the idealgas constant, *T* is the absolute temperature, and *M* is the molecular weight. The sound velocity in an ideal gas only depends on temperature and remains unchanged at pressure modifications if γ is constant. In the case of ideal gases, γ = 1.4 for diatomic gases and γ = 1.33 for triatomic gases. Experimentally, the following values have been measured: 1.404 for N2, 1.401 for O2, 1.404 for CO, 1.32 for H2O, 1.31 for NH3, 1.31 for CH4, and 1.25 for C2H4.

*s mn*

where *vs* is the sound velocity, *L* and *r* are the length and radius of the cylinder, the *k, m, n* indices (non-negative integers) refer to the values of the longitudinal, azimuthal, and radial

> <sup>d</sup> ( ) <sup>0</sup> d *mJ z*

In deducing Eq. (3), it was assumed that there was no phase shift on reflection of the pressure wave from the cavity walls caused either by wall compliance or boundary layer effects. If we depart from the assumption of complete wall rigidity, the boundary layer can be seen to cause significant frequency deviations from the above formula. To evaluate the frequency from Eq. (3), we must know the sound velocity, which may vary with frequency and pressure due to molecular relaxation effects and the nonideal behavior of the gas.

In reality, frequencies at the resonances are somewhat smaller. The corresponding resonance frequencies for PA resonators with open-open ends can be obtained from the following

( ) <sup>0</sup> 2

where the quantity Δ*L* is the so-called end correction, which should be added to the length of the pipe for each open end. Physically, the end correction can be understood as an effect of the mismatch between the one-dimensional acoustic field inside the pipe and the threedimensional field outside that is radiated by the open end. The end correction can be approximated by the following expression: Δ*L* ≅ 0.6*r*, where *r* is the radius of the pipe (Miklos et al., 2001). More precisely, the end correction slightly decreases with frequency; therefore the resonance frequencies of an open pipe are not harmonically related but slightly stretched. In our experimental setup, the resonance frequency for 0.96 ppmV of ethylene in pure nitrogen is 564 Hz at *L* = 30 cm. By taking *vs* = 343 m/s in nitrogen at 22oC (the sound velocity in nitrogen of 330 m/s at 0oC was corrected for the room temperature), we have Δ*L*

( )1/2

for triatomic gases. Experimentally, the following values have been measured: 1.404 for N2,

1.401 for O2, 1.404 for CO, 1.32 for H2O, 1.31 for NH3, 1.31 for CH4, and 1.25 for C2H4.

 = *Cp*/*Cv* is the ratio of specific heats at constant pressure and volume, *R* is the idealgas constant, *T* is the absolute temperature, and *M* is the molecular weight. The sound velocity in an ideal gas only depends on temperature and remains unchanged at pressure

γ

≅ 0.2 cm for the two open ends of our PA resonator and Δ*L* ≅ 0.6*r* (*r* = 0.35 cm).

is constant. In the case of ideal gases,

α

<sup>10</sup> = 1.8412,

2

*<sup>v</sup> <sup>k</sup> <sup>f</sup> L r* <sup>α</sup> = + <sup>π</sup>

*kmn*

α

α

<sup>02</sup> = 7.0153,

longitudinal mode, *k* = 1, *m* = 0, *n* = 0 and *f*100 = *f*0 = *vs*/2*L*.

α

modes, respectively, and

<sup>01</sup> = 3.8317,

expression (Morse & Ingard, 1986):

In an ideal gas, the sound velocity is given by:

(α<sup>00</sup> = 0, α

where γ

modifications if

γ

1/2 <sup>2</sup> <sup>2</sup>

*mn* is the *n*-th root of the derivative of the *m*-th Bessel function:

<sup>11</sup> = 5.3311,

α

*<sup>s</sup> <sup>v</sup> <sup>f</sup> L L* <sup>=</sup> + Δ , (5)

*v RT M <sup>s</sup>* = γ / , (6)

= 1.4 for diatomic gases and

γ= 1.33

, (3)

<sup>12</sup> = 8.5360, etc.). For the first

*<sup>z</sup>* <sup>=</sup> (4)

For nonideal gases, the sound velocity can be approximately calculated by the following formula:

$$\upsilon v\_s = \left[ \left\{ \left( RT + 2Bp \right) / M \right\}^{1/2} \right]^{1/2},\tag{7}$$

where *B* is the second virial coefficient and *p* is the pressure*.* 

Little attention has been given to the role of the buffer gas (defined as the optically nonabsorbing gaseous component in photoacoustic detectors). In principle, the molecular weight and the thermodynamic and transport properties of the buffer gas should have a significant impact on the photoacoustic signal. One would also expect the energy transfer between the absorbing species and the buffer gas to play an important role in PA detection (Thomas III et al., 1978; Gondal, 1997). In a mixture of ideal gases, the sound velocity *<sup>s</sup> v* and consequently the resonant frequencies of a PA resonator depend on the effective specific heat ratio and the average mass of the mixture:

$$
\overline{\upsilon}\_s = \left(\overline{\gamma}RT \;/\,\,\overline{M}\right)^{1/2}\,\,\,\,\,\tag{8}
$$

where the specific heat ratio γ and the average molecular weight *M* are:

$$\overline{\gamma} = \frac{\boldsymbol{\infty} \mathbf{C}\_p^b + (1 - \boldsymbol{\chi}) \mathbf{C}\_p^a}{\boldsymbol{\infty} \mathbf{C}\_v^b + (1 - \boldsymbol{\chi}) \mathbf{C}\_v^a} \; \; \tag{9}$$

$$
\overline{M} = \mathfrak{x}M^b + (1 - \mathfrak{x})M^a \,. \tag{10}
$$

Here *<sup>b</sup> Cp* , *<sup>b</sup> Cv* , *<sup>a</sup> Cp* and *<sup>a</sup> Cv* are the heat capacities of the buffer and absorbing gases, respectively; *M<sup>b</sup>* and *M<sup>a</sup>* are their molecular weights; and *x* is the fractional concentration of the buffer gas. When the molecular weight of the buffer gas is increased, the resonance frequency of the PA resonator shifts to lower values. In conclusion, the resonance frequency is a sensitive function of temperature and gas composition, both of which influence the speed of sound.

At a fixed temperature, *vs* also depends on the water content in the air (Rooth et al., 1990):

$$\boldsymbol{\upsilon}\_{s} = \boldsymbol{\upsilon}\_{s0}^{\cdot} \left[ \mathbf{1} - \frac{p\_w}{p\_{air}} \left( \frac{\boldsymbol{\gamma}\_w}{\boldsymbol{\gamma}\_{air}} - \frac{\mathbf{5}}{\mathbf{8}} \right) \right]. \tag{11}$$

Here γ*w* and γ*air* are the ratios of the specific heats of water vapor and air. The partial pressures of water and air are denoted as *pw* and *pair*. The sound velocity in dry air is written as ' *<sup>s</sup>*<sup>0</sup> *v* . The increase of the resonance frequency of a 30-cm long longitudinal resonator at ambient temperature is 0.90 Hz for 1% of water vapors added to the gas. For all practical purposes, the variation of the resonance frequency with the CO2 concentration is negligible: -0.15 Hz per 1000 ppmV. For a given water vapor concentration, the resonance frequency provides information about the gas temperature inside the resonator. In most cases, the PA cell resonance frequency has to be determined experimentally.

CO2 Laser Photoacoustic Spectroscopy: I. Principles 17

In a carefully designed high quality resonator, the contribution of the first three effects can be minimized. The dominant contribution is caused by the viscous and thermal boundary layer losses. Throughout the major portion of the resonator volume the expansion and contraction of the gas occur adiabatically. We neglect heat conduction and viscous losses in the volume of the gas because the acoustic power loss from these effects is very small. However, the wall consists of a material with a thermal conduction coefficient much greater than that of the gas. Thermal dissipation occurs because expansion and contraction of the gas do not proceed adiabatically near the walls, where the process will change to isothermal. The temperature variation changes exponentially from the adiabatic propagation regime in the gas to a zero value at the wall. This leads to heat conduction within a transition region (thermal boundary layer), which is responsible for the thermal dissipation process. Outside a thin boundary layer with thickness *dh*, near the wall, the thermal losses can be neglected:

1/2

. (12)

is the density of mass, *Cp* is the molar heat

, (13)

are much smaller than the radius of the PA

= *Cp*/*Cv* = 1.4. As a result,

ν = (2μ/ρω0)1/2 =

γ

2

*<sup>K</sup> <sup>d</sup>*

*p*

*C* <sup>=</sup> ρω

ρ

The viscous dissipation can be explained by the boundary conditions imposed by the walls. At the surface, the tangential component of the acoustic velocity is zero, whereas inside the cavity, it is proportional to the acoustic pressure gradient. Thus, viscoelastic dissipation occurs in a transition region with a thickness *dv*, which is called the viscous boundary layer:

> 1/2 2 *<sup>v</sup> <sup>d</sup>* <sup>μ</sup> <sup>=</sup> ρω

> > ν

reached when the wavelength of sound is comparable to the cross-sectional dimensions of

of nitrogen at standard pressure (*p* = 1 atm) and room temperature: *K* = 2.552x10-2 W/(m K),

the values for the thermal and viscous boundary layer thicknesses are, respectively: *dh* =

2.2(*f*0)-1/2 (mm Hz1/2) ≅ 0.093 mm (at *f*0 = 564 Hz). Therefore, at atmospheric pressure and

The volumetric or bulk losses are caused by processes that tend to establish equilibrium in

Friction due to compressional motion and the transformation of organized energy into heat due to temperature gradients are responsible for the free space viscous and thermal losses.

ρ

0*Cp*)1/2 = 2.6(*f*0)-1/2 (mm Hz1/2) ≅ 0.110 mm (at *f*0 = 564 Hz) and *d*

audio frequencies, both boundary layers are only a fraction of a millimeter thick.

4. relaxational damping (dissipative relaxation processes within polyatomic gases).

<< *r*), which yields a lower frequency limit. The upper frequency limit is

= 1.142 kg/m3 and

*<sup>s</sup>* = *vs*/*f*<sup>0</sup> ≅ *r*). The magnitude of *dh* and *dv* can be calculated by using the properties

*h*

Here *K* is the thermal conductivity of the gas,

is the viscosity coefficient.

= 1.76x10-5 Pa s, *Cp* = 1.04x103 J/(kg K),

the propagating wave. These damping processes are: 1. free space viscous and thermal dissipation;

ν

Equations (12) and (13) are only valid if *dh* and *d*

= 2π*f* is the angular frequency.

capacity, and

where μ

the tube (

μ

(2*K*/ρω

resonator (*dh*, *d*

λ

2. diffusion effects; 3. radiation effects; and

ω

Since the resonance frequency is proportional to the sound velocity, the temperature dependence of the sound velocity is directly mirrored by the resonance frequency. The sound velocity in air has a temperature coefficient of about 0.18%/oC, thus a frequency shift δ*f* ≅ 0.0018*f*0Δ*T* is expected for a temperature change Δ*T* (oC) (Miklos et al., 2001). The true resonance frequency may therefore deviate from the fixed modulation frequency by δ*f*. Then the PA signal will not be excited at the peak of the resonance, but slightly to one side. Since a detuning from the resonance peak by 0.46 (Δ*f*(10%)/Δ*f*(FWHM) = 16/35) results in a 10% drop of the PA signal (see Fig. 5), the detuning should be smaller than ±0.23*f*0/*Q* for 10% signal stability. This stability can be ensured, if the condition *Q*Δ*T* ≤ 128 (δ*f* ≤ 0.23Δ*f* or 0,0018*f*0Δ*T* ≤ 0.23Δ*f* or *Q*Δ*T* ≤ 0.23/0.0018) is fulfilled (Δ*T* ≤ 7.9oC in our case for *Q* =16.1). The corresponding condition for PA signal stability of 2% can be written as *Q*Δ*T* ≤ 64 (Δ*T* ≤ 4oC in our case). These examples clearly show that low-*Q* photoacoustic resonators are not sensitive to temperature variations and consequently do not need temperature stabilization or active tracking of the resonance to adjust the modulation frequency.

Fig. 5. Resonance curve of our PA cell showing the full width at half maximum (FWHM) and the full widths for a signal drop of 2% and 10% from its maximum.

#### **3.3 Dissipation processes**

The various dissipation processes occurring in an acoustic cavity were first discussed at length by Kamm (Kamm, 1976). The energy accumulation attainable in a standing wave of a resonant cavity is many times larger than the energy loss occurring during a single period of an acoustic oscillation. This acoustical amplification effect is limited, however, by various dissipation processes. The losses can be divided into surface effects and volumetric ones (Johnson et al., 1982). The surface losses are due to the interaction of the standing wave with the internal resonator surface and may be subdivided into the following dissipation processes:


Since the resonance frequency is proportional to the sound velocity, the temperature dependence of the sound velocity is directly mirrored by the resonance frequency. The sound velocity in air has a temperature coefficient of about 0.18%/oC, thus a frequency shift

*f* ≅ 0.0018*f*0Δ*T* is expected for a temperature change Δ*T* (oC) (Miklos et al., 2001). The true

the PA signal will not be excited at the peak of the resonance, but slightly to one side. Since a detuning from the resonance peak by 0.46 (Δ*f*(10%)/Δ*f*(FWHM) = 16/35) results in a 10% drop of the PA signal (see Fig. 5), the detuning should be smaller than ±0.23*f*0/*Q* for 10% signal stability. This stability can be ensured, if the condition *Q*Δ*T* ≤ 128 (δ*f* ≤ 0.23Δ*f* or 0,0018*f*0Δ*T* ≤ 0.23Δ*f* or *Q*Δ*T* ≤ 0.23/0.0018) is fulfilled (Δ*T* ≤ 7.9oC in our case for *Q* =16.1). The corresponding condition for PA signal stability of 2% can be written as *Q*Δ*T* ≤ 64 (Δ*T* ≤ 4oC in our case). These examples clearly show that low-*Q* photoacoustic resonators are not sensitive to temperature variations and consequently do not need temperature stabilization

1.0 Cell 2

564

<sup>560</sup> <sup>568</sup> Δ*f* (2%)

Fig. 5. Resonance curve of our PA cell showing the full width at half maximum (FWHM)

540 550 560 570 580 590

<sup>547</sup> <sup>582</sup> Δ*f* (FWHM)

Δ*f* (10%) 556 572

Chopper frequency *f* (Hz)

The various dissipation processes occurring in an acoustic cavity were first discussed at length by Kamm (Kamm, 1976). The energy accumulation attainable in a standing wave of a resonant cavity is many times larger than the energy loss occurring during a single period of an acoustic oscillation. This acoustical amplification effect is limited, however, by various dissipation processes. The losses can be divided into surface effects and volumetric ones (Johnson et al., 1982). The surface losses are due to the interaction of the standing wave with the internal resonator surface and may be subdivided into the following dissipation processes:

3. losses due to wave scattering at surface obstructions such as gas inlet/outlet,

4. viscous and thermal dissipation in the boundary layer at the smooth internal surfaces.

and the full widths for a signal drop of 2% and 10% from its maximum.

**3.3 Dissipation processes** 

1. compliance of the chamber walls;

microphones, and windows;

2. dissipation at the microphone diaphragm;

0.7

0.8

PA signal *V* (%)

0.9

δ*f*. Then

resonance frequency may therefore deviate from the fixed modulation frequency by

or active tracking of the resonance to adjust the modulation frequency.

δ

In a carefully designed high quality resonator, the contribution of the first three effects can be minimized. The dominant contribution is caused by the viscous and thermal boundary layer losses. Throughout the major portion of the resonator volume the expansion and contraction of the gas occur adiabatically. We neglect heat conduction and viscous losses in the volume of the gas because the acoustic power loss from these effects is very small. However, the wall consists of a material with a thermal conduction coefficient much greater than that of the gas. Thermal dissipation occurs because expansion and contraction of the gas do not proceed adiabatically near the walls, where the process will change to isothermal. The temperature variation changes exponentially from the adiabatic propagation regime in the gas to a zero value at the wall. This leads to heat conduction within a transition region (thermal boundary layer), which is responsible for the thermal dissipation process. Outside a thin boundary layer with thickness *dh*, near the wall, the thermal losses can be neglected:

$$d\_h = \left(\frac{2K}{\text{pooC}\_p}\right)^{1/2}.\tag{12}$$

Here *K* is the thermal conductivity of the gas, ρ is the density of mass, *Cp* is the molar heat capacity, and ω= 2π*f* is the angular frequency.

The viscous dissipation can be explained by the boundary conditions imposed by the walls. At the surface, the tangential component of the acoustic velocity is zero, whereas inside the cavity, it is proportional to the acoustic pressure gradient. Thus, viscoelastic dissipation occurs in a transition region with a thickness *dv*, which is called the viscous boundary layer:

$$d\_v = \left(\frac{2\mu}{\rho \alpha}\right)^{1/2} \text{ \textsuperscript{\textsuperscript{\textsuperscript{\textsuperscript{\textsuperscript{\boxminus}}}}}} \text{ \textsuperscript{\textsuperscript{\textsuperscript{\boxminus}}}} \text{ \textsuperscript{\textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \textsuperscript{\boxminus}} \text{ \} \end{bmatrix} \begin{array}{c \, \boxminus} \text{ \emph{\prime}} \text{ \emph{\prime}} \text{ \emph{\prime}} \text{ \end{array} \tag{13}$$

where μis the viscosity coefficient.

Equations (12) and (13) are only valid if *dh* and *d*ν are much smaller than the radius of the PA resonator (*dh*, *d*ν << *r*), which yields a lower frequency limit. The upper frequency limit is reached when the wavelength of sound is comparable to the cross-sectional dimensions of the tube (λ*<sup>s</sup>* = *vs*/*f*<sup>0</sup> ≅ *r*). The magnitude of *dh* and *dv* can be calculated by using the properties of nitrogen at standard pressure (*p* = 1 atm) and room temperature: *K* = 2.552x10-2 W/(m K), μ = 1.76x10-5 Pa s, *Cp* = 1.04x103 J/(kg K), ρ = 1.142 kg/m3 and γ = *Cp*/*Cv* = 1.4. As a result, the values for the thermal and viscous boundary layer thicknesses are, respectively: *dh* = (2*K*/ρω0*Cp*)1/2 = 2.6(*f*0)-1/2 (mm Hz1/2) ≅ 0.110 mm (at *f*0 = 564 Hz) and *d*ν = (2μ/ρω0)1/2 = 2.2(*f*0)-1/2 (mm Hz1/2) ≅ 0.093 mm (at *f*0 = 564 Hz). Therefore, at atmospheric pressure and audio frequencies, both boundary layers are only a fraction of a millimeter thick.

The volumetric or bulk losses are caused by processes that tend to establish equilibrium in the propagating wave. These damping processes are:


Friction due to compressional motion and the transformation of organized energy into heat due to temperature gradients are responsible for the free space viscous and thermal losses.

CO2 Laser Photoacoustic Spectroscopy: I. Principles 19

In practice, we only include three contributions: viscous and thermal dissipation in the boundary layer at the smooth internal surfaces (surface loss), free space viscous and thermal

The transformation of the absorbed laser energy into heat is usually modeled by a simple relaxation process, while the well-known acoustic-wave equation is applied to calculate the sound-pressure field. The laws of fluid mechanics and thermodynamics can be used to model the acoustic and thermal wave generation in gases. The governing physical equations are the laws of conservation of energy, momentum, mass, and the thermodynamic equation of state. The physical quantities characterizing the acoustic and thermal processes are the

, and the three components of the particle velocity

**r r <sup>r</sup>** , (18)

, and **v** (and by neglecting the influence of the

≈ *d*ν

() ( ) , , *Ht It* = α*<sup>p</sup>* **r r** , (19)

, *dh*) nor for gases

ρ

derived for the acoustic pressure changes, *p* (Miklos et al., 2001):

2

equation (18) is not valid for capillary tubes with a small diameter (2*r* 

with exceptionally high viscosity or heat conductivity.

amplitude of heat production rate, *H*, is given by:

ρ

2 2

thermal and viscous interactions of the gas), a linear (inhomogeneous) wave equation can be

( ) ( )( ) ( ) <sup>2</sup>

where *H*(**r**,*t*) is the heat density deposited in the gas by light absorption. The term on the right-hand side of the equation describes the heat input changes over time. When the heat input is constant, this term is zero and no pressure wave is generated. Thus, the heat input must be modulated, which requires that the laser radiation be also amplitude or frequency modulated. A modulated laser beam generates periodic sound due to the periodic localized heating of the gas. From an acoustic point of view, the PA cell is a linear acoustic system, which responds as a whole to the disturbance generated by light absorption. The differential

When the absorbing gas can be modeled by a two-level system consisting of the vibrational ground and the excited state, Meyer and Sigrist (Meyer & Sigrist, 1990) found that the

where *I*(**r**,*t*) is the intensity of the laser beam. This equation is valid only when the laser beam is slowly chopped in the kHz range or below, and in the absence of optical saturation. If the cross-sectional dimensions of a resonator are much smaller than the acoustic wavelength, the excited sound field develops a spatial variation only along the length of the resonator, i.e., a one-dimensional acoustic field is generated. A narrow pipe (or tube) can be regarded as a one-dimensional acoustic resonator. A pressure wave propagating in the pipe will be reflected by an open end with the opposite phase. Through multiple reflections a standing wave pattern with pressure nodes will be formed. Therefore, open pipes should have resonances when the pipe length is equal to an integer multiple of the half wavelength. Bernegger and Sigrist (Bernegger & Sigrist, 1987) proved that the plane acoustic wave propagation can be modeled by the one-dimensional analogue of the electrical current flow

, , , 1 *<sup>s</sup> p t H t v pt <sup>t</sup> <sup>t</sup>* ∂ ∂ − ∇ = γ− <sup>∂</sup> <sup>∂</sup>

dissipation, and relaxation losses (volumetric losses).

**3.5 Pressure amplitude** 

temperature *T*, pressure *p*, density

vector **v**. By eliminating the variables *T*,

These two processes are often called Stokes-Kirchhoff losses and are small compared with surface damping. Diffusion and radiation effects are normally very small. Nevertheless, radiation losses through openings, e.g., pipes connecting the resonator to buffer volumes, cannot be neglected. The radiation losses can be reduced by increasing the acoustic input impedance of the openings. This is achieved by terminating the cavity resonator at the openings with acoustic band-stop filters, which prevent sound escape from the resonator. Relaxational effects can add a significant contribution in diatomic and polyatomic molecules. The reason for the relaxational losses is the phase difference between gas pressure and density in the dispersion region, leading to an irreversible conversion of sound energy into thermal energy.

#### **3.4 Quality factor**

The amount of signal enhancement that occurs when the laser is modulated at a resonance frequency is determined by the quality factor. At resonance, the amplitude of the PA signal is *Q* times larger than the amplitude far from the resonance frequency, i.e., the amplification is equal to the value of the *Q* factor. The quality factor of the system, *Q*, is the ratio between the energy stored in a specific mode (the acoustic wave) and the energy losses per cycle of this acoustic wave:

$$Q = \frac{2\pi \,\text{accumulated energy}}{\text{energy lost over one period}}.\tag{14}$$

For high *Q* values the quality factor can be deduced dividing the resonance frequency by its bandwidth at the 0.707 amplitude point:

$$Q = \frac{f\_0}{\Delta f} = \frac{\mathbf{o}\_0}{\Delta \mathbf{o}} \tag{15}$$

where *f*0 and Δ*f* are the resonance frequency and the full-width value of the resonance profile (ω0 = 2π*f*0 and Δω = 2πΔ*f*). The full width is measured between the points where the amplitude of the resonance profile is at 1/ 2 the peak value amplitude (half-maximum values of the intensity). Therefore, Δ*f* is also called the full width at half maximum (FWHM). *Q* is typically between 10 and 50 for longitudinal resonators, but can be as high as 1000 for spherical cavities.

Also, the quality factor can be calculated as (Kamm, 1976; Bernegger & Sigrist, 1987):

$$Q = \frac{2S}{2\pi r \left[ d\_v + \left( \gamma - 1 \right) d\_h \right]} \Big/ \tag{16}$$

where *S* stands for the cross section of the resonator tube and *r* for the radius of the tube. By introducing the radius (*r* = 3.5 mm) of the PA resonator we used and the values for the thermal and viscous boundary layer thicknesses determined in the previous section, Eq. (16) yields *Q* = 14.2, in agreement with the experimentally determined value (*Q* = 16.1).

The overall *Q* factor for a resonance may be found by summing all the losses, expressed as 1/*Qi*:

$$\frac{1}{\mathcal{Q}\_{\text{tot}}} = \sum\_{i} \frac{1}{\mathcal{Q}\_{i}}.\tag{17}$$

In practice, we only include three contributions: viscous and thermal dissipation in the boundary layer at the smooth internal surfaces (surface loss), free space viscous and thermal dissipation, and relaxation losses (volumetric losses).

#### **3.5 Pressure amplitude**

18 CO2 Laser – Optimisation and Application

These two processes are often called Stokes-Kirchhoff losses and are small compared with surface damping. Diffusion and radiation effects are normally very small. Nevertheless, radiation losses through openings, e.g., pipes connecting the resonator to buffer volumes, cannot be neglected. The radiation losses can be reduced by increasing the acoustic input impedance of the openings. This is achieved by terminating the cavity resonator at the openings with acoustic band-stop filters, which prevent sound escape from the resonator. Relaxational effects can add a significant contribution in diatomic and polyatomic molecules. The reason for the relaxational losses is the phase difference between gas pressure and density in the dispersion region, leading to an irreversible conversion of sound

The amount of signal enhancement that occurs when the laser is modulated at a resonance frequency is determined by the quality factor. At resonance, the amplitude of the PA signal is *Q* times larger than the amplitude far from the resonance frequency, i.e., the amplification is equal to the value of the *Q* factor. The quality factor of the system, *Q*, is the ratio between the energy stored in a specific mode (the acoustic wave) and the energy losses per cycle of

2 accumulated energy

For high *Q* values the quality factor can be deduced dividing the resonance frequency by its

0 0 *<sup>f</sup> <sup>Q</sup> <sup>f</sup>*

where *f*0 and Δ*f* are the resonance frequency and the full-width value of the resonance profile

of the resonance profile is at 1/ 2 the peak value amplitude (half-maximum values of the intensity). Therefore, Δ*f* is also called the full width at half maximum (FWHM). *Q* is typically between 10 and 50 for longitudinal resonators, but can be as high as 1000 for spherical cavities.

> 2 2 1 *<sup>h</sup> <sup>S</sup> <sup>Q</sup> rd d* <sup>ν</sup> <sup>=</sup> π + γ−

where *S* stands for the cross section of the resonator tube and *r* for the radius of the tube. By introducing the radius (*r* = 3.5 mm) of the PA resonator we used and the values for the thermal and viscous boundary layer thicknesses determined in the previous section, Eq. (16)

The overall *Q* factor for a resonance may be found by summing all the losses, expressed as 1/*Qi*: 1 1 *Q Q tot <sup>i</sup> <sup>i</sup>*

( )

Also, the quality factor can be calculated as (Kamm, 1976; Bernegger & Sigrist, 1987):

yields *Q* = 14.2, in agreement with the experimentally determined value (*Q* = 16.1).

= 2πΔ*f*). The full width is measured between the points where the amplitude

energy lost over one period *<sup>Q</sup>* <sup>π</sup> <sup>=</sup> . (14)

<sup>ω</sup> = = Δ Δω , (15)

, (16)

<sup>=</sup> , (17)

energy into thermal energy.

**3.4 Quality factor** 

this acoustic wave:

0 = 2π*f*0 and Δ

(ω

bandwidth at the 0.707 amplitude point:

ω

The transformation of the absorbed laser energy into heat is usually modeled by a simple relaxation process, while the well-known acoustic-wave equation is applied to calculate the sound-pressure field. The laws of fluid mechanics and thermodynamics can be used to model the acoustic and thermal wave generation in gases. The governing physical equations are the laws of conservation of energy, momentum, mass, and the thermodynamic equation of state. The physical quantities characterizing the acoustic and thermal processes are the temperature *T*, pressure *p*, density ρ, and the three components of the particle velocity vector **v**. By eliminating the variables *T*, ρ, and **v** (and by neglecting the influence of the thermal and viscous interactions of the gas), a linear (inhomogeneous) wave equation can be derived for the acoustic pressure changes, *p* (Miklos et al., 2001):

$$\frac{\partial^2 p(\mathbf{r}, t)}{\partial t^2} - v\_s^2 \nabla^2 p(\mathbf{r}, t) = (\gamma - 1) \frac{\partial H(\mathbf{r}, t)}{\partial t},\tag{18}$$

where *H*(**r**,*t*) is the heat density deposited in the gas by light absorption. The term on the right-hand side of the equation describes the heat input changes over time. When the heat input is constant, this term is zero and no pressure wave is generated. Thus, the heat input must be modulated, which requires that the laser radiation be also amplitude or frequency modulated. A modulated laser beam generates periodic sound due to the periodic localized heating of the gas. From an acoustic point of view, the PA cell is a linear acoustic system, which responds as a whole to the disturbance generated by light absorption. The differential equation (18) is not valid for capillary tubes with a small diameter (2*r* ≈ *d*ν, *dh*) nor for gases with exceptionally high viscosity or heat conductivity.

When the absorbing gas can be modeled by a two-level system consisting of the vibrational ground and the excited state, Meyer and Sigrist (Meyer & Sigrist, 1990) found that the amplitude of heat production rate, *H*, is given by:

$$H\left(\mathbf{r},t\right) = \alpha\_p I\left(\mathbf{r},t\right) \,. \tag{19}$$

where *I*(**r**,*t*) is the intensity of the laser beam. This equation is valid only when the laser beam is slowly chopped in the kHz range or below, and in the absence of optical saturation.

If the cross-sectional dimensions of a resonator are much smaller than the acoustic wavelength, the excited sound field develops a spatial variation only along the length of the resonator, i.e., a one-dimensional acoustic field is generated. A narrow pipe (or tube) can be regarded as a one-dimensional acoustic resonator. A pressure wave propagating in the pipe will be reflected by an open end with the opposite phase. Through multiple reflections a standing wave pattern with pressure nodes will be formed. Therefore, open pipes should have resonances when the pipe length is equal to an integer multiple of the half wavelength.

Bernegger and Sigrist (Bernegger & Sigrist, 1987) proved that the plane acoustic wave propagation can be modeled by the one-dimensional analogue of the electrical current flow

CO2 Laser Photoacoustic Spectroscopy: I. Principles 21

Based on this formula, we can estimate the magnitude of the cell constant. By introducing in Eq. (21) or Eq. (22) the values for our medium-*Q* resonator (*r* = 3.5 mm, *L* = 30 cm, *Q* = 16.1 and *f*0 = 564 Hz; *Seff* ≅ 0.4 cm2, Δ*f* = 35 Hz), it follows *C* = 4720 Pa cm/W, which is almost twice as much as the experimentally measured value (2500 Pa cm/W). If an open resonator is built into a closed PA cell, then the pressure generated by the PA effect will be distributed over the entire closed volume. Therefore, the total volume of the PA cell must be taken into account instead of the volume of the resonator. A PA resonator optimized for high-*Q* performance (*Seff* ∼80 cm2, *Q* ∼1000 at *f*0 = 1 kHz) has a cell constant of about 800 Pa cm/W. The cell constant of a low-*Q* resonator is a complicated function of several parameters, and therefore cannot be determined with sufficient accuracy by calculation. It has to be determined experimentally by calibration measurements using certified gas mixtures.

The possibilities for improving the cell constant of acoustic resonators are limited (Miklos et al., 2001). The only parameter that can really be changed over a broader range is the effective cross section of the cell. A reduction of the cell diameter will increase the cell constant. A lower limit is set by the diameter and divergence of the laser beam employed. The cell constant for modulated measurements is inversely proportional to the FWHM value of the resonance profile. Unfortunately, the half width cannot be reduced indefinitely, because it scales approximately with the surface-to-volume ratio of the resonator. As the cross section of the cell is reduced, the surface-to-volume ratio increases. It is therefore impossible to achieve small cross sections and a small bandwidth (high *Q*) simultaneously. The smallest

diameter used in practical systems is several millimeters, the largest about 10 cm.

( )

*<sup>p</sup> <sup>V</sup>* γ− α <sup>=</sup> <sup>ω</sup>

maximum in the SNR for a certain combination of cell size and modulation frequency.

the cylindrical laser beam propagates exactly along the cylinder axis.

0

It should be noted that the amplitude of the PA pressure signal is a function of (1) the heat

relaxation times of the absorbing gas, and (5) damping effects of the buffer gas (*Q*). The first four factors contribute to the power going into the sound wave, and the last mechanism determines the *Q* of the resonances. From Eq. (23) it follows that the amplitude of the pressure wave (the PA pressure signal) is proportional to the absorption coefficient and laser power, but inversely proportional to the modulation frequency and effective cross section *V*/*L* of the PA resonator. Thus, the signal increases with decreasing resonator dimensions and modulation frequency. As the noise increases with a decrease of these parameters, there is a

For resonant operation, the modulation frequency is tuned to one of the resonance modes of

acoustic resonator are excited as a result. The resonance amplitude is proportional to *Q*, while the amplitudes of the other resonances are inversely proportional to the quantity 2 2 ω −ω*<sup>m</sup>* . Therefore, distant resonances will not be excited efficiently. Certain resonances can be suppressed for special symmetry conditions, e.g., azimuthal modes cannot be excited if

The measured PA signal also depends on the exact position of the microphone in the resonator. The signal detected by the microphone is proportional to the integral average of

*<sup>m</sup>*. Not only the *m-*th mode, but all the other modes of the

1 *p L LP QG*

), (2) laser power (*PL*), (3) modulation frequency (

. (23)

ω

0), (4) vibrational

Combining Eqs. (20) and (21), we have:

γ

ω = ω

capacity of the mixture (

the PA resonator, i.e.,

in a transmission line. According to this theory, a cell constant *C* (Pa cm/W) only dependent on the geometry of the cell (it includes the losses of the PA resonator), which relates the pressure amplitude *p* with the absorbed laser power *PL*, can be defined at resonance frequency:

$$p = \mathbb{C}\left(\alpha = \alpha\_0\right) \alpha\_p P\_{\mathbb{L}, \mathcal{I}} \tag{20}$$

where *p* (N/m2 = Pa) is the pressure response of the cell, α*<sup>p</sup>* (cm-1) is the absorption coefficient at a given pressure of the gas at the laser wavelength, and *PL* (W) is the laser power. The units of *C* are given in Pa cm/W based on the usual dimensions of *p*, α*<sup>p</sup>*, and *PL*. Here, the angular frequency is ω0 = 2π*f*0, where *f*0 is the resonance frequency; for a longitudinal resonant cell, the first resonance frequency is *f*<sup>0</sup> = *vs*/2*L* (Eq. 3), so that ω0 = π*vs*/*L*. *C* is usually determined by calibration measurements, where one single absorbing substance with known absorption spectrum is investigated.

Equation (20) implies that for a reasonably small laser power (no saturation), slow modulation frequency ω0 (ω0τ << 1, where τ is the thermal relaxation time characteristic for the cooling of the gas to equilibrium), and small absorption (α*pL* << 1), the sound pressure amplitude depends linearly on the absorption coefficient and the laser power.

#### **3.6 Cell constant**

For a given PA cell geometry ("high-*Q*" case), Kreuzer (Kreuzer, 1977) deduced that:

$$C\left(\alpha\_0\right) = \frac{\left(\gamma - 1\right)LQG}{\alpha\_0 V},\tag{21}$$

where *V* is the volume of the PA resonator and *G* a geometrical factor (depending on the transverse beam profile but not on the cell length) on the order of 1 Pa m3/W s (Bijnen et al. (Bijnen et al., 1996) found a value *G* = 1.2 Pa m3/W s for their specific experimental conditions). Since the quantities in Eq. (21) are independent of the laser power and absorption coefficient, these factors can be regarded as characteristic setup quantities for PA resonators. The quantity *C* describes the sensitivity of the PA resonator at a given resonance frequency. It is widely known as the 'cell constant'. It depends on the size of the resonator, the frequency, and the *Q* factor of the resonance selected for PA detection. It also depends on the spatial overlap of the laser beam and the standing acoustic wave pattern. Its 'cell constant' name is therefore misleading, as it characterizes the complete measurement arrangement (including the acoustic resonator with a selected resonance, microphone position, and laser beam profile with spatial location) rather than the mere PA cell. Moreover, it depends on frequency, and its value differs for different resonance modes. Therefore, it would more appropriately be called a 'PA setup constant' (Miklos et al., 2001) rather than a 'cell constant'. However, since the name 'cell constant' is already established in the literature, we will continue to use it hereinafter.

As the cell constant is inversely proportional to an effective cross section defined by *Seff* = *V*/*L* and ω0/*Q* = Δω(Eq. 15), it follows that:

$$C\left(\text{co}\_{0}\right) = \frac{\left(\gamma - 1\right)G}{\Delta \text{coS}\_{\text{eff}}}\,. \tag{22}$$

in a transmission line. According to this theory, a cell constant *C* (Pa cm/W) only dependent on the geometry of the cell (it includes the losses of the PA resonator), which relates the pressure amplitude *p* with the absorbed laser power *PL*, can be defined at resonance frequency:

coefficient at a given pressure of the gas at the laser wavelength, and *PL* (W) is the laser

*vs*/*L*. *C* is usually determined by calibration measurements, where one single absorbing

Equation (20) implies that for a reasonably small laser power (no saturation), slow

τ

For a given PA cell geometry ("high-*Q*" case), Kreuzer (Kreuzer, 1977) deduced that:

ω =

( ) ( ) <sup>0</sup>

<sup>1</sup> *LQG <sup>C</sup>*

γ −

where *V* is the volume of the PA resonator and *G* a geometrical factor (depending on the transverse beam profile but not on the cell length) on the order of 1 Pa m3/W s (Bijnen et al. (Bijnen et al., 1996) found a value *G* = 1.2 Pa m3/W s for their specific experimental conditions). Since the quantities in Eq. (21) are independent of the laser power and absorption coefficient, these factors can be regarded as characteristic setup quantities for PA resonators. The quantity *C* describes the sensitivity of the PA resonator at a given resonance frequency. It is widely known as the 'cell constant'. It depends on the size of the resonator, the frequency, and the *Q* factor of the resonance selected for PA detection. It also depends on the spatial overlap of the laser beam and the standing acoustic wave pattern. Its 'cell constant' name is therefore misleading, as it characterizes the complete measurement arrangement (including the acoustic resonator with a selected resonance, microphone position, and laser beam profile with spatial location) rather than the mere PA cell. Moreover, it depends on frequency, and its value differs for different resonance modes. Therefore, it would more appropriately be called a 'PA setup constant' (Miklos et al., 2001) rather than a 'cell constant'. However, since the name 'cell constant' is already established in

As the cell constant is inversely proportional to an effective cross section defined by *Seff* =

( ) ( ) <sup>0</sup>

ω =

*C*

1 *eff G*

*S* γ −

0

ω

*V*

power. The units of *C* are given in Pa cm/W based on the usual dimensions of *p*,

longitudinal resonant cell, the first resonance frequency is *f*<sup>0</sup> = *vs*/2*L* (Eq. 3), so that

where *p* (N/m2 = Pa) is the pressure response of the cell,

substance with known absorption spectrum is investigated.

the cooling of the gas to equilibrium), and small absorption (

ω0 (ω0τ

the literature, we will continue to use it hereinafter.

(Eq. 15), it follows that:

ω

ω0 = 2π

<< 1, where

amplitude depends linearly on the absorption coefficient and the laser power.

Here, the angular frequency is

modulation frequency

**3.6 Cell constant** 

*V*/*L* and

ω0/*Q* = Δ

π

( ) <sup>0</sup> *<sup>p</sup> <sup>L</sup> p* = ω=ω α *C P* , (20)

α

*f*0, where *f*0 is the resonance frequency; for a

is the thermal relaxation time characteristic for

α

*<sup>p</sup>* (cm-1) is the absorption

*pL* << 1), the sound pressure

, (21)

Δω . (22)

α

*<sup>p</sup>*, and *PL*.

ω0 = Based on this formula, we can estimate the magnitude of the cell constant. By introducing in Eq. (21) or Eq. (22) the values for our medium-*Q* resonator (*r* = 3.5 mm, *L* = 30 cm, *Q* = 16.1 and *f*0 = 564 Hz; *Seff* ≅ 0.4 cm2, Δ*f* = 35 Hz), it follows *C* = 4720 Pa cm/W, which is almost twice as much as the experimentally measured value (2500 Pa cm/W). If an open resonator is built into a closed PA cell, then the pressure generated by the PA effect will be distributed over the entire closed volume. Therefore, the total volume of the PA cell must be taken into account instead of the volume of the resonator. A PA resonator optimized for high-*Q* performance (*Seff* ∼80 cm2, *Q* ∼1000 at *f*0 = 1 kHz) has a cell constant of about 800 Pa cm/W. The cell constant of a low-*Q* resonator is a complicated function of several parameters, and therefore cannot be determined with sufficient accuracy by calculation. It has to be determined experimentally by calibration measurements using certified gas mixtures.

The possibilities for improving the cell constant of acoustic resonators are limited (Miklos et al., 2001). The only parameter that can really be changed over a broader range is the effective cross section of the cell. A reduction of the cell diameter will increase the cell constant. A lower limit is set by the diameter and divergence of the laser beam employed. The cell constant for modulated measurements is inversely proportional to the FWHM value of the resonance profile. Unfortunately, the half width cannot be reduced indefinitely, because it scales approximately with the surface-to-volume ratio of the resonator. As the cross section of the cell is reduced, the surface-to-volume ratio increases. It is therefore impossible to achieve small cross sections and a small bandwidth (high *Q*) simultaneously. The smallest diameter used in practical systems is several millimeters, the largest about 10 cm.

Combining Eqs. (20) and (21), we have:

$$p = \frac{(\gamma - 1)\alpha\_p L P\_L Q G}{\alpha\_0 V}.\tag{23}$$

It should be noted that the amplitude of the PA pressure signal is a function of (1) the heat capacity of the mixture (γ), (2) laser power (*PL*), (3) modulation frequency (ω0), (4) vibrational relaxation times of the absorbing gas, and (5) damping effects of the buffer gas (*Q*). The first four factors contribute to the power going into the sound wave, and the last mechanism determines the *Q* of the resonances. From Eq. (23) it follows that the amplitude of the pressure wave (the PA pressure signal) is proportional to the absorption coefficient and laser power, but inversely proportional to the modulation frequency and effective cross section *V*/*L* of the PA resonator. Thus, the signal increases with decreasing resonator dimensions and modulation frequency. As the noise increases with a decrease of these parameters, there is a maximum in the SNR for a certain combination of cell size and modulation frequency.

For resonant operation, the modulation frequency is tuned to one of the resonance modes of the PA resonator, i.e., ω = ω*<sup>m</sup>*. Not only the *m-*th mode, but all the other modes of the acoustic resonator are excited as a result. The resonance amplitude is proportional to *Q*, while the amplitudes of the other resonances are inversely proportional to the quantity 2 2 ω −ω*<sup>m</sup>* . Therefore, distant resonances will not be excited efficiently. Certain resonances can be suppressed for special symmetry conditions, e.g., azimuthal modes cannot be excited if the cylindrical laser beam propagates exactly along the cylinder axis.

The measured PA signal also depends on the exact position of the microphone in the resonator. The signal detected by the microphone is proportional to the integral average of

CO2 Laser Photoacoustic Spectroscopy: I. Principles 23

In a longitudinally excited resonator, a smaller acoustic gain, as a consequence of a relatively

Fig. 6. Graphical representation of Eq. (26): dependence of the normalized cell constant on

123

According to Eqs. (24-26), to obtain a higher acoustic signal in a longitudinally excited resonator with a low *Q*-factor (a higher *C*), it is necessary to have a resonator with a large length and a small diameter. Yet, narrowing the tube diameter and increasing the tube length are restricted by the divergence of the laser beam over the length of the cell. The maximum length is limited by the minimum frequency at which the cell is to be operated or

α

minimum possible diameter is set by the beam diameter or the volume-to-surface ratio that is needed to minimize adsorption and desorption at the cell walls. A too small diameter of the PA cell gives rise to high PA background signals due to absorption of the wings of the gaussian laser beam profile. On the other hand, a high quality factor is required in order to decrease the background signal caused by window heating. In conclusion, the optimization of the PA cell geometry depends on the specific experimental conditions and the application

When the resonance contributions are included, the photoacoustic voltage signal can be obtained at a given operating frequency simply by multiplying the pressure response (Eq.

absorption coefficient at a given wavelength; *C* (Pa cm W-1), the cell constant; *SM* (V Pa-1), the microphone responsivity; *PL* (W), the cw laser power (unchopped value; 2x measured average value); and *c* (atm), the trace gas concentration (usually given in units of per cent, ppmV, ppbV or pptV). This equation reveals that the photoacoustic signal is linearly dependent on laser power. Thus, sensitive measurements benefit from using as much laser power as is reasonably available. Moreover, the signal is directly dependent on the number of molecules in the optical path (trace gas concentration), which means that this technique is

α*p* = α*c*):

*max* that is to be detected (*L* << 1/

*L* = 3*L*<sup>0</sup> *L* = 2*L*<sup>0</sup>

*r*/*r*<sup>0</sup> *L* = *L*<sup>0</sup>

*V CS P c* = α *<sup>M</sup> <sup>L</sup>* , (27)

α

α

(cm-1 atm-1), the gas

*max*). The

tube radius and resonator length.

for which it is designed.

**3.8 Voltage signal** 

by the maximum absorption coefficient

20) by the microphone responsivity (*V* = *pSM* and

where: *V* (V) is the photoacoustic signal (peak-to-peak value);

low *Q* value, is compensated for by the signal gain due to the smaller diameter.

1

0

2

3

*C*/*C*<sup>0</sup>

the pressure over the microphone membrane. Since mostly miniature microphones are applied in photoacoustics, the integral can be approximated by the value of the pressure amplitude at the microphone location.

Angeli et al. (Angeli et al., 1992) reported a dependency of the cell constant on the kind of calibration gas. They concluded that the cell constant could not be determined unambiguously by a calibration measurement using a single absorbing species, indicating the "nonabsolute" character of photoacoustic spectroscopy. This result would have severe implications and would render analyses of multicomponent gas mixtures very difficult or impossible. Fortunately, Thöny and Sigrist (Thöny & Sigrist, 1995) proved that detailed investigations including a number of different gases and measurements on numerous laser transitions contradict those observations and revealed the expected independence of the cell constant within the measurement errors.

#### **3.7 Optimization of the PA cell geometry**

Since the PA signal is inversely proportional to the cell volume and modulation frequency, high PA signal levels can be obtained by taking a small cell volume (< 10 cm3) and low modulation frequencies (< 100 Hz). However, noise sources (intrinsic noise of the microphone, amplifier noise, external acoustic noise) show a characteristic 1/*f* frequency dependence, and therefore the SNR of such a gas-microphone cell is usually quite small. The SNR of a PA cell can be increased by applying higher modulation frequencies (in the kHz region) and acoustic amplification of the PA signal. For this reason, resonant PA cells operating on longitudinal, azimuthal, radial, or Helmholtz resonances have been developed. Furthermore, resonant cells can be designed for multipass or intracavity operation.

A qualitative behavior for *Q* and ω0 can be derived from simple geometrical considerations. So, for *Q*, the energy stored in a specific mode is proportional to the cell volume (∝ *r*2*L*), while the energy losses per cycle of the acoustic wave are proportional to the cell surface (2π*rL*) and to the thicknesses *dh* ≈ *d*ν = *d* ∝ ω<sup>0</sup>-1/2 ∝ *L*1/2. Therefore:

$$
\partial \mathfrak{h} \lnot L^{\mathfrak{i}} \, \tag{24}
$$

$$\mathcal{Q}(a\mathfrak{b}) \lnot \left(r\text{\textquotedblleft}L/r\text{\textquotedblleft}L^{1/2}\right) \lnot rL^{-1/2},\tag{25}$$

and

$$\mathbf{C}(\alpha\_0) \approx \text{(L)} (r\mathbf{L}^{\cdot 1/2}) / \text{(}\mathbf{L}^{\cdot 1}\text{)} (r\mathbf{2}\mathbf{L}) \approx r\mathbf{^{1}L^{1/2}}.\tag{26}$$

which is represented graphically in Fig. 6. These equations show that the product *Q*(ω0)*C*(ω0) is nearly independent of the cell dimensions for any kind of resonant PA cell. The operation of the cell in a longitudinal mode is more advantageous because it makes it possible to optimize the resonance frequency and the *Q*-factor independently, which cannot be achieved in the case of radial resonance.

Cell geometries with large diameter-to-length ratios designed to excite the resonance in the radial or azimuthal acoustic modes possess high *Q* values and high resonance frequencies, but have low cell constants. PA cells with high *Q* values are sensitive to long-term drifts (e.g., due to thermal expansion if the temperature is not carefully controlled), so that they require an active locking of the modulation frequency on the resonance frequency of the cell.

the pressure over the microphone membrane. Since mostly miniature microphones are applied in photoacoustics, the integral can be approximated by the value of the pressure

Angeli et al. (Angeli et al., 1992) reported a dependency of the cell constant on the kind of calibration gas. They concluded that the cell constant could not be determined unambiguously by a calibration measurement using a single absorbing species, indicating the "nonabsolute" character of photoacoustic spectroscopy. This result would have severe implications and would render analyses of multicomponent gas mixtures very difficult or impossible. Fortunately, Thöny and Sigrist (Thöny & Sigrist, 1995) proved that detailed investigations including a number of different gases and measurements on numerous laser transitions contradict those observations and revealed the expected independence of the cell

Since the PA signal is inversely proportional to the cell volume and modulation frequency, high PA signal levels can be obtained by taking a small cell volume (< 10 cm3) and low modulation frequencies (< 100 Hz). However, noise sources (intrinsic noise of the microphone, amplifier noise, external acoustic noise) show a characteristic 1/*f* frequency dependence, and therefore the SNR of such a gas-microphone cell is usually quite small. The SNR of a PA cell can be increased by applying higher modulation frequencies (in the kHz region) and acoustic amplification of the PA signal. For this reason, resonant PA cells operating on longitudinal, azimuthal, radial, or Helmholtz resonances have been developed.

So, for *Q*, the energy stored in a specific mode is proportional to the cell volume (∝ *r*2*L*), while the energy losses per cycle of the acoustic wave are proportional to the cell surface

which is represented graphically in Fig. 6. These equations show that the product

The operation of the cell in a longitudinal mode is more advantageous because it makes it possible to optimize the resonance frequency and the *Q*-factor independently, which cannot

Cell geometries with large diameter-to-length ratios designed to excite the resonance in the radial or azimuthal acoustic modes possess high *Q* values and high resonance frequencies, but have low cell constants. PA cells with high *Q* values are sensitive to long-term drifts (e.g., due to thermal expansion if the temperature is not carefully controlled), so that they require an active locking of the modulation frequency on the resonance frequency of the cell.

0) is nearly independent of the cell dimensions for any kind of resonant PA cell.

<sup>0</sup>-1/2 ∝ *L*1/2. Therefore:

0 can be derived from simple geometrical considerations.

0) ∝ (*r*2*L*/*rLL*1/2) ∝ *rL*-1/2, (25)

0) ∝ (*L*)(*rL*-1/2)/( *L*-1)( *r*2*L*) ∝ *r*-1L1/2. (26)

<sup>0</sup> ∝ *L*-1, (24)

Furthermore, resonant cells can be designed for multipass or intracavity operation.

ω

ω

ν = *d* ∝ ω

*Q*(ω

*C*(ω

be achieved in the case of radial resonance.

amplitude at the microphone location.

constant within the measurement errors.

A qualitative behavior for *Q* and

(2π*rL*) and to the thicknesses *dh* ≈ *d*

and

*Q*(ω0)*C*(ω

**3.7 Optimization of the PA cell geometry** 

In a longitudinally excited resonator, a smaller acoustic gain, as a consequence of a relatively low *Q* value, is compensated for by the signal gain due to the smaller diameter.

Fig. 6. Graphical representation of Eq. (26): dependence of the normalized cell constant on tube radius and resonator length.

According to Eqs. (24-26), to obtain a higher acoustic signal in a longitudinally excited resonator with a low *Q*-factor (a higher *C*), it is necessary to have a resonator with a large length and a small diameter. Yet, narrowing the tube diameter and increasing the tube length are restricted by the divergence of the laser beam over the length of the cell. The maximum length is limited by the minimum frequency at which the cell is to be operated or by the maximum absorption coefficient α*max* that is to be detected (*L* << 1/α*max*). The minimum possible diameter is set by the beam diameter or the volume-to-surface ratio that is needed to minimize adsorption and desorption at the cell walls. A too small diameter of the PA cell gives rise to high PA background signals due to absorption of the wings of the gaussian laser beam profile. On the other hand, a high quality factor is required in order to decrease the background signal caused by window heating. In conclusion, the optimization of the PA cell geometry depends on the specific experimental conditions and the application for which it is designed.

#### **3.8 Voltage signal**

When the resonance contributions are included, the photoacoustic voltage signal can be obtained at a given operating frequency simply by multiplying the pressure response (Eq. 20) by the microphone responsivity (*V* = *pSM* and α*p* = α*c*):

$$V = \mathfrak{\alpha} \mathbb{C} S\_M P\_L \mathfrak{c} \text{ \(\mathfrak{\alpha}\)}\tag{27}$$

where: *V* (V) is the photoacoustic signal (peak-to-peak value); α (cm-1 atm-1), the gas absorption coefficient at a given wavelength; *C* (Pa cm W-1), the cell constant; *SM* (V Pa-1), the microphone responsivity; *PL* (W), the cw laser power (unchopped value; 2x measured average value); and *c* (atm), the trace gas concentration (usually given in units of per cent, ppmV, ppbV or pptV). This equation reveals that the photoacoustic signal is linearly dependent on laser power. Thus, sensitive measurements benefit from using as much laser power as is reasonably available. Moreover, the signal is directly dependent on the number of molecules in the optical path (trace gas concentration), which means that this technique is

CO2 Laser Photoacoustic Spectroscopy: I. Principles 25

been predicted (Sigrist, 1986) and experimentally proved (Harren et al., 1990). Such sensitivity makes it possible to detect many trace constituents in the sub-ppbV range. Theoretical calculations (see Section 2) predict the linearity of the signal response over a concentration range as broad as 7 orders of magnitude. This wide dynamic range, characteristic of LPAS, is important for air pollution monitoring, as it helps conduct measurements in polluted areas at the source (emission) as well as in rural areas (immission)

A PA signal may become saturated due to either a large concentration of the measured analyte or high laser power levels. We showed in Section 2 that, in the case of ethylene, the signal starts to saturate at a concentration of 65 ppmV. As a matter of fact, Thöny and Sigrist (Thöny & Sigrist, 1995) observed weak saturation effects on 10P(14) CO2 laser transition for a concentration of 100 ppmV of ethylene. The degree of saturation is gas dependent. We found (Section 2.3) that a deviation of ~3% from linear behavior resulted in an optical

By increasing laser intensity, the excitation pumping rate of the molecules grows higher, and a molecule is more likely to absorb a nearby photon before it relaxes to the ground state. So, as the molecules in the excited state increase in numbers, the number of molecules which can absorb laser radiation is reduced. The gas actually becomes as though more transparent to laser radiation, and the effective absorption coefficient per unit laser power is lowered; this is called laser power saturation. Saturation due to nonlinear absorption of the laser power only occurs in focused high-power laser beams or when the PA cell is placed intracavity in a laser, so that the laser power can be on the order of tens of watts or even higher than 100 W. The pumping rate to a higher vibrational-rotational level is proportional to the laser light intensity; in the case of saturation it exceeds the collisional de-excitation rates.

Harren et al. (Harren et al., 1990) studied the saturation effects by placing the PA cell intracavity of a waveguide CO2 laser. Extracavity, the ratio between 10P(14) and 10P(16) lines is 5.96 ± 0.2. Intracavity, this ratio becomes 2.8 ± 0.3 (47% from its extracavity value) at an intracavity laser power of 130 W (for a laser beam waist of 0.282 mm, that is at a laser intensity higher than 200 kW/cm2). By lowering the intracavity laser power, this ratio increases to its extracavity value. This effect is caused by saturation of the transitions in

rate due to the high intracavity power. When the laser beam waist is increased to 1.02 mm (laser intensity is decreased to 15.9 kW/cm2), the ratio of the absorption coefficients of C2H4 on the 10P(14) and 10P(16) CO2 laser lines increased to 4.7 ± 0.5 (78% of its extracavity value). To compensate for the saturation effect, these authors used an absorption coefficient of 23.7 cm-1atm-1 (78% of 30.4 cm-1atm-1 at an intracavity power of 100 W) for C2H4 at the

By using an intracavity arrangement where the CO2 laser power was varied between 10 and 70 W, Groot (Groot, 2002) measured the saturation parameter of ethylene for several laser

10) through collisions becomes slow in comparison with the pump

α

/(1 + *P*/*Ps*), where *Ps* (W) is the laser power saturation

C2H4 at the 10P(14) CO2 laser line. Depletion from the vibrational excited level (

*cmin* ≅10-10 cm-1 for 1 W incident laser power have

ν

*<sup>e</sup>* to the intrinsic absorption

7) via other

α*min* = α

detection limits on the order of

(Sigrist et al., 1989).

density

α

vibrational levels (e.g.,

10P(14) CO2 laser line.

α

is given by

coefficient

ν

lines. The relation of the effective absorption coefficient

α*e* = α

*Lc* = 0.06.

**3.9 Saturation effects** 

truly a "zero-baseline" approach, since no signal will be generated if the target molecules are not present.

Equation (27) is valid as long as absorption is small (α*pL* << 1), and the modulation frequency is higher than the inverse of the molecular diffusion time but lower than the inverse of the molecular relaxation time. The PA signal is linearly dependent on the absorption coefficient, cell constant, microphone responsivity, incident laser power, and absorbent trace gas concentration. Thus, by doubling *Q* (and consequently *C*), or the microphone responsivity, or the laser power, or the number of absorbing molecules in the optical path, the voltage will also double. The peak-to-peak value of the signal is obtained by multiplying by 2 2 the rms voltage amplitude measured by the lock-in amplifier. As a rule, another parameter is used to characterize the PA cell, namely:

$$R = \mathbb{C}S\_{M'} \tag{28}$$

where *R* (V cm/W) is the (voltage) responsivity of the PA cell or the calibration constant. The cell constant *C* is multiplied by the responsivity of the microphone given in V/Pa units. A comparison of different PA cells can be made independently of the application in terms of this figure of merit. However, the cell characterization can be used only if a calibrated microphone is available. In this way, Eq. (27) becomes:

$$V = \mathfrak{\alpha} RP\_L \mathfrak{c} \text{ .} \tag{29}$$

To increase the detection sensitivity, we have to ensure: a) a cell constant as large as possible (optimization of the PA resonator); b) a large microphone responsivity; c) a laser power as high as possible, provided that saturation does not become a limiting factor; d) a narrow bandwidth of the lock-in amplifier, and e) a high absorption coefficient of the trace gas to be measured at the laser wavelength. It is also useful to increase the number *n* of microphones (connected in series), but this number is limited by the dimensions of the PA cell. The summation of the signals from the single microphones results in an *n*-times higher effective PA signal, because the total responsivity *SM to*t is increased *n*-fold, i.e.:

$$S\_{Mut} = nS\_M \,. \tag{30}$$

On the other hand, the incoherent noise only increases by *n* . One thus obtains:

$$\text{SNR}\_{\text{tot}} = \sqrt{n} \,\text{SNR} \,\,. \tag{31}$$

The minimum measurable voltage signal *V* = *Vmin* is obtained at SNR = 1, where the minimum detectable concentration *c* = *cmin* can be recorded:

$$
\sigma\_{\text{min}} = \frac{V\_{\text{min}}}{\alpha P\_L R} \,. \tag{32}
$$

The sensitivity of PA instruments increases with the laser power, as *V* ∝ α*PL*. However, the voltage signal does not depend on the length of the absorption path. Furthermore, in contrast to other techniques based on absorption spectroscopy, the response of the acoustic detector is independent of the electromagnetic radiation wavelength as long as the absorption coefficient is fixed. According to theoretical considerations, extremely low detection limits on the order of α*min* = α*cmin* ≅10-10 cm-1 for 1 W incident laser power have been predicted (Sigrist, 1986) and experimentally proved (Harren et al., 1990). Such sensitivity makes it possible to detect many trace constituents in the sub-ppbV range. Theoretical calculations (see Section 2) predict the linearity of the signal response over a concentration range as broad as 7 orders of magnitude. This wide dynamic range, characteristic of LPAS, is important for air pollution monitoring, as it helps conduct measurements in polluted areas at the source (emission) as well as in rural areas (immission) (Sigrist et al., 1989).

#### **3.9 Saturation effects**

24 CO2 Laser – Optimisation and Application

truly a "zero-baseline" approach, since no signal will be generated if the target molecules

frequency is higher than the inverse of the molecular diffusion time but lower than the inverse of the molecular relaxation time. The PA signal is linearly dependent on the absorption coefficient, cell constant, microphone responsivity, incident laser power, and absorbent trace gas concentration. Thus, by doubling *Q* (and consequently *C*), or the microphone responsivity, or the laser power, or the number of absorbing molecules in the optical path, the voltage will also double. The peak-to-peak value of the signal is obtained by multiplying by 2 2 the rms voltage amplitude measured by the lock-in amplifier. As a

where *R* (V cm/W) is the (voltage) responsivity of the PA cell or the calibration constant. The cell constant *C* is multiplied by the responsivity of the microphone given in V/Pa units. A comparison of different PA cells can be made independently of the application in terms of this figure of merit. However, the cell characterization can be used only if a calibrated

To increase the detection sensitivity, we have to ensure: a) a cell constant as large as possible (optimization of the PA resonator); b) a large microphone responsivity; c) a laser power as high as possible, provided that saturation does not become a limiting factor; d) a narrow bandwidth of the lock-in amplifier, and e) a high absorption coefficient of the trace gas to be measured at the laser wavelength. It is also useful to increase the number *n* of microphones (connected in series), but this number is limited by the dimensions of the PA cell. The summation of the signals from the single microphones results in an *n*-times higher effective

The minimum measurable voltage signal *V* = *Vmin* is obtained at SNR = 1, where the

min

*c*

The sensitivity of PA instruments increases with the laser power, as *V* ∝

min

*L V*

*P R* <sup>=</sup> <sup>α</sup>

voltage signal does not depend on the length of the absorption path. Furthermore, in contrast to other techniques based on absorption spectroscopy, the response of the acoustic detector is independent of the electromagnetic radiation wavelength as long as the absorption coefficient is fixed. According to theoretical considerations, extremely low

α

*R CS* = *<sup>M</sup>* , (28)

*V RP c* = α *<sup>L</sup>* . (29)

*S nS Mtot M* = . (30)

SNR SNR tot = *n* . (31)

. (32)

α

*PL*. However, the

*pL* << 1), and the modulation

Equation (27) is valid as long as absorption is small (

rule, another parameter is used to characterize the PA cell, namely:

PA signal, because the total responsivity *SM to*t is increased *n*-fold, i.e.:

minimum detectable concentration *c* = *cmin* can be recorded:

On the other hand, the incoherent noise only increases by *n* . One thus obtains:

microphone is available. In this way, Eq. (27) becomes:

are not present.

A PA signal may become saturated due to either a large concentration of the measured analyte or high laser power levels. We showed in Section 2 that, in the case of ethylene, the signal starts to saturate at a concentration of 65 ppmV. As a matter of fact, Thöny and Sigrist (Thöny & Sigrist, 1995) observed weak saturation effects on 10P(14) CO2 laser transition for a concentration of 100 ppmV of ethylene. The degree of saturation is gas dependent. We found (Section 2.3) that a deviation of ~3% from linear behavior resulted in an optical density α*Lc* = 0.06.

By increasing laser intensity, the excitation pumping rate of the molecules grows higher, and a molecule is more likely to absorb a nearby photon before it relaxes to the ground state. So, as the molecules in the excited state increase in numbers, the number of molecules which can absorb laser radiation is reduced. The gas actually becomes as though more transparent to laser radiation, and the effective absorption coefficient per unit laser power is lowered; this is called laser power saturation. Saturation due to nonlinear absorption of the laser power only occurs in focused high-power laser beams or when the PA cell is placed intracavity in a laser, so that the laser power can be on the order of tens of watts or even higher than 100 W. The pumping rate to a higher vibrational-rotational level is proportional to the laser light intensity; in the case of saturation it exceeds the collisional de-excitation rates.

Harren et al. (Harren et al., 1990) studied the saturation effects by placing the PA cell intracavity of a waveguide CO2 laser. Extracavity, the ratio between 10P(14) and 10P(16) lines is 5.96 ± 0.2. Intracavity, this ratio becomes 2.8 ± 0.3 (47% from its extracavity value) at an intracavity laser power of 130 W (for a laser beam waist of 0.282 mm, that is at a laser intensity higher than 200 kW/cm2). By lowering the intracavity laser power, this ratio increases to its extracavity value. This effect is caused by saturation of the transitions in C2H4 at the 10P(14) CO2 laser line. Depletion from the vibrational excited level (ν7) via other vibrational levels (e.g., ν10) through collisions becomes slow in comparison with the pump rate due to the high intracavity power. When the laser beam waist is increased to 1.02 mm (laser intensity is decreased to 15.9 kW/cm2), the ratio of the absorption coefficients of C2H4 on the 10P(14) and 10P(16) CO2 laser lines increased to 4.7 ± 0.5 (78% of its extracavity value). To compensate for the saturation effect, these authors used an absorption coefficient of 23.7 cm-1atm-1 (78% of 30.4 cm-1atm-1 at an intracavity power of 100 W) for C2H4 at the 10P(14) CO2 laser line.

By using an intracavity arrangement where the CO2 laser power was varied between 10 and 70 W, Groot (Groot, 2002) measured the saturation parameter of ethylene for several laser lines. The relation of the effective absorption coefficient α*<sup>e</sup>* to the intrinsic absorption coefficient α is given by α*e* = α/(1 + *P*/*Ps*), where *Ps* (W) is the laser power saturation

CO2 Laser Photoacoustic Spectroscopy: I. Principles 27

c. Coherent photoacoustic background signal. This signal, which is always present in the PA detector, is caused by the laser beam, yet not by light absorption in the bulk of the gas. Rather it is due to laser beam heating of the windows and of the absorbates at their surfaces, and heating of the PA resonator walls by the reflected or scattered light owing to imperfections of the focusing lens, windows and inner walls of the PA resonator. This signal is in phase with, and at the same frequency as, the laser intensity modulation. Therefore, it is not filtered out by the lock-in amplifier connected to the microphone. Thus, a background signal proportional to the laser power becomes the

The background signal in the PA cells may arise from several sources, some of which are

1. Window surface absorption: the molecules absorbed on the window surface and/or the window surface itself absorb the modulated laser radiation, and the resulting gas

2. Window bulk absorption: even the highest quality ZnSe window substrates exhibit a

3. Off-axis radiation within the cell: light scattered from the windows and at the edge of the chopper blade may strike the inside walls of the PA resonator, where it may be

5. Small amounts of contamination that may outgas from the cell materials, seals, and so forth. The detection limit of the PA cell is determined by the combined effect of the intrinsic stochastic noise of the microphone, acoustic background noise, and photoacoustic background signal. Background signals are deterministic, and to the extent that they can be quantified and minimized, do not reduce the performance of the cell significantly. The detection limit is defined either at a signal-to-noise ratio of unity (SNR = 1) or at a signal-to-

The amplifier input noise and microphone noise are gaussian in nature, that is, the amount of noise is proportional to the square root of the bandwidth in which the noise is measured. All of these noise sources are incoherent. The input noise of the SR830 lock-in amplifier used in our experiments is about 6 nV (rms)/ Hz . Microphone noise, which is manifested as a noise voltage present at the microphone output terminals, can be expressed as a product between the normalized noise pressure value owing to both thermal agitation of the diaphragm and cartridge responsivity at the corresponding frequency and the square root of the measurement bandwidth. The electrical noise of Knowles EK models electret microphones is 40 nV (rms)/ Hz . The overall random noise of multiple sources is determined by taking the square root of the sum of the squares of all the individual incoherent noise figures. For gaussian noise, the peak-to-peak value is about 5 times the rms noise value, while for the two other types of noises, the rms value must be multiplied by a factor of 2 2 ≅ 2.8 to obtain the peak-to-peak amplitude. Electrical noise usually has a broadband frequency spectrum and can be reduced efficiently by narrowband filtering of the signal, as is done in the phase sensitive detection. A detection bandwidth of 0.25 Hz was set (a time constant of 1 second) in all of our measurements. Electrical noise can be reduced by using state-of-the-art (and therefore very expensive) lock-in amplifiers and/or by using longer time averaging (the noise decreases with

the square root of the averaging time) at the cost of longer measurement times.

main factor that limits sensitivity.

heating in the cell generates a pressure pulse.

4. Light scattering or absorption due to microaerosols.

residual window absorption of ∼10-3 cm-1.

listed below (Gerlach & Amer, 1980):

absorbed and produce a signal.

background ratio of unity (SBR = 1).

parameter and represents a measure for the relaxation rate. At *P* = *Ps*, the absorption coefficient decreases to half its initial value. The following values were obtained for *Ps*: 178 W at 10P(8) line; 102 W at 10P(10); 112 W at 10P(12); 51.8 W at 10P(14); 101 W at 10P(16); 128 W at 10P(18), and 112 W at 10P(20). The strongest saturation effect was observed at 10P(14) line, where the absorption coefficient is the largest. The saturation for this line at a laser power of 130 W corresponds to the equivalent absorption coefficient α*e* = 0.285α. The stronger saturation in this case compared with the results of Harren et al. (Harren et al., 1990) could be accounted for by a tighter focusing of the laser beam (smaller beam waist). As a matter of fact, saturation is determined by the laser beam intensity (irradiance) rather than the laser power. Power saturation does not depend on the gas concentration in the PA cell (if the absorbing gas concentration is not too high).

#### **4. Noises and limiting factors**

#### **4.1 Noises**

In order to obtain an optimum SNR, noise control and interfering signals have to be taken into account (Dutu et al., 1994a; Dutu et al., 1994b). These limiting factors are discussed in the following two sections.

Noise plays an important role in all photoacoustic measurements and is of particular importance in the detection of ultralow gas concentrations, because the noise level limits the ultimate sensitivity. In the photoacoustic literature, the detection level is usually defined by the SNR, where the noise is given by the microphone signal measured with the laser light blocked. However, when light hits the PA cell, an additional background signal is generated which exists even when the absorbing species are not present in the detector. The background signal is often larger than the noise signal, and therefore the detection limit or sensitivity has to be defined by the signal-to-background ratio (SBR) in most experiments. Unfortunately, it is common practice to consider only the SNR. This procedure yields an extrapolated detection limit that may be far too small. The background signal is usually determined with a nonabsorbing gas, such as nitrogen, in the PA detector. It is influenced by many system properties, such as the pointing stability, the beam divergence, and the diameter of the laser beam.

For photoacoustic spectroscopy, "noise" often has a structure that is coherent with the signal from the target species, and therefore should more appropriately be treated as a background signal, not as noise. The background signal can be determined by measuring the acoustic signal in the absence of absorbers (i.e., with pure nitrogen), but with the same flow and in the same pressure conditions as those used for the sample gases.

The sensitivity-limiting factors which are encountered in LPAS can be classified into three categories:


parameter and represents a measure for the relaxation rate. At *P* = *Ps*, the absorption coefficient decreases to half its initial value. The following values were obtained for *Ps*: 178 W at 10P(8) line; 102 W at 10P(10); 112 W at 10P(12); 51.8 W at 10P(14); 101 W at 10P(16); 128 W at 10P(18), and 112 W at 10P(20). The strongest saturation effect was observed at 10P(14) line, where the absorption coefficient is the largest. The saturation for this line at a laser

stronger saturation in this case compared with the results of Harren et al. (Harren et al., 1990) could be accounted for by a tighter focusing of the laser beam (smaller beam waist). As a matter of fact, saturation is determined by the laser beam intensity (irradiance) rather than the laser power. Power saturation does not depend on the gas concentration in the PA

In order to obtain an optimum SNR, noise control and interfering signals have to be taken into account (Dutu et al., 1994a; Dutu et al., 1994b). These limiting factors are discussed in

Noise plays an important role in all photoacoustic measurements and is of particular importance in the detection of ultralow gas concentrations, because the noise level limits the ultimate sensitivity. In the photoacoustic literature, the detection level is usually defined by the SNR, where the noise is given by the microphone signal measured with the laser light blocked. However, when light hits the PA cell, an additional background signal is generated which exists even when the absorbing species are not present in the detector. The background signal is often larger than the noise signal, and therefore the detection limit or sensitivity has to be defined by the signal-to-background ratio (SBR) in most experiments. Unfortunately, it is common practice to consider only the SNR. This procedure yields an extrapolated detection limit that may be far too small. The background signal is usually determined with a nonabsorbing gas, such as nitrogen, in the PA detector. It is influenced by many system properties, such as the pointing stability, the beam divergence, and the

For photoacoustic spectroscopy, "noise" often has a structure that is coherent with the signal from the target species, and therefore should more appropriately be treated as a background signal, not as noise. The background signal can be determined by measuring the acoustic signal in the absence of absorbers (i.e., with pure nitrogen), but with the same flow and in

The sensitivity-limiting factors which are encountered in LPAS can be classified into three

a. Electrical noise, by which we mean any random fluctuation, whether electronic or acoustic, which does not have a fixed phase relation with the modulation of the laser

b. Coherent acoustic background noise, meaning a signal caused by the modulation process, but not attributable to the presence of the light beam in the PA cell. This signal is at the same frequency as, and locked in phase with respect to, the laser intensity

the same pressure conditions as those used for the sample gases.

intensity. It determines the ultimate detector sensitivity.

α

*e* = 0.285

α. The

power of 130 W corresponds to the equivalent absorption coefficient

cell (if the absorbing gas concentration is not too high).

**4. Noises and limiting factors** 

the following two sections.

diameter of the laser beam.

categories:

modulation.

**4.1 Noises** 

c. Coherent photoacoustic background signal. This signal, which is always present in the PA detector, is caused by the laser beam, yet not by light absorption in the bulk of the gas. Rather it is due to laser beam heating of the windows and of the absorbates at their surfaces, and heating of the PA resonator walls by the reflected or scattered light owing to imperfections of the focusing lens, windows and inner walls of the PA resonator. This signal is in phase with, and at the same frequency as, the laser intensity modulation. Therefore, it is not filtered out by the lock-in amplifier connected to the microphone. Thus, a background signal proportional to the laser power becomes the main factor that limits sensitivity.

The background signal in the PA cells may arise from several sources, some of which are listed below (Gerlach & Amer, 1980):


The detection limit of the PA cell is determined by the combined effect of the intrinsic stochastic noise of the microphone, acoustic background noise, and photoacoustic background signal. Background signals are deterministic, and to the extent that they can be quantified and minimized, do not reduce the performance of the cell significantly. The detection limit is defined either at a signal-to-noise ratio of unity (SNR = 1) or at a signal-tobackground ratio of unity (SBR = 1).

The amplifier input noise and microphone noise are gaussian in nature, that is, the amount of noise is proportional to the square root of the bandwidth in which the noise is measured. All of these noise sources are incoherent. The input noise of the SR830 lock-in amplifier used in our experiments is about 6 nV (rms)/ Hz . Microphone noise, which is manifested as a noise voltage present at the microphone output terminals, can be expressed as a product between the normalized noise pressure value owing to both thermal agitation of the diaphragm and cartridge responsivity at the corresponding frequency and the square root of the measurement bandwidth. The electrical noise of Knowles EK models electret microphones is 40 nV (rms)/ Hz . The overall random noise of multiple sources is determined by taking the square root of the sum of the squares of all the individual incoherent noise figures. For gaussian noise, the peak-to-peak value is about 5 times the rms noise value, while for the two other types of noises, the rms value must be multiplied by a factor of 2 2 ≅ 2.8 to obtain the peak-to-peak amplitude. Electrical noise usually has a broadband frequency spectrum and can be reduced efficiently by narrowband filtering of the signal, as is done in the phase sensitive detection. A detection bandwidth of 0.25 Hz was set (a time constant of 1 second) in all of our measurements. Electrical noise can be reduced by using state-of-the-art (and therefore very expensive) lock-in amplifiers and/or by using longer time averaging (the noise decreases with the square root of the averaging time) at the cost of longer measurement times.

CO2 Laser Photoacoustic Spectroscopy: I. Principles 29

the noise-equivalent absorption one must multiply 1.5x10-9 W cm-1/ *Hz* by *B*1/2*P*-1, where *B* is the bandwidth and *P* the laser power. In order to get an idea of the sensitivity that can be achieved for a representative trace gas, the equivalent ethylene concentration that would give the same signal level is also tabulated. To get the noise-equivalent ethylene

Our coherent acoustical background was 2.6 μV or 9.2x10-5 Pa, equivalent to an absorption of 2.6x10-8 W cm-1. To get the equivalent absorption coefficient divide the latter number by *PL* (5.9x10-9 cm-1). This background signal is dependent on the location of the PA cell in

The coherent photoacoustic background was 2.7 μV/W, or 9.6x10-5 Pa/W, assuming the beam was optimally aligned. This is equivalent to an absorption coefficient of 2.7x10-8 cm-1, or an ethylene concentration of about 0.89 ppbV, independent of the laser power. Since the noise and coherent acoustical background can be made negligible by using high laser power, as is done in intracavity operation, the coherent photoacoustic background will be

In order to obtain a maximized SNR, a resonance frequency under 1 kHz is necessary. Under 1 kHz, the noise level is determined by the 1/*f* amplifier noise, showing a frequency

Below 1 kHz, the 1/*f* amplifier noise is the main source. Above 1 kHz, the frequency independent Brownian noise takes over. Since the pressure amplitude is inversely proportional to the square root of the resonance frequency (*p* ∝ *C*, Eq. 20), a convenient resonance can be found between 500 and 1500 Hz. This limits the choice to a cell length of 100-300 mm. If optimal signal enhancement were the only argument, one would rather choose a large (300 mm) resonator (*C* ∝ *L*1/2, Eq. 26). Shorter resonator lengths are necessary in the case of an intracavity setup due to the limited space inside the cavity. Also, a fast time

When the sample gas is flown continuously through the detector, acoustical noise can be produced, if the gas flow is turbulent, if acoustical noise from the surroundings is coupled directly into the detector sample space or into the tubes connected to the detector and then propagated into the detector, or if acoustic disturbances from the pump running the sample gas through the detector are propagated through the tubes. Thick detector and tube walls, small flow rates, mounting of the cell and chopper in separate sound insulating boxes, etc.

The background signal can be minimized by placing the windows at nodes of the mode being excited and by introducing buffer volumes at both ends of the cell. The ratio of buffer to resonator diameters must be large enough, and the buffer length has to be equal to one-

Interference of other absorbing substances may impair the theoretical detection limit in a multicomponent analysis of the real atmosphere. Such interference may be caused by other

<sup>0</sup>-1/2 (because *C* ∝ *Q*/

ω

ω<sup>0</sup>-1/2.

ω

0, *Q* ∝ (*dv*, *dh*)-1 and (*dv*, *dh*) ∝

<sup>0</sup>1/2. Above 1 kHz, where the

ω0-

concentration, multiply 4.9x10-11 W / *Hz* by *B*1/2*P*-1.

. Together with *C* ∝

response of the cell requires a short cell length.

must be chosen to suppress these noise contributions.

1/2, see Sections 3.6, 3.4 and 3.3), we get a SNR proportional to

1/*f* amplifier noise is negligible, the SNR is proportional to

the ultimate limit of sensitivity.

ω

fourth of resonator length.

**4.2 Gas interference** 

behavior of 1/

relation to the sound sources associated with the modulation process.

ω

The two types of coherent background, however, are extremely narrowband signals at the same frequency as the modulation and hence cannot be filtered out. In addition, since the signal and the coherent photoacoustic background signal are both proportional to laser power, no improvement will be achieved as the laser power is increased.

Table 2 shows the magnitudes of these limiting factors in the case Brewster windows are used. We expressed each factor in several different sets of units (Dutu et al., 1994b): voltage, pressure amplitude, equivalent absorption coefficient that would give the same pressure amplitude, and the concentration of ethylene that would be required to give that much absorption.


a The equivalent peak-to-peak pressure was obtained by dividing the peak-to-peak noise level to microphone sensitivity: 2 2 *<sup>i</sup> VN* /*SM*, where *<sup>i</sup> VN* is either *<sup>e</sup> VN* , *ac VN* or *<sup>b</sup> VN* (in our case, *SM* = 8x10-2 V/Pa) b The equivalent absorption was obtained by dividing the peak-to-peak noise level to cell responsivity: 2 2 *<sup>i</sup> VN* /*R*, where *<sup>i</sup> VN* is either *<sup>e</sup> VN* , *ac VN* or *<sup>b</sup> VN* (in our case, *R* = 280 V cm/W)

c The equivalent C2H4 concentration was obtained by dividing the equivalent absorption to the C2H4 absorption coefficient at one atmosphere pressure of the gas at the 10P(14) laser wavelength (α*<sup>p</sup>* = 30.4 cm-1) d We expressed the coherent acoustical background noise in V independent of the bandwidth, as did Gerlach and Amer (Gerlach & Amer, 1980) and Beck (Beck, 1985) (and not in V/ *Hz* as used by Harren et al. (Harren et al., 1990)); our measurements show that the acoustical background noise was independent of the lock-in bandwidth when the equivalent noise bandwidth (ENBW, the effective bandwidth for gaussian noise) of the low pass filter was varied between 0.08 Hz and 8 Hz (the lock-in time constant *T* was changed between 0.3 and 30 s, where ENBW = 1/(4*<sup>T</sup>*) for a slope of 6 dB/oct) e The coherent photoacoustical background signal was measured in pure nitrogen at atmospheric pressure (1011 mbar) and at a temperature of 22oC: 12 μV at a laser power of 4.4 W for 10P(14) line of the CO2 laser; this signal was the same both in a static gas or at a flow rate of 50 sccm (standard cubic centimeters per minute)

f The same as the limiting sensitivity of the cell, *Scell* 

g With a laser power *PL* = 4.4 W, the minimum measurable concentration of ethylene was 0.2 ppbV, the same as the limiting measurable concentration of ethylene, *clim* (Table 2, Part II)

h The same as the minimum measurable absorption coefficient, α*min* (Table 2, Part II)

i The same as the minimum detectable concentration, *cmin* (Table 2, Part II)

Table 2. Noises measured in our PA system.

The limiting electrical noise measured at resonance frequency was *<sup>e</sup> VN* = 0.15 μV / Hz . At atmospheric pressure, the acoustic background noise was *ac VN* = 2.6 μV (at resonance frequency) under normal working conditions. A photoacoustic background signal of *<sup>b</sup> VN* (nitrogen) = 2.7 μV/W was observed, in phase and at resonance frequency, as the cell was filled with pure N2 at atmospheric pressure.

To determine the actual levels of noises that would be observed in practice, the random electrical noise level of 0.15 μV/ *Hz* , for example, must be multiplied by *B*1/2. Also, to get

The two types of coherent background, however, are extremely narrowband signals at the same frequency as the modulation and hence cannot be filtered out. In addition, since the signal and the coherent photoacoustic background signal are both proportional to laser

Table 2 shows the magnitudes of these limiting factors in the case Brewster windows are used. We expressed each factor in several different sets of units (Dutu et al., 1994b): voltage, pressure amplitude, equivalent absorption coefficient that would give the same pressure amplitude,

> **Equivalent pressurea**

5.3x10-6 Pa/ Hz

9.2x10-5 Pa

9.5x10-5 Pa/W

**Equivalent absorptionb** 

1.5x10-9 W cm-1/ Hz

2.6x10-8 W cm-1 f

2.7x10-8

cm-1 h 8.9x10-10 i

**Equivalent C2H4 concentrationc** 

4.9x10-11 W / Hz

8.6x10-10 W g

α

and the concentration of ethylene that would be required to give that much absorption.

a The equivalent peak-to-peak pressure was obtained by dividing the peak-to-peak noise level to

absorption coefficient at one atmosphere pressure of the gas at the 10P(14) laser wavelength (

2 *<sup>i</sup> VN* /*R*, where *<sup>i</sup> VN* is either *<sup>e</sup> VN* , *ac VN* or *<sup>b</sup> VN* (in our case, *R* = 280 V cm/W)

same as the limiting measurable concentration of ethylene, *clim* (Table 2, Part II)

The same as the minimum detectable concentration, *cmin* (Table 2, Part II)

microphone sensitivity: 2 2 *<sup>i</sup> VN* /*SM*, where *<sup>i</sup> VN* is either *<sup>e</sup> VN* , *ac VN* or *<sup>b</sup> VN* (in our case, *SM* = 8x10-2 V/Pa) b The equivalent absorption was obtained by dividing the peak-to-peak noise level to cell responsivity: 2

*<sup>p</sup>* = 30.4 cm-1) d We expressed the coherent acoustical background noise in V independent of the bandwidth, as did

g With a laser power *PL* = 4.4 W, the minimum measurable concentration of ethylene was 0.2 ppbV, the

The limiting electrical noise measured at resonance frequency was *<sup>e</sup> VN* = 0.15 μV / Hz . At atmospheric pressure, the acoustic background noise was *ac VN* = 2.6 μV (at resonance frequency) under normal working conditions. A photoacoustic background signal of *<sup>b</sup> VN* (nitrogen) = 2.7 μV/W was observed, in phase and at resonance frequency, as the cell was

To determine the actual levels of noises that would be observed in practice, the random electrical noise level of 0.15 μV/ *Hz* , for example, must be multiplied by *B*1/2. Also, to get

α

*min* (Table 2, Part II)

c The equivalent C2H4 concentration was obtained by dividing the equivalent absorption to the C2H4

Gerlach and Amer (Gerlach & Amer, 1980) and Beck (Beck, 1985) (and not in V/ *Hz* as used by Harren et al. (Harren et al., 1990)); our measurements show that the acoustical background noise was independent of the lock-in bandwidth when the equivalent noise bandwidth (ENBW, the effective bandwidth for gaussian noise) of the low pass filter was varied between 0.08 Hz and 8 Hz (the lock-in time constant *T* was changed between 0.3 and 30 s, where ENBW = 1/(4*<sup>T</sup>*) for a slope of 6 dB/oct) e The coherent photoacoustical background signal was measured in pure nitrogen at atmospheric pressure (1011 mbar) and at a temperature of 22oC: 12 μV at a laser power of 4.4 W for 10P(14) line of the CO2 laser; this signal was the same both in a static gas or at a flow rate of 50 sccm (standard cubic

power, no improvement will be achieved as the laser power is increased.

**(rms) value** 

0.15 μV/ Hz

2.6 μV

2.7 μV/W

**Noise type Root-mean-square** 

Electrical noise, *<sup>e</sup> VN*

Coherent acoustic background noised, *ac VN*

Coherent photoacoustic background signale, *<sup>b</sup> VN*

centimeters per minute)

The same as the limiting sensitivity of the cell, *Scell* 

Table 2. Noises measured in our PA system.

filled with pure N2 at atmospheric pressure.

h The same as the minimum measurable absorption coefficient,

f

i

the noise-equivalent absorption one must multiply 1.5x10-9 W cm-1/ *Hz* by *B*1/2*P*-1, where *B* is the bandwidth and *P* the laser power. In order to get an idea of the sensitivity that can be achieved for a representative trace gas, the equivalent ethylene concentration that would give the same signal level is also tabulated. To get the noise-equivalent ethylene concentration, multiply 4.9x10-11 W / *Hz* by *B*1/2*P*-1.

Our coherent acoustical background was 2.6 μV or 9.2x10-5 Pa, equivalent to an absorption of 2.6x10-8 W cm-1. To get the equivalent absorption coefficient divide the latter number by *PL* (5.9x10-9 cm-1). This background signal is dependent on the location of the PA cell in relation to the sound sources associated with the modulation process.

The coherent photoacoustic background was 2.7 μV/W, or 9.6x10-5 Pa/W, assuming the beam was optimally aligned. This is equivalent to an absorption coefficient of 2.7x10-8 cm-1, or an ethylene concentration of about 0.89 ppbV, independent of the laser power. Since the noise and coherent acoustical background can be made negligible by using high laser power, as is done in intracavity operation, the coherent photoacoustic background will be the ultimate limit of sensitivity.

In order to obtain a maximized SNR, a resonance frequency under 1 kHz is necessary. Under 1 kHz, the noise level is determined by the 1/*f* amplifier noise, showing a frequency behavior of 1/ω. Together with *C* ∝ ω<sup>0</sup>-1/2 (because *C* ∝ *Q*/ω0, *Q* ∝ (*dv*, *dh*)-1 and (*dv*, *dh*) ∝ ω0- 1/2, see Sections 3.6, 3.4 and 3.3), we get a SNR proportional to ω<sup>0</sup>1/2. Above 1 kHz, where the 1/*f* amplifier noise is negligible, the SNR is proportional to ω<sup>0</sup>-1/2.

Below 1 kHz, the 1/*f* amplifier noise is the main source. Above 1 kHz, the frequency independent Brownian noise takes over. Since the pressure amplitude is inversely proportional to the square root of the resonance frequency (*p* ∝ *C*, Eq. 20), a convenient resonance can be found between 500 and 1500 Hz. This limits the choice to a cell length of 100-300 mm. If optimal signal enhancement were the only argument, one would rather choose a large (300 mm) resonator (*C* ∝ *L*1/2, Eq. 26). Shorter resonator lengths are necessary in the case of an intracavity setup due to the limited space inside the cavity. Also, a fast time response of the cell requires a short cell length.

When the sample gas is flown continuously through the detector, acoustical noise can be produced, if the gas flow is turbulent, if acoustical noise from the surroundings is coupled directly into the detector sample space or into the tubes connected to the detector and then propagated into the detector, or if acoustic disturbances from the pump running the sample gas through the detector are propagated through the tubes. Thick detector and tube walls, small flow rates, mounting of the cell and chopper in separate sound insulating boxes, etc. must be chosen to suppress these noise contributions.

The background signal can be minimized by placing the windows at nodes of the mode being excited and by introducing buffer volumes at both ends of the cell. The ratio of buffer to resonator diameters must be large enough, and the buffer length has to be equal to onefourth of resonator length.

#### **4.2 Gas interference**

Interference of other absorbing substances may impair the theoretical detection limit in a multicomponent analysis of the real atmosphere. Such interference may be caused by other

CO2 Laser Photoacoustic Spectroscopy: I. Principles 31

Another method is a multicomponent analysis approach. The PA spectrum of an arbitrary gas mixture is represented by a linear combination of the absorption spectra of all constituents. Hence, the absorption spectra of all expected constituents that contribute to the total absorption have to be determined prior to the analysis of a multicomponent gas mixture. Let us assume a nitrogen atmosphere including a mixture of *n* absorbing gases at unknown concentration levels *c*1, *c*2, ... , *cn*, low enough to assure linearity. The PA signal

) of the *n* absorbing compounds *j* (*j* = 1, 2, ... , *n*) with their concentration *cj* and their

α*j*(λ

each compound. In some cases, the calculation becomes more complicated due to different phases of photoacoustic signals generated by the individual constituents of the mixture. For some components, e.g. CO2, a temporal delay in the production of the PA signal may occur. This effect is known as kinetic cooling and results in a phase shift of the PA signal. So, the PA signal has to be considered as the vector sum of the individual signals from each compound:

> () () () () 1 1 *n n*

where *R* (V cm/W) is the cell responsivity. By sequentially tuning the laser to *m* different

photoacoustic signals *Vi* from which we derive a set of *m* linear equations for the unknown

power), and *m* ≥ *n* (it should be noted that the system of linear equations is only well defined if the number *m* of laser transitions is higher than the number of gas components *j*);

laser power at that wavelength. The measurements result in PA signals *Vi* from all components *j* in the gas mixture which absorb on the wavelength of the laser transition,

The minimum number of measurements at different laser wavelengths must be equal to at

11 1 11 1

*n nn n nn*

*n n*

... ... :::: ... ...

*bb aa*

= =

1 1

= = *n*

*i Vbc ijij* <sup>1</sup>

for *j* = 1, 2, ... , *n*. The coefficients *bji* have units of atm V-1. If the number *m* of CO2 laser lines used to carry out the analysis of a gas mixture is equal to or higher than the number *n* of absorbing components in the sample (whose CO2 laser absorption coefficients are known), the unknown concentrations of each *n* component can be determined with the proper

*bb aa*

() ()

*ij* is the absorption coefficient of the *j-*th trace absorbant gas at wavelength

least the number of unknown trace gases, *m* = *n*. In this case we can define:

*B*

λ

*j j V V RP c* = =

*j L jj*

1 1 *n n i i i ij i j ij j j j V RP c a c*

= =

λ= λ= λ α λ , (33)

λ= αλ = , (34)

*ij* (a constant for a given gas, a given wavelength and a given laser

1

−

) is the sum of the individual signals from

*<sup>i</sup>*, *i* = 1, 2, ... , *m*, we obtain *m* measured

λ

. (35)

. (36)

*<sup>i</sup>*, while *Pi* is the

λ*i*.

*V*(λ

wavelength-dependent absorption coefficients

wavelengths (discrete CO2-laser transitions)

concentration levels *cj*:

λ

*i*), *aij* = *RPi*

α

where *Pi* = *PL*(

Therefore,

α

molecular systems present in the environment or substances that are entrained by the carrier flux. If an interfering species is present in the environment, its effect can be minimized by either the introduction of scrubbers and cryogenic traps or the use of dual beam techniques using two PA cells. Sample-entrained interfering species present a more serious problem, since they will be present only near the source and therefore cannot be eliminated by dual beam spectroscopy.

In ambient air, one finds CO2 concentrations of 330-365 ppmV (0.033%-0.0365%) (Sigrist, 1986; Harren et al., 1990; Rooth et al., 1990). This level may rise to about 1% in the practical conditions of an agricultural application. This poses a serious practical problem. The CO2 molecule possesses absorption vibrational band transitions *v*<sup>1</sup> → *v*3 (1000 → 0001) and 2*v*<sup>2</sup> → *v*3 (0200 → 0001) which are weak, while the lower levels are barely populated at room temperature (∼1%). However, due to the exact coincidence of these vibrational-rotational transitions with the CO2 laser lines and the relatively high concentration of CO2 in comparison with trace gases like C2H4, carbon dioxide is inevitably excited by CO2 laser radiation, and the related photoacoustic signal may exceed the trace signal by many orders of magnitude. The absorption coefficient increases strongly with temperature, but is independent of the CO2 concentration over a wide range. A 1.5% concentration of CO2 has an absorption strength comparable to 1 ppmV of C2H4 (for CO2 at the 10P(14) laser line, α(CO2) = 2.1x10-3 atm-1cm-1 and *c*(C2H4) = *c*(CO2)α(CO2)/α(C2H4) = 10-6 atm = 1 ppmV). At the 10P(14) line of CO2, 360 ppmV of CO2 has an absorption coefficient equal to that of 24.8 ppbV of C2H4. Similarly, at the 9R(30) line of CO2 at 21oC, the same concentration of CO2 has an absorption coefficient equal to that of 13.5 ppbV of NH3. Water vapor exhibits a broad continuum with occasional weak lines in the frequency range of the CO2 laser (for H2O at the 10P(14) laser line, α(H2O) = 2.85x10-5 atm-1cm-1). The two dominant peaks are the absorption lines on 10R(20) and the most favorable for ambient air measurement, the 10P(40) laser transition. The absorption of 1% of water vapor in air (50% relative humidity at 18oC) is about the same as that of 9.4 ppbV of C2H4 at the 10P(14) line or 5 ppbV of NH3 at the 9R(30) line of CO2 (Rooth et al., 1990). However, at a constant temperature the absorption coefficient α(H2O) depends on the water vapor concentration *x* and appears to obey the relation: α(H2O) = α0*x*, where α0 is a constant. The natural unpolluted atmosphere contains H2O at a concentration level of ~1.5%.

Ammonia (a colorless, poisonous gas with a characteristic smell and well solvable in water) is vibrationally excited to the ν2 state, usually by means of the *saR*(5, *K*) transitions at λ = 9.22 μm. These levels can be excited by the 9R(30) line of the CO2 laser, where the absorption coefficient α(NH3) has a value of 56 cm-1 atm-1 (Rooth et al., 1990). Ammonia is present in the atmosphere in concentrations ranging from below 0.1 ppbV over open water up to several tens of ppbV in areas with intensive livestock breeding.

Due to the additive character of the photoacoustic signal under normal atmospheric conditions, the presence of a large amount of water vapor and carbon dioxide impedes C2H4 detection in the low-concentration range (ppbV). Consequently, some means of selective spectral discrimination is required if ethylene is to be detected interference free in the matrix of absorbing gases. There are several ways to overcome this problem. The first is to remove CO2 from the flowing sample by absorption on a KOH (potassium hydroxide)-based scrubber inserted between the sampling cell and the PA cell (a specific chemical reaction results: KOH → K2CO3 and water). In this way, concentrations below 1 ppmV CO2 (equivalent to a concentration of 0.07 ppbV of C2H4) can be achieved without influencing the C2H4 concentration.

molecular systems present in the environment or substances that are entrained by the carrier flux. If an interfering species is present in the environment, its effect can be minimized by either the introduction of scrubbers and cryogenic traps or the use of dual beam techniques using two PA cells. Sample-entrained interfering species present a more serious problem, since they will be present only near the source and therefore cannot be eliminated by dual

In ambient air, one finds CO2 concentrations of 330-365 ppmV (0.033%-0.0365%) (Sigrist, 1986; Harren et al., 1990; Rooth et al., 1990). This level may rise to about 1% in the practical conditions of an agricultural application. This poses a serious practical problem. The CO2 molecule possesses absorption vibrational band transitions *v*<sup>1</sup> → *v*3 (1000 → 0001) and 2*v*<sup>2</sup> → *v*3 (0200 → 0001) which are weak, while the lower levels are barely populated at room temperature (∼1%). However, due to the exact coincidence of these vibrational-rotational transitions with the CO2 laser lines and the relatively high concentration of CO2 in comparison with trace gases like C2H4, carbon dioxide is inevitably excited by CO2 laser radiation, and the related photoacoustic signal may exceed the trace signal by many orders of magnitude. The absorption coefficient increases strongly with temperature, but is independent of the CO2 concentration over a wide range. A 1.5% concentration of CO2 has an absorption strength comparable to 1 ppmV of C2H4 (for CO2 at the 10P(14) laser line,

> α(CO2)/α

(H2O) = 2.85x10-5 atm-1cm-1). The two dominant peaks are the

(H2O) depends on the water vapor concentration *x* and appears to

2 state, usually by means of the *saR*(5, *K*) transitions at

0 is a constant. The natural unpolluted atmosphere

the 10P(14) line of CO2, 360 ppmV of CO2 has an absorption coefficient equal to that of 24.8 ppbV of C2H4. Similarly, at the 9R(30) line of CO2 at 21oC, the same concentration of CO2 has an absorption coefficient equal to that of 13.5 ppbV of NH3. Water vapor exhibits a broad continuum with occasional weak lines in the frequency range of the CO2 laser (for H2O at

absorption lines on 10R(20) and the most favorable for ambient air measurement, the 10P(40) laser transition. The absorption of 1% of water vapor in air (50% relative humidity at 18oC) is about the same as that of 9.4 ppbV of C2H4 at the 10P(14) line or 5 ppbV of NH3 at the 9R(30) line of CO2 (Rooth et al., 1990). However, at a constant temperature the

Ammonia (a colorless, poisonous gas with a characteristic smell and well solvable in water)

9.22 μm. These levels can be excited by the 9R(30) line of the CO2 laser, where the absorption

the atmosphere in concentrations ranging from below 0.1 ppbV over open water up to

Due to the additive character of the photoacoustic signal under normal atmospheric conditions, the presence of a large amount of water vapor and carbon dioxide impedes C2H4 detection in the low-concentration range (ppbV). Consequently, some means of selective spectral discrimination is required if ethylene is to be detected interference free in the matrix of absorbing gases. There are several ways to overcome this problem. The first is to remove CO2 from the flowing sample by absorption on a KOH (potassium hydroxide)-based scrubber inserted between the sampling cell and the PA cell (a specific chemical reaction results: KOH → K2CO3 and water). In this way, concentrations below 1 ppmV CO2 (equivalent to a concentration of 0.07 ppbV of C2H4) can be achieved without influencing the C2H4 concentration.

(NH3) has a value of 56 cm-1 atm-1 (Rooth et al., 1990). Ammonia is present in

(C2H4) = 10-6 atm = 1 ppmV). At

λ=

beam spectroscopy.

the 10P(14) laser line,

absorption coefficient

α

obey the relation:

coefficient

(CO2) = 2.1x10-3 atm-1cm-1 and *c*(C2H4) = *c*(CO2)

α

α

(H2O) =

contains H2O at a concentration level of ~1.5%.

α

ν

several tens of ppbV in areas with intensive livestock breeding.

0*x*, where

α

α

is vibrationally excited to the

α

Another method is a multicomponent analysis approach. The PA spectrum of an arbitrary gas mixture is represented by a linear combination of the absorption spectra of all constituents. Hence, the absorption spectra of all expected constituents that contribute to the total absorption have to be determined prior to the analysis of a multicomponent gas mixture. Let us assume a nitrogen atmosphere including a mixture of *n* absorbing gases at unknown concentration levels *c*1, *c*2, ... , *cn*, low enough to assure linearity. The PA signal *V*(λ) of the *n* absorbing compounds *j* (*j* = 1, 2, ... , *n*) with their concentration *cj* and their wavelength-dependent absorption coefficients α*j*(λ) is the sum of the individual signals from each compound. In some cases, the calculation becomes more complicated due to different phases of photoacoustic signals generated by the individual constituents of the mixture. For some components, e.g. CO2, a temporal delay in the production of the PA signal may occur. This effect is known as kinetic cooling and results in a phase shift of the PA signal. So, the PA signal has to be considered as the vector sum of the individual signals from each compound:

$$V\left(\lambda\right) = \sum\_{j=1}^{n} V\_{j}\left(\lambda\right) = RP\_{L}\left(\lambda\right)\sum\_{j=1}^{n} c\_{j}\alpha\_{j}\left(\lambda\right),\tag{33}$$

where *R* (V cm/W) is the cell responsivity. By sequentially tuning the laser to *m* different wavelengths (discrete CO2-laser transitions) λ*<sup>i</sup>*, *i* = 1, 2, ... , *m*, we obtain *m* measured photoacoustic signals *Vi* from which we derive a set of *m* linear equations for the unknown concentration levels *cj*:

$$V\_i\left(\lambda\_i\right) = RP\_i \sum\_{j=1}^n \alpha\_{ij}\left(\lambda\_i\right)c\_j = \sum\_{j=1}^n a\_{ij}c\_j \tag{34}$$

where *Pi* = *PL*(λ*i*), *aij* = *RPi*α*ij* (a constant for a given gas, a given wavelength and a given laser power), and *m* ≥ *n* (it should be noted that the system of linear equations is only well defined if the number *m* of laser transitions is higher than the number of gas components *j*); α*ij* is the absorption coefficient of the *j-*th trace absorbant gas at wavelength λ*<sup>i</sup>*, while *Pi* is the laser power at that wavelength. The measurements result in PA signals *Vi* from all components *j* in the gas mixture which absorb on the wavelength of the laser transition, λ*i*. The minimum number of measurements at different laser wavelengths must be equal to at least the number of unknown trace gases, *m* = *n*. In this case we can define:

$$B = \begin{pmatrix} b\_{11} \dots b\_{1u} \\ \vdots & \vdots \\ b\_{n1} \dots b\_{nu} \end{pmatrix} = \begin{pmatrix} a\_{11} \dots a\_{1u} \\ \vdots & \vdots \\ a\_{n1} \dots a\_{nn} \end{pmatrix}^{-1} \tag{35}$$

Therefore,

$$c\_j = \sum\_{i=1}^{m} b\_{ji} V\_i \, . \tag{36}$$

for *j* = 1, 2, ... , *n*. The coefficients *bji* have units of atm V-1. If the number *m* of CO2 laser lines used to carry out the analysis of a gas mixture is equal to or higher than the number *n* of absorbing components in the sample (whose CO2 laser absorption coefficients are known), the unknown concentrations of each *n* component can be determined with the proper

CO2 Laser Photoacoustic Spectroscopy: I. Principles 33

θ

Hz and an excitation at 9R(28) CO2 line (9.23 µm) (Rooth et al., 1990).

vapor concentration. The corresponding experimental data are plotted for a frequency of 560

In Fig. 8, the phase of the calculated heat production rate for a CO2 – N2 – O2 – H2O mixture is plotted as a function of the concentrations *CO*<sup>2</sup> *c* and *H O*<sup>2</sup> *c* [19]. The data used for this plot were those for 10R(20) CO2 laser transition, i.e., *I*0 = 20 W/cm2, *H O*<sup>2</sup> σ = 3.5x10-23 cm2 and <sup>σ</sup> <sup>2</sup>*OH* = 1.0x10-22 cm2, and a chopper frequency *f* = 2650 Hz. As demonstrated in Fig. 8, the phase reversal only occurs within rather narrow concentration ranges. Thus, a heat-rate phase different from 0o or 180o is rarely expected for low H2O and CO2 concentrations.

Fig. 8. Calculated phase of heat production rate for a CO2 – N2 – O2 – H2O mixture as function of the concentrations *CO*<sup>2</sup> *c* and *H O*<sup>2</sup> *c* and for *<sup>N</sup>*<sup>2</sup> *c* = 0.8 and *<sup>O</sup>*<sup>2</sup> *c* = 0.2 (Meyer & Sigrist, 1990).

The multicomponent analysis can utilize the phase information of the photoacoustic response to suppress the CO2 signal. A high concentration of CO2 yields a phase shift of the signal with respect to the acoustic signal of ethylene. A combined signal for a CO2-C2H4 mixture is less than the sum of both individual amplitudes (vectorially added). The zero phase of the two-phase vector lock-in amplifier is adjusted to pure C2H4 absorption, and thus a mixture of CO2 and C2H4 in air is measured on two CO2 laser transitions. One obtains four pieces of information, i.e. the CO2-C2H4 mixture phase shift and absorption coefficients

for air with 340 ppmV CO2 as a function of water

Fig. 7. Predicted amplitude R and phase

selection of laser lines. The solution of sets of simultaneous equations is generally required to estimate the concentrations of each species in a multicomponent mixture and select the optimal wavelengths for a fixed number of laser lines. The selection of CO2 laser wavelengths for the optimum detection of a single species in the presence of interferences can usually be carried out by comparing the corresponding laser absorption profiles.

This method was used by Perlmutter et al. (Perlmutter et al., 1979), who observed a minus sign of the calculated CO2 concentration level. The minus sign stems from the fact that the absorption coefficients of CO2 were taken to be positive in the numerical analysis. Actually the absorption coefficients of CO2 present in nitrogen at low concentration levels (up to ~0.5%), at CO2 laser transitions, are of negative sign. The absolute values are unchanged. This minus sign is associated with the kinetic cooling effect. They found experimentally that in a longitudinal resonant PA cell (chopping frequency = 1 kHz) the CO2 gives a 180o ± 10o out-of-phase PA signal relative to operation with normal gases like ethylene. This is true when CO2 is present at concentration levels up to ~0.5% in nitrogen. At concentration levels higher than ~0.5%, the kinetic cooling phase deviation does not exceed ~180o and highly depends on concentration, thus leading to an increasing PA signal level.

A crucial feature of photoacoustics on gas mixtures is the molecular dynamics involved in the conversion of internal molecular energy to heat (Olaffson et al., 1989; Henningsen et al., 1990). This is particularly important when dealing with mixtures involving CO2 and N2. The near degeneracy between the fundamental asymmetric stretch of CO2 (2349 cm-1) and the N2 *v* = 1 vibration (2331 cm-1) leads to a large cross section for resonant energy transfer. In a CO2 laser, this mechanism is used to advantage by adding N2 to the gas mixture in order to increase the pump rate by energy transfer from the vibrationally excited N2 to CO2 in the ground state. In our case, the situation is reversed. Thus, following absorption of CO2 laser radiation, an excited CO2 molecule transfers its excitation energy to N2, where it resides for a long time owing to the metastable character of the excited N2 levels (the lifetime of the vibrational level *v* = 1 is ≅ 1 ms at 1 atm; 1 atm = 101.325 kPa). Since the CO2 molecule was initially taken out of an excited state, and the transition was a hot band transition, there now is a non-equilibrium situation among the CO2 vibrational levels, and equilibrium is eventually restored at the expense of translational energy. Thus, following radiation absorption, a transient cooling of the CO2 gas takes place, and the effect is therefore referred to as kinetic cooling. In trace gas detection, this means that the photoacoustic phase of the CO2 signal will be significantly different from the phase of the trace gas signal, where no kinetic cooling is involved. The situation is further complicated if water is present in the gas mixture, since water molecules are effective in deexciting the metastable N2 levels and hence in reducing the phase contrast. The presence of 1% water vapors speeds up the relaxation of vibrationally excited N2, and this effect reduces the phase contrast to about 135o down from 180o. This phase contrast is a very important aid in the analysis of mixtures where one of the components is strongly dominant, since a quantitative analysis of the phase contrast may provide information about the H2O concentration.

The presence of H2O and CO2 will always influence the measurement of C2H4 and NH3 concentrations. These background gases absorb CO2 laser radiation and produce simultaneously occurring photoacoustic signals. A comparison of the predicted amplitude and phase of the photoacoustic signal with experimental data is given in Fig. 7 (Rooth et al., 1990).

selection of laser lines. The solution of sets of simultaneous equations is generally required to estimate the concentrations of each species in a multicomponent mixture and select the optimal wavelengths for a fixed number of laser lines. The selection of CO2 laser wavelengths for the optimum detection of a single species in the presence of interferences

This method was used by Perlmutter et al. (Perlmutter et al., 1979), who observed a minus sign of the calculated CO2 concentration level. The minus sign stems from the fact that the absorption coefficients of CO2 were taken to be positive in the numerical analysis. Actually the absorption coefficients of CO2 present in nitrogen at low concentration levels (up to ~0.5%), at CO2 laser transitions, are of negative sign. The absolute values are unchanged. This minus sign is associated with the kinetic cooling effect. They found experimentally that in a longitudinal resonant PA cell (chopping frequency = 1 kHz) the CO2 gives a 180o ± 10o out-of-phase PA signal relative to operation with normal gases like ethylene. This is true when CO2 is present at concentration levels up to ~0.5% in nitrogen. At concentration levels higher than ~0.5%, the kinetic cooling phase deviation does not exceed ~180o and highly

A crucial feature of photoacoustics on gas mixtures is the molecular dynamics involved in the conversion of internal molecular energy to heat (Olaffson et al., 1989; Henningsen et al., 1990). This is particularly important when dealing with mixtures involving CO2 and N2. The near degeneracy between the fundamental asymmetric stretch of CO2 (2349 cm-1) and the N2 *v* = 1 vibration (2331 cm-1) leads to a large cross section for resonant energy transfer. In a CO2 laser, this mechanism is used to advantage by adding N2 to the gas mixture in order to increase the pump rate by energy transfer from the vibrationally excited N2 to CO2 in the ground state. In our case, the situation is reversed. Thus, following absorption of CO2 laser radiation, an excited CO2 molecule transfers its excitation energy to N2, where it resides for a long time owing to the metastable character of the excited N2 levels (the lifetime of the vibrational level *v* = 1 is ≅ 1 ms at 1 atm; 1 atm = 101.325 kPa). Since the CO2 molecule was initially taken out of an excited state, and the transition was a hot band transition, there now is a non-equilibrium situation among the CO2 vibrational levels, and equilibrium is eventually restored at the expense of translational energy. Thus, following radiation absorption, a transient cooling of the CO2 gas takes place, and the effect is therefore referred to as kinetic cooling. In trace gas detection, this means that the photoacoustic phase of the CO2 signal will be significantly different from the phase of the trace gas signal, where no kinetic cooling is involved. The situation is further complicated if water is present in the gas mixture, since water molecules are effective in deexciting the metastable N2 levels and hence in reducing the phase contrast. The presence of 1% water vapors speeds up the relaxation of vibrationally excited N2, and this effect reduces the phase contrast to about 135o down from 180o. This phase contrast is a very important aid in the analysis of mixtures where one of the components is strongly dominant, since a quantitative analysis of the phase contrast may

The presence of H2O and CO2 will always influence the measurement of C2H4 and NH3 concentrations. These background gases absorb CO2 laser radiation and produce simultaneously occurring photoacoustic signals. A comparison of the predicted amplitude and phase of the photoacoustic signal with experimental data is given in Fig. 7 (Rooth et al.,

can usually be carried out by comparing the corresponding laser absorption profiles.

depends on concentration, thus leading to an increasing PA signal level.

provide information about the H2O concentration.

1990).

Fig. 7. Predicted amplitude R and phase θ for air with 340 ppmV CO2 as a function of water vapor concentration. The corresponding experimental data are plotted for a frequency of 560 Hz and an excitation at 9R(28) CO2 line (9.23 µm) (Rooth et al., 1990).

In Fig. 8, the phase of the calculated heat production rate for a CO2 – N2 – O2 – H2O mixture is plotted as a function of the concentrations *CO*<sup>2</sup> *c* and *H O*<sup>2</sup> *c* [19]. The data used for this plot were those for 10R(20) CO2 laser transition, i.e., *I*0 = 20 W/cm2, *H O*<sup>2</sup> σ = 3.5x10-23 cm2 and <sup>σ</sup> <sup>2</sup>*OH* = 1.0x10-22 cm2, and a chopper frequency *f* = 2650 Hz. As demonstrated in Fig. 8, the phase reversal only occurs within rather narrow concentration ranges. Thus, a heat-rate phase different from 0o or 180o is rarely expected for low H2O and CO2 concentrations.

Fig. 8. Calculated phase of heat production rate for a CO2 – N2 – O2 – H2O mixture as function of the concentrations *CO*<sup>2</sup> *c* and *H O*<sup>2</sup> *c* and for *<sup>N</sup>*<sup>2</sup> *c* = 0.8 and *<sup>O</sup>*<sup>2</sup> *c* = 0.2 (Meyer & Sigrist, 1990).

The multicomponent analysis can utilize the phase information of the photoacoustic response to suppress the CO2 signal. A high concentration of CO2 yields a phase shift of the signal with respect to the acoustic signal of ethylene. A combined signal for a CO2-C2H4 mixture is less than the sum of both individual amplitudes (vectorially added). The zero phase of the two-phase vector lock-in amplifier is adjusted to pure C2H4 absorption, and thus a mixture of CO2 and C2H4 in air is measured on two CO2 laser transitions. One obtains four pieces of information, i.e. the CO2-C2H4 mixture phase shift and absorption coefficients

CO2 Laser Photoacoustic Spectroscopy: I. Principles 35

the difference in the two signals yields the CO2 concentration with the help of Eq. (37); the fourth line, 9R(30) together with 9R(28) provides the NH3 concentration). Nägele and Sigrist (Nägele & Sigrist, 2000) recorded the PA signal on two transitions for each compound, carefully selected for maximum absorption, minimum absorption interference, and good laser performance. In addition, they measured the PA signal on two laser transitions (10P(12), 10P(40)), for which all of the investigated gases exhibit negligible absorption, to verify the constant background signal. Therefore, the spectra to monitor ethylene (10P(14), 10P(16)), ethanol (9P(8), 9P(32)), methanol (9P(34), 9P(36)), and CO2 (10P(20), 9R(20)) comprise ten different transitions. Thus cross references are possible and the background signal, which is the same for these lines, can be subtracted. This extension to several laser lines yields better detection limits and selectivity, although the time for one full

Based on previous discussion, PA spectroscopy, performed with tunable CO2 lasers as radiation

i. Its high sensitivity makes it possible to measure absorption coefficients on the order of 10-8 cm-1, corresponding to densities of μg/m3 or concentrations of ppbV (10-9 atm) for

iv. It has high selectivity, meaning that it can clearly distinguish among various compounds; v. The experimental setup is rather simple, immune to interference, and, for example, does

vi. Relative portability for *in situ* measurements (carried on mobile trailers in the

vii. Operational simplicity and real time data analysis make it capable of performing quasi

x. Specially designed PA cells can perform continuous measurements on flowing gas mixtures, i.e., a much better temporal resolution can be achieved than the one provided

The outstanding features of the PA cell, most importantly its small size, simplicity, and robustness, cannot be fully utilized unless it is combined with a suitable laser source. The recent commercial availability of sealed-off, medium-power (50 W), grating-tunable CO2 lasers has paved the way to the development of instrumentation with excellent sensitivity and compact footprints that can be readily deployed in industrial or medical settings. Further improvements are possible by using resonant PA cells with high *Q* factors (limited, though, by

Other laser sources were successfully applied in photoacoustic spectroscopy. Recent developments in compact near-infrared (NIR) and IR all-solid-state tunable lasers, such as the tunable semiconductor lasers, quantum-cascade lasers, and devices utilizing non-linear

fluctuations of the modulation frequency), multipass, or intracavity arrangements.

viii. The calibration with certified gases and gas mixtures is straightforward and reliable; ix. Detection linearity and a wide dynamic range of at least 6 orders of magnitude are offered (from several fractions of ppbV to tens of ppmV), i.e., the same apparatus can be

sources, offers the following main characteristics relevant to *in situ* trace gas monitoring:

iii. A large number of gases and vapors are measurable with the same instrument;

ii. The PA cell responsivity is independent of radiation wavelength;

troposphere or on balloon-borne systems to the stratosphere);

used for low (immission) and high (emission) concentrations.

not require cryogenic cooling of the IR detectors, etc.;

measurement increases with the number of lines.

**5. Conclusions** 

most substances;

continuous measurements;

by, *inter alia*, gas chromatography.

for both lines. From this, with known absorption coefficients for both lines, the CO2 and C2H4 concentrations can be extracted (Rooth et al., 1990). A good estimate is obtained from the difference between the two measured signals *Va* and *Vb*. Putting *Va* = *Ra*exp(*i*θ*<sup>a</sup>*) and *Vb* = *Rb*exp(*i*θ*<sup>b</sup>*) the magnitude of the difference is found with the cosine rule:

$$\mathbb{E}\left|\boldsymbol{V}\_{a} - \boldsymbol{V}\_{b}\right| = \left[\boldsymbol{R}\_{a}^{2} + \boldsymbol{R}\_{b}^{2} - 2\boldsymbol{R}\_{a}\boldsymbol{R}\_{b}\cos\left(\boldsymbol{\Theta}\_{a} - \boldsymbol{\Theta}\_{b}\right)\right]^{1/2}.\tag{37}$$

Here it is only the difference between the two phase angles that is required, so absolute calibrations can be avoided. This approach has the advantage that a high laser power can be used, and no partial failure of the scrubber can falsify the C2H4 concentration.

In a multicomponent mixture, this effect can be taken into account by measuring the amplitudes *Vi* of the PA signal at the laser transitions *i* as well as its phases θ*<sup>i</sup>*, where the number *i* = 1... *m* stands for the discrete CO2 laser transitions with the powers *P*(λ*<sup>i</sup>*) = *Pi*. Thus, similar to Eq. (34) we have the following equation for the PA signal amplitude:

$$\mathbf{V}\_i \mathbf{\dot{\mathbf{\bar{v}}}} \cos \Theta\_i = \mathbf{R} P\_i \sum\_{j=1}^n \mathbf{c}\_j \mathbf{\alpha}\_{ij} \left(\lambda\_i \right) \cos \Theta\_{ij} \tag{38}$$

with *i* =1... *m*, *j* = 1... *n*, *n* ≤ *m*, where *cj* is the concentration of the gas component *j* and α*ij* is the absorption coefficient of the gas compound *j* at the laser transition *i*. The phase θ*ij* is a mathematical aid for easy calculation. It is nearly independent of the laser transition *i* for a certain gas component and can thus be written as θ*<sup>j</sup>*. In our wavelength range it is only CO2 which shows a phase θ*j* = π, whereas all the other gases studied so far show a phase θ*<sup>j</sup>* = 0. In real measurements small deviations of the phases from the predicted ones occur due to measurement errors. Nevertheless, the approximation θ*ij* = θ*<sup>j</sup>* = 0 for all the other air compounds is well justified. It should be noted that the system of linear equations is only well defined if the number of gas components *j* is smaller than the number *m* of laser transitions, i.e., for *n* ≤ *m*. Based on measurements of the signals *Vi*, phases θ*<sup>j</sup>*, and laser powers *Pi*, and knowing the absorption coefficients α*ij* from literature data or calibration measurements, the unknown concentrations *cj* can be derived by solving the above equation system. The algorithm of the data analysis has been described by Meyer and Sigrist (Meyer & Sigrist, 1990). For multicomponent mixtures an algorithm, e.g., a nonlinear Levenberg-Marquardt fit (Moeckli et al., 1998) is employed to fit the measured spectrum on the basis of calibration spectra of the individual compounds.

The concentrations of C2H4, CO2, and H2O in nitrogen at atmospheric pressure can be determined by measuring the PA signals using three CO2 laser transitions, e.g., 10P(14), 10P(20) and 10R(20) (Sigrist et al., 1989). The 10P(14) and 10R(20) transitions coincide with sharp peaks of the IR spectra of C2H4 (α = 30.4 cm-1atm-1) and H2O (α = 8.36x10-4 cm-1atm-1), respectively. The 10P(20) line that is used to measure CO2 concentration (α = 2.2x10-3 cm-1atm-1) could be replaced by many other transitions without much change in sensitivity, because CO2 is relatively spectrally flat.

Rooth et al. (Rooth et al., 1990) determined the H2O, CO2, and NH3 contents in ambient air by using four laser transitions (10R(20) is used to compute water vapor concentration using the absorption coefficient at the actual gas temperature; the influence of the CO2 absorption on the measurement of H2O is also taken into account by using the 9R(18) and 9R(28) lines; the difference in the two signals yields the CO2 concentration with the help of Eq. (37); the fourth line, 9R(30) together with 9R(28) provides the NH3 concentration). Nägele and Sigrist (Nägele & Sigrist, 2000) recorded the PA signal on two transitions for each compound, carefully selected for maximum absorption, minimum absorption interference, and good laser performance. In addition, they measured the PA signal on two laser transitions (10P(12), 10P(40)), for which all of the investigated gases exhibit negligible absorption, to verify the constant background signal. Therefore, the spectra to monitor ethylene (10P(14), 10P(16)), ethanol (9P(8), 9P(32)), methanol (9P(34), 9P(36)), and CO2 (10P(20), 9R(20)) comprise ten different transitions. Thus cross references are possible and the background signal, which is the same for these lines, can be subtracted. This extension to several laser lines yields better detection limits and selectivity, although the time for one full measurement increases with the number of lines.

#### **5. Conclusions**

34 CO2 Laser – Optimisation and Application

for both lines. From this, with known absorption coefficients for both lines, the CO2 and C2H4 concentrations can be extracted (Rooth et al., 1990). A good estimate is obtained from

Here it is only the difference between the two phase angles that is required, so absolute calibrations can be avoided. This approach has the advantage that a high laser power can be

In a multicomponent mixture, this effect can be taken into account by measuring the

1 cos cos *n i i i j ij i ij j*

mathematical aid for easy calculation. It is nearly independent of the laser transition *i* for a

real measurements small deviations of the phases from the predicted ones occur due to

compounds is well justified. It should be noted that the system of linear equations is only well defined if the number of gas components *j* is smaller than the number *m* of laser

measurements, the unknown concentrations *cj* can be derived by solving the above equation system. The algorithm of the data analysis has been described by Meyer and Sigrist (Meyer & Sigrist, 1990). For multicomponent mixtures an algorithm, e.g., a nonlinear Levenberg-Marquardt fit (Moeckli et al., 1998) is employed to fit the measured spectrum on the basis of

The concentrations of C2H4, CO2, and H2O in nitrogen at atmospheric pressure can be determined by measuring the PA signals using three CO2 laser transitions, e.g., 10P(14), 10P(20) and 10R(20) (Sigrist et al., 1989). The 10P(14) and 10R(20) transitions coincide with

1atm-1) could be replaced by many other transitions without much change in sensitivity,

Rooth et al. (Rooth et al., 1990) determined the H2O, CO2, and NH3 contents in ambient air by using four laser transitions (10R(20) is used to compute water vapor concentration using the absorption coefficient at the actual gas temperature; the influence of the CO2 absorption on the measurement of H2O is also taken into account by using the 9R(18) and 9R(28) lines;

=

with *i* =1... *m*, *j* = 1... *n*, *n* ≤ *m*, where *cj* is the concentration of the gas component *j* and

the absorption coefficient of the gas compound *j* at the laser transition *i*. The phase

( )

θ

, whereas all the other gases studied so far show a phase

α

= 30.4 cm-1atm-1) and H2O (

θ*ij* = θ

θ= α λ θ , (38)

*<sup>j</sup>*. In our wavelength range it is only CO2

*ij* from literature data or calibration

α

( ) 1/2 2 2 | | 2 cos *V V R R RR a b a b ab a b* − = + − θ −θ . (37)

θ

θ

*<sup>a</sup>*) and *Vb* =

*<sup>i</sup>*, where the

α*ij* is

θ*ij* is a

*<sup>j</sup>*, and laser

θ*<sup>j</sup>* = 0. In

*<sup>j</sup>* = 0 for all the other air

θ

= 8.36x10-4 cm-1atm-1),

= 2.2x10-3 cm-

α

λ*<sup>i</sup>*) = *Pi*.

the difference between the two measured signals *Va* and *Vb*. Putting *Va* = *Ra*exp(*i*

*<sup>b</sup>*) the magnitude of the difference is found with the cosine rule:

used, and no partial failure of the scrubber can falsify the C2H4 concentration.

amplitudes *Vi* of the PA signal at the laser transitions *i* as well as its phases

*V RP c*

transitions, i.e., for *n* ≤ *m*. Based on measurements of the signals *Vi*, phases

α

respectively. The 10P(20) line that is used to measure CO2 concentration (

certain gas component and can thus be written as

measurement errors. Nevertheless, the approximation

powers *Pi*, and knowing the absorption coefficients

calibration spectra of the individual compounds.

sharp peaks of the IR spectra of C2H4 (

because CO2 is relatively spectrally flat.

θ*j* = π

which shows a phase

number *i* = 1... *m* stands for the discrete CO2 laser transitions with the powers *P*(

Thus, similar to Eq. (34) we have the following equation for the PA signal amplitude:

*Rb*exp(*i*θ

> Based on previous discussion, PA spectroscopy, performed with tunable CO2 lasers as radiation sources, offers the following main characteristics relevant to *in situ* trace gas monitoring:


The outstanding features of the PA cell, most importantly its small size, simplicity, and robustness, cannot be fully utilized unless it is combined with a suitable laser source. The recent commercial availability of sealed-off, medium-power (50 W), grating-tunable CO2 lasers has paved the way to the development of instrumentation with excellent sensitivity and compact footprints that can be readily deployed in industrial or medical settings. Further improvements are possible by using resonant PA cells with high *Q* factors (limited, though, by fluctuations of the modulation frequency), multipass, or intracavity arrangements.

Other laser sources were successfully applied in photoacoustic spectroscopy. Recent developments in compact near-infrared (NIR) and IR all-solid-state tunable lasers, such as the tunable semiconductor lasers, quantum-cascade lasers, and devices utilizing non-linear

CO2 Laser Photoacoustic Spectroscopy: I. Principles 37

harmonic of a Nd:YAG laser and their IR tuning range is limited to approximately 2 µm. Difference frequency generation (DFG) is certainly the most promising technique for the extension of the tuning range of an existing tunable laser to the mid IR (2.5-4.5 µm) (Fischer & Sigrist, 2002). Spectrometers using DFG were applied to monitoring, for example, formaldehyde in ambient air at 3.53 µm (Rehle et al., 2001) and volcanic gases (CH4, CO2,

Angeli, G.Z.; Solyom, A.M.; Miklos, A. & Bicanic, D.D. (1992). Calibration of a Windowless

Beck, S.M. (1985). Cell Coatings to Minimize Sample (NH3 and N2H4) Adsorption for Low-

Beenen, A. & Niessner, R. (1998). Development of Photoacoustic Gas Sensor for In-Situ and

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Photoacoustic Simultaneous Detection of Methane and Ethylene by Means of a 1.63-µm Diode Laser. *Appl. Phys. B,* Vol.74, No.3, (February 2002), pp. 273-278, ISSN

Sensitivity, Near- Infrared Tunable-Diode-Laser-Based Photoacoustic Water-Vapor-Detection System for Automated Operation. *Meas. Sci. Technol.,* Vol.10, No.11,

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**6. References** 

optical mixing in non-linear crystals (OPOs, difference frequency generators (DFGs), optical parametric amplifiers (OPAs)), have significantly advanced the application of photoacoustic techniques in sensitive trace gas analysis.

NIR diode lasers are becoming more and more popular due to recent development of cheap high-quality, compact sources having a spectral emission which falls in the absorption range of many molecules of great practical interest. The range of the available NIR diode lasers spans from about 0.8 to 2.1 µm. Many gases like methane, acetylene, CO, and CO2 exhibit overtone absorptions in the 1.55-1.65 µm wavelength region which can be covered by a conventional external cavity diode laser (ECDL). Detection limits are lower compared with measurements in the fundamental absorption region but still sufficient for many applications. A combination of diode lasers with PA detection was used by various authors to detect ammonia (Fehér et al., 1994; Schmohl et al., 2002), methane (Schäfer et al., 1998), elemental carbon (Petzold et al., 1995), toluene (Beenen et al., 1998), and water vapor (Bozóki et al., 1999). Different experimental arrangements such as external cavity diode lasers (Sneider et al., 1997) or intracavity PA cells (Bozóki et al., 1996) were tested. At present, 1.6 µm diode lasers, coinciding with the first vibrational overtones and combination bands of molecules containing a CH bond, are those that – in the NIR range – provide the best tradeoff between cost and molecular detection efficiency (Boschetti et al., 2002).

Recent progress with quantum-cascade lasers makes them attractive sources in the important 3- to 5-µm spectral range. This area is important not only because the characteristic absorption bands of, among others, CO, N2O, HCl and CH2O, lie herein, but also because there is an atmospheric transparent window in this range. Soon after the first appearance of these lasers, gas monitoring applications using various detection schemes were reported (Sharpe et al., 1998; Kosterev et al., 2008). Quantum-cascade lasers were used to detect ammonia and water vapor at 8.5 µm (Paldus et al., 1999), NO at 5.2 µm (Menzel et al., 2001), 12CH4, 13CH4 and N2O isotopomers at 8.1 µm (Gagliardi et al., 2002), trace gases (CH4, N2O, H2O) in laboratory air at 7.9 µm (Kosterev & Tittel, 2002), carbon dioxide, methanol and ammonia at 10.1/10.3 µm (Hofstetter et al., 2001), CH4 and NO at 7.9 µm and 5.3 µm (Grossel et al, 2006; Grossel et al., 2007) and simultaneously CO and SO2 at 4.56 µm and 7.38 µm (Liu et al., 2011). In contrast to semiconductor (diode) lasers, quantum-cascade lasers are unipolar light sources based on only one type of carrier, usually electrons, making intraband transitions between confined energy levels within the conduction band. The term "cascade" comes from the fact that the confined energy levels are arranged the way of a waterfall, so that electrons undergoing lasing transitions travel from one stage to the next, just like water does in a multiple-step water cascade. Therefore, one electron can emit sequentially up to *n* photons when *n* steps are present. The emission wavelength of a quantum-cascade laser is determined not by the semiconductor bandgap but by the quantum confinement in the quantum wells created by the quantum-well material and the barrier material. Therefore, quantum-cascade lasers can span a wide wavelength range using the same material system. Quantum-cascade lasers with wavelengths from 3.5 to 13 µm have been fabricated by use of the same material system (InGaAs wells and InAlAs barriers).

Widely tunable, narrowband optical parametric oscillator (OPO)-based laser sources were used for trace gas spectroscopy in the fundamental C-H stretch vibration region (3-5 µm) (Bohren et al., 1997), to detect ethane at 3.34 µm (Kühnemann et al., 1998; van Herpen et al., 2002), N2O at 2.86 µm (Costopoulos et al., 2002), or methane at 3.39 µm (Miklós et al., 2002). Most of today's commercial OPOs are based on BaB2O4 crystals (BBO) pumped by the third harmonic of a Nd:YAG laser and their IR tuning range is limited to approximately 2 µm. Difference frequency generation (DFG) is certainly the most promising technique for the extension of the tuning range of an existing tunable laser to the mid IR (2.5-4.5 µm) (Fischer & Sigrist, 2002). Spectrometers using DFG were applied to monitoring, for example, formaldehyde in ambient air at 3.53 µm (Rehle et al., 2001) and volcanic gases (CH4, CO2, HCl, SO2, H 2O vapor) at 3.3-4.4 µm (Richter et al., 2002).

#### **6. References**

36 CO2 Laser – Optimisation and Application

optical mixing in non-linear crystals (OPOs, difference frequency generators (DFGs), optical parametric amplifiers (OPAs)), have significantly advanced the application of photoacoustic

NIR diode lasers are becoming more and more popular due to recent development of cheap high-quality, compact sources having a spectral emission which falls in the absorption range of many molecules of great practical interest. The range of the available NIR diode lasers spans from about 0.8 to 2.1 µm. Many gases like methane, acetylene, CO, and CO2 exhibit overtone absorptions in the 1.55-1.65 µm wavelength region which can be covered by a conventional external cavity diode laser (ECDL). Detection limits are lower compared with measurements in the fundamental absorption region but still sufficient for many applications. A combination of diode lasers with PA detection was used by various authors to detect ammonia (Fehér et al., 1994; Schmohl et al., 2002), methane (Schäfer et al., 1998), elemental carbon (Petzold et al., 1995), toluene (Beenen et al., 1998), and water vapor (Bozóki et al., 1999). Different experimental arrangements such as external cavity diode lasers (Sneider et al., 1997) or intracavity PA cells (Bozóki et al., 1996) were tested. At present, 1.6 µm diode lasers, coinciding with the first vibrational overtones and combination bands of molecules containing a CH bond, are those that – in the NIR range – provide the best trade-

Recent progress with quantum-cascade lasers makes them attractive sources in the important 3- to 5-µm spectral range. This area is important not only because the characteristic absorption bands of, among others, CO, N2O, HCl and CH2O, lie herein, but also because there is an atmospheric transparent window in this range. Soon after the first appearance of these lasers, gas monitoring applications using various detection schemes were reported (Sharpe et al., 1998; Kosterev et al., 2008). Quantum-cascade lasers were used to detect ammonia and water vapor at 8.5 µm (Paldus et al., 1999), NO at 5.2 µm (Menzel et al., 2001), 12CH4, 13CH4 and N2O isotopomers at 8.1 µm (Gagliardi et al., 2002), trace gases (CH4, N2O, H2O) in laboratory air at 7.9 µm (Kosterev & Tittel, 2002), carbon dioxide, methanol and ammonia at 10.1/10.3 µm (Hofstetter et al., 2001), CH4 and NO at 7.9 µm and 5.3 µm (Grossel et al, 2006; Grossel et al., 2007) and simultaneously CO and SO2 at 4.56 µm and 7.38 µm (Liu et al., 2011). In contrast to semiconductor (diode) lasers, quantum-cascade lasers are unipolar light sources based on only one type of carrier, usually electrons, making intraband transitions between confined energy levels within the conduction band. The term "cascade" comes from the fact that the confined energy levels are arranged the way of a waterfall, so that electrons undergoing lasing transitions travel from one stage to the next, just like water does in a multiple-step water cascade. Therefore, one electron can emit sequentially up to *n* photons when *n* steps are present. The emission wavelength of a quantum-cascade laser is determined not by the semiconductor bandgap but by the quantum confinement in the quantum wells created by the quantum-well material and the barrier material. Therefore, quantum-cascade lasers can span a wide wavelength range using the same material system. Quantum-cascade lasers with wavelengths from 3.5 to 13 µm have been fabricated by use of the same material system (InGaAs wells and InAlAs barriers).

Widely tunable, narrowband optical parametric oscillator (OPO)-based laser sources were used for trace gas spectroscopy in the fundamental C-H stretch vibration region (3-5 µm) (Bohren et al., 1997), to detect ethane at 3.34 µm (Kühnemann et al., 1998; van Herpen et al., 2002), N2O at 2.86 µm (Costopoulos et al., 2002), or methane at 3.39 µm (Miklós et al., 2002). Most of today's commercial OPOs are based on BaB2O4 crystals (BBO) pumped by the third

off between cost and molecular detection efficiency (Boschetti et al., 2002).

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**2** 

 *Romania* 

**CO2 Laser Photoacoustic Spectroscopy:** 

*Department of Lasers, National Institute for Laser, Plasma, and Radiation Physics, Bucharest* 

In this chapter, the main components of an instrument based on laser photoacoustic spectroscopy (LPAS) principles are described in detail. Special emphasis is laid on the home-built, frequency-stabilized, line-tunable CO2-laser source and the resonant photoacoustic cell. All of the parameters that are characteristic to the photoacoustic cell, including the limiting sensitivity of the system, are measured and compared with the best results reported by other authors. Approaches to improve current sensor performance are also discussed. Other aspects of a functional photoacoustic instrument, such as the gas

Two experimental set-ups were designed and characterized with the photoacoustic (PA) cell in an external configuration: the first one with a low power CO2 laser where the saturation effects are negligible, and a second one with a high power CO2 laser where the saturation effects are important. In the first case, the minimum detectable concentration was 0.9 ppbV (parts per billion by volume), while in the second case this parameter was improved to 0.21 ppbV. Comparing with the best results published previously in the literature, our minimum detectable concentration is better by a factor of 4.2 in the first case and by a factor of 18 in the

The next section is dealing with several applications developed in our laboratory. We present a precise measurement of the absorption coefficients of ethylene and ammonia at CO2 laser wavelengths. For ethylene, the values obtained at 10-µm band excellently agree with other measurements reported in the literature, while important differences were found for the absorption coefficients at 9-µm band. Other applications in plant physiology and medicine (lipid peroxidation and measurement of human biomarkers) are briefly reviewed. Exhaled breath air analysis represents an attractive and promising novel approach for noninvasive detection of human biomarkers associated with different diseases. Due to extremely low level of the substances of interest in exhaled breath air and the interference of many components at a given laser wavelength, we investigated several measures to increase the accuracy for a single trace gas measurement: a) We studied the efficiency of absorptive trapping and cryogenic trapping to remove carbon dioxide and water vapors from exhaled breath samples. As a result, we found the minimum volume for the KOH trap and the optimum flow rate for transferring gas samples from collecting bags to the photoacoustic (PA) cell. b) We refined breath sample collection procedures from patients under medical

handling system and data acquisition and processing, are outlined.

**1. Introduction** 

second case.

**II. Instrumentation and Applications** 

Dan C. Dumitras, Ana Maria Bratu and Cristina Popa

Photoacoustic and Absorption Spectroscopy. *Appl. Phys. B,* Vol.66, No.4, (April 1998), pp. 511-516, ISSN 0946-2171


### **CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications**

Dan C. Dumitras, Ana Maria Bratu and Cristina Popa *Department of Lasers, National Institute for Laser, Plasma, and Radiation Physics, Bucharest Romania* 

#### **1. Introduction**

42 CO2 Laser – Optimisation and Application

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In this chapter, the main components of an instrument based on laser photoacoustic spectroscopy (LPAS) principles are described in detail. Special emphasis is laid on the home-built, frequency-stabilized, line-tunable CO2-laser source and the resonant photoacoustic cell. All of the parameters that are characteristic to the photoacoustic cell, including the limiting sensitivity of the system, are measured and compared with the best results reported by other authors. Approaches to improve current sensor performance are also discussed. Other aspects of a functional photoacoustic instrument, such as the gas handling system and data acquisition and processing, are outlined.

Two experimental set-ups were designed and characterized with the photoacoustic (PA) cell in an external configuration: the first one with a low power CO2 laser where the saturation effects are negligible, and a second one with a high power CO2 laser where the saturation effects are important. In the first case, the minimum detectable concentration was 0.9 ppbV (parts per billion by volume), while in the second case this parameter was improved to 0.21 ppbV. Comparing with the best results published previously in the literature, our minimum detectable concentration is better by a factor of 4.2 in the first case and by a factor of 18 in the second case.

The next section is dealing with several applications developed in our laboratory. We present a precise measurement of the absorption coefficients of ethylene and ammonia at CO2 laser wavelengths. For ethylene, the values obtained at 10-µm band excellently agree with other measurements reported in the literature, while important differences were found for the absorption coefficients at 9-µm band. Other applications in plant physiology and medicine (lipid peroxidation and measurement of human biomarkers) are briefly reviewed.

Exhaled breath air analysis represents an attractive and promising novel approach for noninvasive detection of human biomarkers associated with different diseases. Due to extremely low level of the substances of interest in exhaled breath air and the interference of many components at a given laser wavelength, we investigated several measures to increase the accuracy for a single trace gas measurement: a) We studied the efficiency of absorptive trapping and cryogenic trapping to remove carbon dioxide and water vapors from exhaled breath samples. As a result, we found the minimum volume for the KOH trap and the optimum flow rate for transferring gas samples from collecting bags to the photoacoustic (PA) cell. b) We refined breath sample collection procedures from patients under medical

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 45

photoacoustic background signal makes it possible to increase the overall sensitivity of the instrument. This was proved by comparing our results with those obtained with intracavity arrangements (see Table 3). Also, the dynamic range of the PA method is considerably reduced by intracavity operation. Optical saturation may occur for molecules with high absorption cross section while uncontrollable signal changes may be obtained at higher overall absorption in the PA cell, because the loss of light intensity influences the gain of the laser. This effect may cause erroneous results when the sample concentration changes are large. Therefore, high-sensitivity single- and multipass extracavity PA detectors offer a

Various modulation methods are applied in PA spectroscopy. It is necessary to distinguish between the modulation of incident radiation and that of sample absorption (Sigrist et al., 1989). The first schemes include the widely used amplitude modulation of the incident radiation by mechanical choppers, electro-optic and acousto-optic modulators as well as the modulation of the laser emission itself by pulsed excitation, Q-switching, and mode-locking. On the other hand, frequency or wavelength modulation of the incident radiation provides the advantage of eliminating the continuum background PA signal caused by wavelengthindependent absorption, e.g., by the cell window. The absorption characteristics of the sample can be modulated based on the Zeeman or Stark effect, i.e., by applying modulated magnetic or electric fields to the sample. Consequently, the absorption wavelength of the sample is varied, which corresponds to a wavelength modulation method. The continuum background is suppressed as a result. For example, a reduction of the background by a factor of 500 was achieved by Stark modulation compared with the one obtained in the same PA cell with conventional amplitude modulation by a chopper (Kavaya et al., 1979). However, it should be noted that the application of the Stark modulation scheme in trace gas detection is restricted to molecules with a permanent electric dipole moment like ammonia (NH3), nitric oxide (NO), etc. Nevertheless, a considerable increase in sensitivity and, even more important, in selectivity in multicomponent mixtures can be achieved.

The light beam was modulated with a high quality, low vibration noise and variable speed (4-4000 Hz) mechanical chopper model DigiRad C-980 or C-995 (30 slot aperture) operated at the appropriate resonant frequency of the cell (564 Hz). The laser beam diameter is typically 5 mm at the point of insertion of the chopper blade and is nearly equal to the width of the chopper aperture. An approximately square waveform was produced with a modulation depth of 100% and a duty cycle of 50% so that the average power measured by the powermeter at the exit of the PA cell is half the cw value. By enclosing the chopper wheel in a housing with a small hole (10 mm) allowing the laser beam to pass, chopperinduced sound vibrations in air that can be transmitted to the microphone detector as noise interference are reduced. A phase reference signal is provided for use with a lock-in amplifier. The generated acoustic waves are detected by microphones mounted in the cell wall, whose signal is fed to a lock-in amplifier locked to the modulation frequency. The lock-in amplifier is a highly flexible signal recovery and analysis instrument, as it is able to measure accurately a single-frequency signal obscured by noise sources many thousands of times larger than itself. It rejects random noise, transients, incoherent discrete frequency interference and harmonics of measurement frequency. A lock-in measures an ac signal and produces a dc output proportional to the ac signal. Because the dc output level is usually greater than the ac input, a lock-in is termed an amplifier. The lock-in can also gauge the phase relationship of two signals at the same frequency. A demodulator, or phase-sensitive

simpler alternative to intracavity devices.

treatment: alveolar collection vs. mixed expiratory collection; collecting bags; preparation of patients (antiseptic mouthwash, avoiding food for at least 12 hours); clean transfer of the gas samples from disposable bags to the PA cell in less than 6 hours. c) We measured the photoacoustic signal at different CO2 laser wavelengths to distinguish the influence of various absorbent gas components in the total content.

One study involved assessment of breath ethylene and ammonia levels in patients with renal failure receiving hemodialysis (HD) treatment. Our measurements demonstrated that HD determines simultaneously a large increase of ethylene concentration in the exhaled breath (due to the oxidative stress) and a reduction of the ammonia concentration, correlated to the blood urea nitrogen level. Analysis of ethylene and ammonia traces from breath may provide insight into severity of oxidative stress and metabolic disturbances and give information for determining efficacy and endpoint of HD.

#### **2. Experimental arrangement**

#### **2.1 General schematic**

The block diagram of the laser photoacoustic spectrometer was presented in the previous chapter (Fig. 2, Part I). The cw, tunable CO2-laser beam is chopped, focused by a ZnSe lens, and introduced in the PA cell. After passing through the PA cell, the power of the laser beam is measured by a laser radiometer Rk-5700 from Laser Probe Inc. with a measuring head RkT-30. Its digital output is introduced in the data acquisition interface module together with the output from the lock-in amplifier. All experimental data are processed and stored by a computer (Dumitras et al., 2007). The frequency stabilized, line tunable CO2 lasers (low power and high power, respectively) will be described in the next section. Both CO2 lasers are used in two parallel measuring lines, where two independent experiments can be conducted simultaneously. A view of the two parallel measurement lines with laser photoacoustic sensors is shown in Fig. 1.

Fig. 1. General view of the PA sensors (two parallel measurement lines).

We decided to use an extracavity arrangement because it has several advantages. In spite of a lower laser power available to excite the absorbing gas in the PA cell, a smaller coherent

treatment: alveolar collection vs. mixed expiratory collection; collecting bags; preparation of patients (antiseptic mouthwash, avoiding food for at least 12 hours); clean transfer of the gas samples from disposable bags to the PA cell in less than 6 hours. c) We measured the photoacoustic signal at different CO2 laser wavelengths to distinguish the influence of

One study involved assessment of breath ethylene and ammonia levels in patients with renal failure receiving hemodialysis (HD) treatment. Our measurements demonstrated that HD determines simultaneously a large increase of ethylene concentration in the exhaled breath (due to the oxidative stress) and a reduction of the ammonia concentration, correlated to the blood urea nitrogen level. Analysis of ethylene and ammonia traces from breath may provide insight into severity of oxidative stress and metabolic disturbances and

The block diagram of the laser photoacoustic spectrometer was presented in the previous chapter (Fig. 2, Part I). The cw, tunable CO2-laser beam is chopped, focused by a ZnSe lens, and introduced in the PA cell. After passing through the PA cell, the power of the laser beam is measured by a laser radiometer Rk-5700 from Laser Probe Inc. with a measuring head RkT-30. Its digital output is introduced in the data acquisition interface module together with the output from the lock-in amplifier. All experimental data are processed and stored by a computer (Dumitras et al., 2007). The frequency stabilized, line tunable CO2 lasers (low power and high power, respectively) will be described in the next section. Both CO2 lasers are used in two parallel measuring lines, where two independent experiments can be conducted simultaneously. A view of the two parallel measurement lines with laser

various absorbent gas components in the total content.

give information for determining efficacy and endpoint of HD.

Fig. 1. General view of the PA sensors (two parallel measurement lines).

We decided to use an extracavity arrangement because it has several advantages. In spite of a lower laser power available to excite the absorbing gas in the PA cell, a smaller coherent

**2. Experimental arrangement** 

photoacoustic sensors is shown in Fig. 1.

**2.1 General schematic** 

photoacoustic background signal makes it possible to increase the overall sensitivity of the instrument. This was proved by comparing our results with those obtained with intracavity arrangements (see Table 3). Also, the dynamic range of the PA method is considerably reduced by intracavity operation. Optical saturation may occur for molecules with high absorption cross section while uncontrollable signal changes may be obtained at higher overall absorption in the PA cell, because the loss of light intensity influences the gain of the laser. This effect may cause erroneous results when the sample concentration changes are large. Therefore, high-sensitivity single- and multipass extracavity PA detectors offer a simpler alternative to intracavity devices.

Various modulation methods are applied in PA spectroscopy. It is necessary to distinguish between the modulation of incident radiation and that of sample absorption (Sigrist et al., 1989). The first schemes include the widely used amplitude modulation of the incident radiation by mechanical choppers, electro-optic and acousto-optic modulators as well as the modulation of the laser emission itself by pulsed excitation, Q-switching, and mode-locking. On the other hand, frequency or wavelength modulation of the incident radiation provides the advantage of eliminating the continuum background PA signal caused by wavelengthindependent absorption, e.g., by the cell window. The absorption characteristics of the sample can be modulated based on the Zeeman or Stark effect, i.e., by applying modulated magnetic or electric fields to the sample. Consequently, the absorption wavelength of the sample is varied, which corresponds to a wavelength modulation method. The continuum background is suppressed as a result. For example, a reduction of the background by a factor of 500 was achieved by Stark modulation compared with the one obtained in the same PA cell with conventional amplitude modulation by a chopper (Kavaya et al., 1979). However, it should be noted that the application of the Stark modulation scheme in trace gas detection is restricted to molecules with a permanent electric dipole moment like ammonia (NH3), nitric oxide (NO), etc. Nevertheless, a considerable increase in sensitivity and, even more important, in selectivity in multicomponent mixtures can be achieved.

The light beam was modulated with a high quality, low vibration noise and variable speed (4-4000 Hz) mechanical chopper model DigiRad C-980 or C-995 (30 slot aperture) operated at the appropriate resonant frequency of the cell (564 Hz). The laser beam diameter is typically 5 mm at the point of insertion of the chopper blade and is nearly equal to the width of the chopper aperture. An approximately square waveform was produced with a modulation depth of 100% and a duty cycle of 50% so that the average power measured by the powermeter at the exit of the PA cell is half the cw value. By enclosing the chopper wheel in a housing with a small hole (10 mm) allowing the laser beam to pass, chopperinduced sound vibrations in air that can be transmitted to the microphone detector as noise interference are reduced. A phase reference signal is provided for use with a lock-in amplifier.

The generated acoustic waves are detected by microphones mounted in the cell wall, whose signal is fed to a lock-in amplifier locked to the modulation frequency. The lock-in amplifier is a highly flexible signal recovery and analysis instrument, as it is able to measure accurately a single-frequency signal obscured by noise sources many thousands of times larger than itself. It rejects random noise, transients, incoherent discrete frequency interference and harmonics of measurement frequency. A lock-in measures an ac signal and produces a dc output proportional to the ac signal. Because the dc output level is usually greater than the ac input, a lock-in is termed an amplifier. The lock-in can also gauge the phase relationship of two signals at the same frequency. A demodulator, or phase-sensitive

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 47

The variation of the background and calibration with transversal or longitudinal translation of the PA cell against the propagation beam direction is very small as long as the laser beam does not strike the walls of the cell. The optimum position of the PA cell against the focusing lens (the center of the resonant tube, i.e. the position of the microphones) is 450 mm (for a focusing length of 400 mm). On extending this optimum distance by 30 mm, the signal is decreased by 0.14%, while when shortening the distance by 60 mm, the signal decreases by 0.61%. The dependence of both signal and background signal on the transversal position of the resonant tube relative to the laser beam is similarly low. We found that the cell calibration and background were virtually invariable for reasonably small longitudinal or

ZnSe, where *n* is the refraction index of the material), the window reflectivity becomes nonzero, and the reflected beam can heat the walls of the cell, making a further contribution to the background signal. Nevertheless, for a ± 10% variation of the angle of incidence relative to the Brewster angle, the reflectance increases from zero to only 2.7% and 1.7%, respectively, meaning that a small deviation from the Brewster angle will not change

Another variable we investigated was the polarization angle of the beam. The cell response in terms of background signal displays a rather broad flat minimum, provided the incidence angle on the window ensures a minimum reflection loss. The data indicate that a deviation of several degrees from vertical polarization can be tolerated. In conclusion, we found that the calibration and background signal were not extremely sensitive to slight misalignments of the beam.

Several authors employed an iris diaphragm in close proximity of the PA cell entrance window to provide spatial filtering in order to reduce the background noise signal caused by off-axis radiation impinging on the internal wall of the chamber. With such a diaphragm, we found that the background signal increased significantly owing to laser beam diffraction at the edges of the aperture. Using high quality optical components (diffraction grating, coupling mirror, lens and windows) together with a well controlled laser beam makes the

We have designed, constructed and optimized a rugged sealed-off CO2 laser (named LIR-25 SF), step-tunable on more than 60 vibrational-rotational lines and frequency stabilized by the use of plasma tube impedance variations detected as voltage fluctuations (the optovoltaic method) (Dumitras et al., 1981; Dumitras et al., 1985; Dutu et al., 1985). The glass tube has an inner diameter of 7 mm and a discharge length of 53 cm. At both ends of the tube we attached ZnSe windows at Brewster angle. The laser is water cooled around the discharge tube. The dc discharge is driven by a high-voltage power supply. The end reflectors of the laser cavity are a piezoelectrically driven, partially (85%) reflecting ZnSe mirror at one end and a line-selecting grating (135 lines/mm, blazed at 10.6 µm) at the other.

A free-running or unstabilized laser is subject to many perturbations of its frequency. First

keeping a constant length is the prime objective in frequency stabilization schemes. Possible perturbations of the cavity length can be divided into two groups: external effects (thermal

θ*B* (θ

*<sup>B</sup>* = arctan*n* = 67.38o for

ν/ν

= Δ*L*/*L*), so

transversal movements of the cell.

**2.2 CO2 lasers** 

As the angle of incidence deviates from the Brewster angle

insertion of an iris diaphragm in the PA instrument unnecessary.

Piezoelectric ceramics such as lead zirconate titanate (PZT) can be used.

of all, changes in cavity length affect the frequency of an oscillating mode (Δ

dramatically the reflectance or the angle of refraction.

detector (PSD), is the basis for a lock-in amplifier. This circuit rectifies the signals coming in at the desired frequency. The PSD output is also a function of the phase angle between the input signal and the amplifier's internal reference signal generated by a phased-locked loop locked to an external reference (chopper). We used a dual-phase, digital lock-in amplifier Stanford Research Systems model SR 830 with the following characteristics: full scale sensitivity, 2 nV - 1 V; input noise, 6 nV (rms)/ Hz at 1 kHz; dynamic reserve, greater than 100 dB; frequency range, 1 mHz – 102 kHz; time constants, 10 μs – 30 s (reference > 200 Hz), or up to 30000 s (reference < 200 Hz).

The diverging IR laser beam is converged by a ZnSe focusing lens (*f* = 400 mm). In this way, a slightly focused laser beam is passed through the photoacoustic cell without wall interactions. The laser beam diameter *D* = 2*w* (or its radius, *w*), which is a very important issue in LPAS, was calculated at different locations on the beam's propagation path (Fig. 2). A too large beam compared to the inner diameter of the resonant tube could increase the coherent photoacoustical background signal to impracticable values. The calculation was made in three steps: a) inside the laser cavity; b) between the laser coupling mirror and the focusing lens, and c) after the focusing lens (including at the center of the PA cell and at the Brewster windows of the cell).

Fig. 2. Geometry of the laser beam from its waist to the exit of the PA cell.

The laser resonator has a stable-type configuration, being made of a diffraction grating equivalent to a totally reflecting flat mirror and a coupling concave spherical mirror with the radius of curvature *R*1 = 10 m. We have calculated the parameters of the ideal gaussian beam inside and outside the laser resonator, i.e., for *M*2 = 1, and we have obtained the following values: *w*0 = 2.91 mm (or a beam waist diameter 2*w*0 = 5.83 mm); *w*1 = 3.02 mm (2*w*1 = 6.04 mm); *w*2 = 3.16 (2*w*2 = 6.32 mm); *w*3 = 1.75 mm (2*w*3 = 3.51 mm); *w*4 = 0.51 mm (2*w*4 = 1.03 mm) and *w*5 = 2.26 mm (2*w*5 = 4.53 mm) (for *Lc* = 690 mm, *L*1 = 1060 mm and *L*2 = 450 mm). It follows that as the laser beam travels along the PA cell, its diameter is small enough compared to the diameter of the resonant tube (7 mm) to avoid wall absorptions, which ensures that the chosen geometry minimizes the coherent photoacoustical background signal, as intended.

The pertinent questions we set out to answer in assessing the performance of our PA cell were whether the chosen geometry minimized the coherent background signal, and how sensitive the background and calibration were to slight beam deviations from the intended path. Obviously, if the calibration would vary significantly with small movements of the beam, the accuracy of measurements made with the PA cell would be adversely affected unless the cell alignment was very carefully adjusted and rigidly fixed.

The variation of the background and calibration with transversal or longitudinal translation of the PA cell against the propagation beam direction is very small as long as the laser beam does not strike the walls of the cell. The optimum position of the PA cell against the focusing lens (the center of the resonant tube, i.e. the position of the microphones) is 450 mm (for a focusing length of 400 mm). On extending this optimum distance by 30 mm, the signal is decreased by 0.14%, while when shortening the distance by 60 mm, the signal decreases by 0.61%. The dependence of both signal and background signal on the transversal position of the resonant tube relative to the laser beam is similarly low. We found that the cell calibration and background were virtually invariable for reasonably small longitudinal or transversal movements of the cell.

As the angle of incidence deviates from the Brewster angle θ*B* (θ*<sup>B</sup>* = arctan*n* = 67.38o for ZnSe, where *n* is the refraction index of the material), the window reflectivity becomes nonzero, and the reflected beam can heat the walls of the cell, making a further contribution to the background signal. Nevertheless, for a ± 10% variation of the angle of incidence relative to the Brewster angle, the reflectance increases from zero to only 2.7% and 1.7%, respectively, meaning that a small deviation from the Brewster angle will not change dramatically the reflectance or the angle of refraction.

Another variable we investigated was the polarization angle of the beam. The cell response in terms of background signal displays a rather broad flat minimum, provided the incidence angle on the window ensures a minimum reflection loss. The data indicate that a deviation of several degrees from vertical polarization can be tolerated. In conclusion, we found that the calibration and background signal were not extremely sensitive to slight misalignments of the beam.

Several authors employed an iris diaphragm in close proximity of the PA cell entrance window to provide spatial filtering in order to reduce the background noise signal caused by off-axis radiation impinging on the internal wall of the chamber. With such a diaphragm, we found that the background signal increased significantly owing to laser beam diffraction at the edges of the aperture. Using high quality optical components (diffraction grating, coupling mirror, lens and windows) together with a well controlled laser beam makes the insertion of an iris diaphragm in the PA instrument unnecessary.

#### **2.2 CO2 lasers**

46 CO2 Laser – Optimisation and Application

detector (PSD), is the basis for a lock-in amplifier. This circuit rectifies the signals coming in at the desired frequency. The PSD output is also a function of the phase angle between the input signal and the amplifier's internal reference signal generated by a phased-locked loop locked to an external reference (chopper). We used a dual-phase, digital lock-in amplifier Stanford Research Systems model SR 830 with the following characteristics: full scale sensitivity, 2 nV - 1 V; input noise, 6 nV (rms)/ Hz at 1 kHz; dynamic reserve, greater than 100 dB; frequency range, 1 mHz – 102 kHz; time constants, 10 μs – 30 s (reference > 200 Hz),

The diverging IR laser beam is converged by a ZnSe focusing lens (*f* = 400 mm). In this way, a slightly focused laser beam is passed through the photoacoustic cell without wall interactions. The laser beam diameter *D* = 2*w* (or its radius, *w*), which is a very important issue in LPAS, was calculated at different locations on the beam's propagation path (Fig. 2). A too large beam compared to the inner diameter of the resonant tube could increase the coherent photoacoustical background signal to impracticable values. The calculation was made in three steps: a) inside the laser cavity; b) between the laser coupling mirror and the focusing lens, and c) after the focusing lens (including at the center of the PA cell and at the

Fig. 2. Geometry of the laser beam from its waist to the exit of the PA cell.

unless the cell alignment was very carefully adjusted and rigidly fixed.

The laser resonator has a stable-type configuration, being made of a diffraction grating equivalent to a totally reflecting flat mirror and a coupling concave spherical mirror with the radius of curvature *R*1 = 10 m. We have calculated the parameters of the ideal gaussian beam inside and outside the laser resonator, i.e., for *M*2 = 1, and we have obtained the following values: *w*0 = 2.91 mm (or a beam waist diameter 2*w*0 = 5.83 mm); *w*1 = 3.02 mm (2*w*1 = 6.04 mm); *w*2 = 3.16 (2*w*2 = 6.32 mm); *w*3 = 1.75 mm (2*w*3 = 3.51 mm); *w*4 = 0.51 mm (2*w*4 = 1.03 mm) and *w*5 = 2.26 mm (2*w*5 = 4.53 mm) (for *Lc* = 690 mm, *L*1 = 1060 mm and *L*2 = 450 mm). It follows that as the laser beam travels along the PA cell, its diameter is small enough compared to the diameter of the resonant tube (7 mm) to avoid wall absorptions, which ensures that the chosen geometry minimizes the coherent photoacoustical

The pertinent questions we set out to answer in assessing the performance of our PA cell were whether the chosen geometry minimized the coherent background signal, and how sensitive the background and calibration were to slight beam deviations from the intended path. Obviously, if the calibration would vary significantly with small movements of the beam, the accuracy of measurements made with the PA cell would be adversely affected

or up to 30000 s (reference < 200 Hz).

Brewster windows of the cell).

background signal, as intended.

We have designed, constructed and optimized a rugged sealed-off CO2 laser (named LIR-25 SF), step-tunable on more than 60 vibrational-rotational lines and frequency stabilized by the use of plasma tube impedance variations detected as voltage fluctuations (the optovoltaic method) (Dumitras et al., 1981; Dumitras et al., 1985; Dutu et al., 1985). The glass tube has an inner diameter of 7 mm and a discharge length of 53 cm. At both ends of the tube we attached ZnSe windows at Brewster angle. The laser is water cooled around the discharge tube. The dc discharge is driven by a high-voltage power supply. The end reflectors of the laser cavity are a piezoelectrically driven, partially (85%) reflecting ZnSe mirror at one end and a line-selecting grating (135 lines/mm, blazed at 10.6 µm) at the other. Piezoelectric ceramics such as lead zirconate titanate (PZT) can be used.

A free-running or unstabilized laser is subject to many perturbations of its frequency. First of all, changes in cavity length affect the frequency of an oscillating mode (Δν/ν = Δ*L*/*L*), so keeping a constant length is the prime objective in frequency stabilization schemes. Possible perturbations of the cavity length can be divided into two groups: external effects (thermal

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 49

The error signal generated by the phase detector can serve to drive the cavity resonance to the center of the laser gain curve. In this way, the electronic feedback loop seeks the center of the lasing gain profile, the lock-in point being the zero crossing of the phase detector response. If the mean mode frequency is lower than the line center frequency, the phase of the observed laser intensity variation is opposite to the one we have where the mode frequency is higher than the line center frequency. The amplitude of the jitter output

In lieu of using an IR detector to sense the laser intensity variation, the cavity length is adjusted using the optovoltaic effect. As the internal laser radiation field intensity is altered by changing the resonant cavity alignment, the discharge impedance, which is proportional to the slope of the curve of laser output power *versus* frequency, is also modulated. The impedance variation is determined by exciting the plasma tube with a high-speed currentregulated power supply and measuring the resulting variation in the voltage drop across the plasma tube (the optovoltaic effect). An intensity variation of 1% is sufficient to change the discharge impedance significantly (~ 0.1%). By using a current regulated power supply, the voltage impedance fluctuation is detected as an ac component of the voltage drop across

Before any attempt is made to stabilize the frequency of a laser, a single frequency output must be ensured. For this purpose, a laser operating in the lowest transversal mode (TEM00) must be designed (Dumitras et al., 1976). The single line operation of the CO2 laser is achieved with a dispersive element (diffraction grating). The cavity length of *Lc* = 690 mm

Calculating the collisional broadening in a mixture of CO2, N2, He, Xe, and H2 at a total

MHz. We therefore conclude that a single frequency operation is obtained when a

To increase the number of oscillating lines, especially those with a smaller gain, and obtain reliable long term operation at a single specific wavelength, some form of wavelength selection introduced in the optical cavity is generally required. As optical dispersion is incorporated by using a diffraction grating or Brewster-angle prisms within the laser cavity, the laser can be made to oscillate on only one vibrational-rotational line, otherwise the particular transition on which the CO2 laser operates depends on the length of the resonator. That is why the total reflecting mirror must be replaced by a diffraction grating, which is tilted about its groove axis to the blaze angle and acts as a frequency selective reflector. Light diffracted into the first order maximum is returned along the optical axis and taken as laser output, while light in other orders as well as any other wavelength is returned off-axis and gets lost. Another advantage of a laser resonator with a grating is that the laser can be

We used a flat diffraction grating with 135 grooves/mm, blazed at 10.6 μm and having a peak efficiency of 96%, mounted in a Littrow configuration. With such a grating, the vibrational-rotational lines emitted by the CO2 laser in the range P(50) – 10.9329 μm and R(44) – 9.1549 μm can be selected by controlling the grating angle in the range 47o33'32'' to 38o10'02'', which can be set to the desired laser transition with a micrometric screw. This grating presents a good dispersion, as the P(18) and P(20) lines (10.4 μm band) are separated by a 6'38'' angular

difference (as compared with 2'49'' for a diffraction grating with 75 grooves/mm).

ν >Δν*<sup>c</sup>*/2).

pressure of 34 mbar gives a collisional full linewidth at half maximum (FWHM) Δ

ν

= *c*/2*Lc* = 217 MHz.

ν*<sup>c</sup>* = 119

corresponds to a separation between two longitudinal modes of Δ

longitudinal mode is tuned on the top of the gain curve (Δ

tuned over the entire oscillating linewidth from the line center.

increases with the frequency offset from the line center.

the plasma tube.

variations of the spacer material, changes in atmospheric conditions, mechanical vibrations, variations in the position of optical components and in magnetic fields) and internal effects, which are generally related to the discharge noise.

Active power stabilization based on a piezo-driven out-coupling mirror is used in our laser. The principle of the stabilization schemes is based on a comparison between the frequency of a single frequency laser (single-mode, single-line) and some stable point of reference. If the laser frequency is different from that of the benchmark, an error-sensing discriminant is used to derive a signal proportional to the deviation. This error signal is used to control the laser oscillating frequency and retune it to the reference one. Such a servo-loop (closed loop feedback) locks the laser frequency to that of the reference. For moderate stability, the CO2 laser line profile can be used as the discriminating curve (Dumitras et al., 1981). This method is more appropriate for the CO2 laser than for other lasers because the CO2 vibrationalrotational line profile is narrow and has much steeper slopes than, for example, that of the neon line in a He-Ne laser. The error signal is produced by allowing the laser resonance cavity to "ride" around the steep part of the line profile slope, and its amplitude is dependent on the change in cavity mirror separation. This scheme requires internal frequency modulation (jittering) of the laser in order to sense the sign of the derived error signal. Stabilization is then obtained by re-establishing the required separation with a servo-system.

The CO2 laser is frequency stabilized to the center of the curve representing its output power *versus* frequency (the molecular resonance) upon the variation of plasma tube impedance, when the optical power extracted from the medium is modulated (Dutu et al., 1985). In this closed-loop active stabilization, the cavity length is controlled by a piezoelectrically driven mirror along the cavity axis, which responds to the sum of a dc control voltage, plus a small jitter signal at some convenient frequency (~500 Hz). As can be seen in Fig. 3, where a curve of laser line gain *versus* frequency is drawn, the small cavity jitter induces a sinusoidal variation in laser output as the cavity mode scans across the transition gain profile, which is compared in phase to the jitter voltage.

Fig. 3. Generation of the error-frequency signal.

variations of the spacer material, changes in atmospheric conditions, mechanical vibrations, variations in the position of optical components and in magnetic fields) and internal effects,

Active power stabilization based on a piezo-driven out-coupling mirror is used in our laser. The principle of the stabilization schemes is based on a comparison between the frequency of a single frequency laser (single-mode, single-line) and some stable point of reference. If the laser frequency is different from that of the benchmark, an error-sensing discriminant is used to derive a signal proportional to the deviation. This error signal is used to control the laser oscillating frequency and retune it to the reference one. Such a servo-loop (closed loop feedback) locks the laser frequency to that of the reference. For moderate stability, the CO2 laser line profile can be used as the discriminating curve (Dumitras et al., 1981). This method is more appropriate for the CO2 laser than for other lasers because the CO2 vibrationalrotational line profile is narrow and has much steeper slopes than, for example, that of the neon line in a He-Ne laser. The error signal is produced by allowing the laser resonance cavity to "ride" around the steep part of the line profile slope, and its amplitude is dependent on the change in cavity mirror separation. This scheme requires internal frequency modulation (jittering) of the laser in order to sense the sign of the derived error signal. Stabilization is then

The CO2 laser is frequency stabilized to the center of the curve representing its output power *versus* frequency (the molecular resonance) upon the variation of plasma tube impedance, when the optical power extracted from the medium is modulated (Dutu et al., 1985). In this closed-loop active stabilization, the cavity length is controlled by a piezoelectrically driven mirror along the cavity axis, which responds to the sum of a dc control voltage, plus a small jitter signal at some convenient frequency (~500 Hz). As can be seen in Fig. 3, where a curve of laser line gain *versus* frequency is drawn, the small cavity jitter induces a sinusoidal variation in laser output as the cavity mode scans across the

which are generally related to the discharge noise.

obtained by re-establishing the required separation with a servo-system.

transition gain profile, which is compared in phase to the jitter voltage.

Fig. 3. Generation of the error-frequency signal.

The error signal generated by the phase detector can serve to drive the cavity resonance to the center of the laser gain curve. In this way, the electronic feedback loop seeks the center of the lasing gain profile, the lock-in point being the zero crossing of the phase detector response. If the mean mode frequency is lower than the line center frequency, the phase of the observed laser intensity variation is opposite to the one we have where the mode frequency is higher than the line center frequency. The amplitude of the jitter output increases with the frequency offset from the line center.

In lieu of using an IR detector to sense the laser intensity variation, the cavity length is adjusted using the optovoltaic effect. As the internal laser radiation field intensity is altered by changing the resonant cavity alignment, the discharge impedance, which is proportional to the slope of the curve of laser output power *versus* frequency, is also modulated. The impedance variation is determined by exciting the plasma tube with a high-speed currentregulated power supply and measuring the resulting variation in the voltage drop across the plasma tube (the optovoltaic effect). An intensity variation of 1% is sufficient to change the discharge impedance significantly (~ 0.1%). By using a current regulated power supply, the voltage impedance fluctuation is detected as an ac component of the voltage drop across the plasma tube.

Before any attempt is made to stabilize the frequency of a laser, a single frequency output must be ensured. For this purpose, a laser operating in the lowest transversal mode (TEM00) must be designed (Dumitras et al., 1976). The single line operation of the CO2 laser is achieved with a dispersive element (diffraction grating). The cavity length of *Lc* = 690 mm corresponds to a separation between two longitudinal modes of Δν = *c*/2*Lc* = 217 MHz. Calculating the collisional broadening in a mixture of CO2, N2, He, Xe, and H2 at a total pressure of 34 mbar gives a collisional full linewidth at half maximum (FWHM) Δν*<sup>c</sup>* = 119 MHz. We therefore conclude that a single frequency operation is obtained when a longitudinal mode is tuned on the top of the gain curve (Δν >Δν*<sup>c</sup>*/2).

To increase the number of oscillating lines, especially those with a smaller gain, and obtain reliable long term operation at a single specific wavelength, some form of wavelength selection introduced in the optical cavity is generally required. As optical dispersion is incorporated by using a diffraction grating or Brewster-angle prisms within the laser cavity, the laser can be made to oscillate on only one vibrational-rotational line, otherwise the particular transition on which the CO2 laser operates depends on the length of the resonator. That is why the total reflecting mirror must be replaced by a diffraction grating, which is tilted about its groove axis to the blaze angle and acts as a frequency selective reflector. Light diffracted into the first order maximum is returned along the optical axis and taken as laser output, while light in other orders as well as any other wavelength is returned off-axis and gets lost. Another advantage of a laser resonator with a grating is that the laser can be tuned over the entire oscillating linewidth from the line center.

We used a flat diffraction grating with 135 grooves/mm, blazed at 10.6 μm and having a peak efficiency of 96%, mounted in a Littrow configuration. With such a grating, the vibrational-rotational lines emitted by the CO2 laser in the range P(50) – 10.9329 μm and R(44) – 9.1549 μm can be selected by controlling the grating angle in the range 47o33'32'' to 38o10'02'', which can be set to the desired laser transition with a micrometric screw. This grating presents a good dispersion, as the P(18) and P(20) lines (10.4 μm band) are separated by a 6'38'' angular difference (as compared with 2'49'' for a diffraction grating with 75 grooves/mm).

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 51

ruggedly. The mirrors can be adjusted in angle by sliding two stainless steel spherical joints with respect to one another. As the mirrors are adjusted into their final position, the adjustment

The diffraction grating is mounted in a similar holder and is rotated by a micrometric screw (0 – 25 mm), as shown in Fig. 6. The laser tube was rigidly mounted in the cavity with two concentric rings, the inner one being adjusted by three screws. This system allows the laser tube axis to fall into line with the mirror centers and provides good transverse stability.

To achieve active stabilization, an automatic frequency control circuit (lock-in stabilizer) is used to maintain an axial mode on the top of the gain curve. The block diagram of the frequency stabilization system based on plasma tube impedance variations is shown in Fig. 7. A sinusoidal signal with a rough frequency of 500 Hz derived from the pilot oscillator is applied to the piezoelectric transducer, resulting in a simultaneous frequency and amplitude

The ac voltage drop across the tube is passed through a tuned amplifier and then synchronously detected. The demodulation of the ac signal is performed in the phasesensitive detector, with phase (continuously adjustable) determined by the phase shift

modulation of the laser output, dependent on the amplitude of the sinusoidal signal.

screws clamp the mirror holder tightly so that no inadvertent movement is possible.

Fig. 5. Homebuilt frequency stabilized CO2 laser model LIR-25 SF.

Fig. 6. Diffraction grating-drive mechanism.

To meet the frequency stability requirements, the laser cavity must be so constructed as to reduce the effects of ambient vibration and thermal variations on the output frequency of the laser. This places less stringent demands on the performance of the servo-system controlling the laser frequency. To minimize the thermal length changes (Δ*L*/*L* = αΔ*T*) in the mirror support structure, a material with a low expansion coefficient has to be used for the spacers between the endplates of the cavity which carry the mirrors. Such a material is Invar, which has an expansion coefficient α = 1.26x10-6/oC. To obtain a passive instability of 3x10-8 for the laser frequency, the temperature variation must not exceed 0.024oC. Such constant temperature is hard to maintain, especially in longer lasers, where high power inputs and high heat dissipation cause large temperature instabilities.

Stiffness is a most desirable attribute for minimizing fractional changes in the cavity length. Special measures were taken against mechanical vibrations (by eliminating high frequency vibrations), variations in the position of optical components (by supporting rigidly any intracavity element) as well as to prevent magnetic fields and acoustically borne vibrations, which can be reduced by shielding the laser with some form of enclosure. The design of the remaining structure was chosen so as to avoid the lowering of the basic first resonance. The joints between the elements of the structure, especially the joints perpendicular to the laser axis, were so designed that they did not have any low frequency resonances. To have a spring constant of the joint high enough and to avoid joints using only the spring force of a few screws to connect significant masses, we used large contact areas under compressional stress. We chose a cylindrical shape for the mechanical structure, including the housing, because of its high resistance to bending deformation. A section through the laser cavity assembly is given in Fig. 4 and a photo of the mechanical structure, laser tube, and control panel is presented in Fig. 5.

Fig. 4. Longitudinal section through the laser cavity assembly.

To keep the weight unchanged and still maintain the required thermal characteristics, the endplates of the cavity which carry the mirror and the diffraction grating were primarily constructed of aluminum. The three invar rods are potted into the aluminum frame so as to ensure intimate contact between the invar rods and the rigid aluminum structure. To remove the problems associated with weak spring-type controls, the mirror holders were designed

To meet the frequency stability requirements, the laser cavity must be so constructed as to reduce the effects of ambient vibration and thermal variations on the output frequency of the laser. This places less stringent demands on the performance of the servo-system

mirror support structure, a material with a low expansion coefficient has to be used for the spacers between the endplates of the cavity which carry the mirrors. Such a material is

3x10-8 for the laser frequency, the temperature variation must not exceed 0.024oC. Such constant temperature is hard to maintain, especially in longer lasers, where high power

Stiffness is a most desirable attribute for minimizing fractional changes in the cavity length. Special measures were taken against mechanical vibrations (by eliminating high frequency vibrations), variations in the position of optical components (by supporting rigidly any intracavity element) as well as to prevent magnetic fields and acoustically borne vibrations, which can be reduced by shielding the laser with some form of enclosure. The design of the remaining structure was chosen so as to avoid the lowering of the basic first resonance. The joints between the elements of the structure, especially the joints perpendicular to the laser axis, were so designed that they did not have any low frequency resonances. To have a spring constant of the joint high enough and to avoid joints using only the spring force of a few screws to connect significant masses, we used large contact areas under compressional stress. We chose a cylindrical shape for the mechanical structure, including the housing, because of its high resistance to bending deformation. A section through the laser cavity assembly is given in Fig. 4 and a photo of the mechanical structure, laser tube, and control

α

= 1.26x10-6/oC. To obtain a passive instability of

Δ*T*) in the

controlling the laser frequency. To minimize the thermal length changes (Δ*L*/*L* =

inputs and high heat dissipation cause large temperature instabilities.

Fig. 4. Longitudinal section through the laser cavity assembly.

To keep the weight unchanged and still maintain the required thermal characteristics, the endplates of the cavity which carry the mirror and the diffraction grating were primarily constructed of aluminum. The three invar rods are potted into the aluminum frame so as to ensure intimate contact between the invar rods and the rigid aluminum structure. To remove the problems associated with weak spring-type controls, the mirror holders were designed

α

Invar, which has an expansion coefficient

panel is presented in Fig. 5.

ruggedly. The mirrors can be adjusted in angle by sliding two stainless steel spherical joints with respect to one another. As the mirrors are adjusted into their final position, the adjustment screws clamp the mirror holder tightly so that no inadvertent movement is possible.

Fig. 5. Homebuilt frequency stabilized CO2 laser model LIR-25 SF.

The diffraction grating is mounted in a similar holder and is rotated by a micrometric screw (0 – 25 mm), as shown in Fig. 6. The laser tube was rigidly mounted in the cavity with two concentric rings, the inner one being adjusted by three screws. This system allows the laser tube axis to fall into line with the mirror centers and provides good transverse stability.

Fig. 6. Diffraction grating-drive mechanism.

To achieve active stabilization, an automatic frequency control circuit (lock-in stabilizer) is used to maintain an axial mode on the top of the gain curve. The block diagram of the frequency stabilization system based on plasma tube impedance variations is shown in Fig. 7. A sinusoidal signal with a rough frequency of 500 Hz derived from the pilot oscillator is applied to the piezoelectric transducer, resulting in a simultaneous frequency and amplitude modulation of the laser output, dependent on the amplitude of the sinusoidal signal.

The ac voltage drop across the tube is passed through a tuned amplifier and then synchronously detected. The demodulation of the ac signal is performed in the phasesensitive detector, with phase (continuously adjustable) determined by the phase shift

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 53

signal is introduced in the phase sensitive detector (PSD module) together with a phase

The error signal is obtained in the output of the electronic dc amplifier module DCA, by processing the output signal of the phase sensitive detector. The DCA module has two modes of operation, namely: (a) gain of ten amplifier with integrating time constant of 1 second; (b) high gain integrator with output slewing rate of about 6 V/s per volt of input. The first mode allows the observation of smoothed output of the demodulator (stabilization discriminator), while the second one is used in closed loop stabilization to observe the error signal. A high voltage amplifier (HVA) that works on the principle of a switching high voltage

The logic electronic system includes four specialized modules, namely: a low voltage stabilized power supply (SPS), a logic drive circuit (LDC), a power meter circuit for laser radiation (PMC), and a beam controller (BCS). Every parameter and state that are monitored or selected in the operation of the frequency stabilized CO2 laser LIR-25 SF are displayed on the rear panel of the laser (Fig. 5) by means of nine light emitting diodes (LED) driven by the panel display circuit (PDC). The output beam of the laser can be sent to either the powermeter head or the exit by a two-position reflecting mirror, controlled by a beam

power supply drives the piezoelectric transducer under the control of the error signal.

ν/ν

POWERMETER CO2 LASER

A supplementary power stabilization is possible by using an additional feedback loop (Dumitras et al., 2006). The principle used for power stabilization took into account the dependence of the output power on discharge current. The new feedback loop (Fig. 8) modifies the discharge current so to maintain the output power at a constant value imposed

The performance of the two feedback loops used for frequency and power stabilization of the CO2 laser were evaluated by using computer data acquisition. It was monitored simultaneously the output power, the discharge current and the temperature inside laser cavity, while the power instability was calculated for a period of 2 minutes. The importance of the two feedback loops to reduce the output power instability can be remarked from these measurements. Thus, when both the frequency stabilization loop and the power

COMPARATOR INTEGRATING AMPLIFIER

= 3x10-8 or Δ

ν

= 1 MHz (3x10-5 cm-1).

CURRENT CONTROLLED HV POWER SUPPLY

shutter circuit and a beam selector switch placed on the rear panel.

Fig. 8. Supplementary feedback loop used for laser power stabilization.

The long-term frequency instability was Δ

LASER

by the reference.

adjustable component of the reference signal from the modulation oscillator.

circuit. The demodulator output is processed by the operational integrator and a high voltage dc amplifier. The dc bias together with this error correction signal is applied to the piezoelectric transducer, thus closing the feedback loop. The error signal generated by the phase detector serves to drive the cavity resonance to the center of the laser gain curve and compensates for the effects of slow drift.

Fig. 7. Block-diagram of the automatic frequency control electronics.

There are fifteen functional modules grouped into three main blocks in accordance with the specific function they play in the operation of the frequency stabilized CO2 laser:


The high-speed current regulated power supply includes three modules namely: the power supply converter – PSC, the power supply feedback – PSF, and the power supply rectifier PSR. The high frequency of the converter makes it possible to minimize the electronic components that are used in making the high voltage transformer and the low pass filter of the high voltage rectifier.

The modulation signal that is needed to scan the laser line profile is generated by a pilot oscillator and applied to the piezoelectric transducer through a modulation amplifier. Both circuits are placed on the same functional module OMA (Oscillator & Modulation Amplifier). For cw CO2 lasers excited by current regulated power supplies, the modulation signal which appears in the emitted radiation can be measured according to the optovoltaic effect using a simple band pass filter like that noted with OVP (Optovoltaic Probe). The detected optovoltaic signal is amplified through a two-stage tuned ac amplifier – ACA. The amplified optovoltaic

circuit. The demodulator output is processed by the operational integrator and a high voltage dc amplifier. The dc bias together with this error correction signal is applied to the piezoelectric transducer, thus closing the feedback loop. The error signal generated by the phase detector serves to drive the cavity resonance to the center of the laser gain curve and

compensates for the effects of slow drift.

Fig. 7. Block-diagram of the automatic frequency control electronics.

the frequency stabilized CO2 operation.

the high voltage rectifier.

There are fifteen functional modules grouped into three main blocks in accordance with the

3. a logic electronic system which allows an efficient operative control and monitoring of

The high-speed current regulated power supply includes three modules namely: the power supply converter – PSC, the power supply feedback – PSF, and the power supply rectifier PSR. The high frequency of the converter makes it possible to minimize the electronic components that are used in making the high voltage transformer and the low pass filter of

The modulation signal that is needed to scan the laser line profile is generated by a pilot oscillator and applied to the piezoelectric transducer through a modulation amplifier. Both circuits are placed on the same functional module OMA (Oscillator & Modulation Amplifier). For cw CO2 lasers excited by current regulated power supplies, the modulation signal which appears in the emitted radiation can be measured according to the optovoltaic effect using a simple band pass filter like that noted with OVP (Optovoltaic Probe). The detected optovoltaic signal is amplified through a two-stage tuned ac amplifier – ACA. The amplified optovoltaic

specific function they play in the operation of the frequency stabilized CO2 laser:

2. a servo control system, which controls the length of the resonant cavity;

1. a high speed current regulated power supply, which excites the cw CO2 laser tube;

signal is introduced in the phase sensitive detector (PSD module) together with a phase adjustable component of the reference signal from the modulation oscillator.

The error signal is obtained in the output of the electronic dc amplifier module DCA, by processing the output signal of the phase sensitive detector. The DCA module has two modes of operation, namely: (a) gain of ten amplifier with integrating time constant of 1 second; (b) high gain integrator with output slewing rate of about 6 V/s per volt of input. The first mode allows the observation of smoothed output of the demodulator (stabilization discriminator), while the second one is used in closed loop stabilization to observe the error signal. A high voltage amplifier (HVA) that works on the principle of a switching high voltage power supply drives the piezoelectric transducer under the control of the error signal.

The logic electronic system includes four specialized modules, namely: a low voltage stabilized power supply (SPS), a logic drive circuit (LDC), a power meter circuit for laser radiation (PMC), and a beam controller (BCS). Every parameter and state that are monitored or selected in the operation of the frequency stabilized CO2 laser LIR-25 SF are displayed on the rear panel of the laser (Fig. 5) by means of nine light emitting diodes (LED) driven by the panel display circuit (PDC). The output beam of the laser can be sent to either the powermeter head or the exit by a two-position reflecting mirror, controlled by a beam shutter circuit and a beam selector switch placed on the rear panel.

The long-term frequency instability was Δν/ν = 3x10-8 or Δν= 1 MHz (3x10-5 cm-1).

A supplementary power stabilization is possible by using an additional feedback loop (Dumitras et al., 2006). The principle used for power stabilization took into account the dependence of the output power on discharge current. The new feedback loop (Fig. 8) modifies the discharge current so to maintain the output power at a constant value imposed by the reference.

Fig. 8. Supplementary feedback loop used for laser power stabilization.

The performance of the two feedback loops used for frequency and power stabilization of the CO2 laser were evaluated by using computer data acquisition. It was monitored simultaneously the output power, the discharge current and the temperature inside laser cavity, while the power instability was calculated for a period of 2 minutes. The importance of the two feedback loops to reduce the output power instability can be remarked from these measurements. Thus, when both the frequency stabilization loop and the power

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 55

To investigate the possibility of using a high power laser in an extracavity configuration, we introduced in the experimental set-up a commercial CO2 laser (Coherent GEM SELECT 50TM laser) (Fig. 10) with output power till 50 W and tunable on 73 different lines (Fig. 11). When this laser is tuned on 10P(14) line, the maximum power delivered after chopper and

Fig. 11. Tunability of the high power CO2 laser with diffraction grating: P(max) = 50 W; Tunability: 9R(8) – 9R(40); 9P(4) – 9P(46); 10R(6) – 10R(36); 10P(6) – 10P(40); No. of lines: 73

9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0

10R(24) 10R(30) 10R(28) 10R(34) 10R(36)

10R(18) 10R(16) 10R(12)

10R(10)

10R(8)

10R(6)

10P(6)

10P(8) 10P(10) 10P(12)

10P(14) 10P(16) 10P(18)

10P(22)

10P(26)

10P(28) 10P(30) 10P(32)

10P(34)

10P(36) 10P(38)

10P(40)

Wavelength (μm)

In the literature the PA cells are often characterized as "nonresonant" or "resonant". This terminology is misleading, because any PA cell can be operated at an acoustic resonance or far from its resonance. Thus, it is preferable to label the system in terms of its nonresonant or

To design an optimum acoustically resonant PA cell to be used in CO2 laser photoacoustic

i. the fraction of laser energy absorbed by the gas must be maximized by increasing either the incident laser power (but maintaining a large SNR) or the optical density of the gas

ii. cell responsivity needs to be as high as possible, because the voltage response is

iii. the microphone responsivity has to be as high as possible, and the use of many

iv. the design must make it possible to operate the cell at an acoustic resonance, and the resonance frequency must lie between 400 and 1000 Hz, where the microphone noise is

v. the quality factor *Q* of the acoustic resonance must not exceed 50 in order to decrease

focusing lens is 14.5 W.

**COHERENT**

9P(22)

9P(12)

9P(10)

9P(6)

9P(4)

9R(12) 9R(10)

9R(14) 9R(18)

9R(20)9R(24)

9R(30) 9R(32) 9R(36)

9R(40)

9R(8)

9P(16)

9P(26)

9P(28)

9P(34)

9P(36) 9P(38) 9P(40) 9P(42) 9P(44)

(10P(14):

0

10

20

30

Power (W)

40

50

λ

**2.3 Photoacoustic cell** 

resonant mode of operation.

(Eq. 2, Part I);

minimal;

= 10.53 µm; 9R(30):

proportional to it (Eq. 29, Part I);

λ

spectroscopy, the following requirements have to be met:

microphones is advisable (Eqs. 30 and 31, Part I);

the influence of small deviations from the resonance frequency;

= 9.22 µm).

9P(46)

stabilization loop are opened and forced hot air perturbation is introduced, the power instability is 10.2%, a value too large for many applications; when the frequency stabilization loop is closed and the power stabilization loop is opened (no perturbation), the power instability is reduced to 1.06%; when the frequency stabilization loop is closed and the power stabilization loop is opened and forced hot air perturbation is introduced into laser cavity, the power instability increases only a little, to 1.57%; and when both the frequency stabilization loop and the power stabilization loop are closed and forced hot air perturbation is introduced, the power instability is reduced drastically, to 0.28%. If there is no perturbation and the two feedback loops are closed, the power instability is only 0.23%. In conclusion, the power instability was reduced by four times with this supplementary feedback loop, from 1% to as low as 0.23% for a period of 2 minutes.

The tunability of our CO2 laser is presented in Fig. 9. We observed the oscillation of 62 different vibrational-rotational lines in both the 10.4 μm and 9.4 μm bands. In this way, the laser was line tunable between 9.2 μm and 10.8 μm with powers varying between 1 and 6.5 W depending on the emitted laser transition. More than 20 lines had output powers in excess of 5 W.

Fig. 9. Tunability of the low power CO2 laser with diffraction grating: P(max) = 6.5 W; Tunability: 9R(8) – 9R(34); 9P(8) – 9P(36); 10R(6) – 10R(36); 10P(6) – 10P(40); No. of lines: 62.

Fig. 10. Coherent GEM SELECT 50TM CO2 laser in the experimental setup.

To investigate the possibility of using a high power laser in an extracavity configuration, we introduced in the experimental set-up a commercial CO2 laser (Coherent GEM SELECT 50TM laser) (Fig. 10) with output power till 50 W and tunable on 73 different lines (Fig. 11). When this laser is tuned on 10P(14) line, the maximum power delivered after chopper and focusing lens is 14.5 W.

Fig. 11. Tunability of the high power CO2 laser with diffraction grating: P(max) = 50 W; Tunability: 9R(8) – 9R(40); 9P(4) – 9P(46); 10R(6) – 10R(36); 10P(6) – 10P(40); No. of lines: 73 (10P(14): λ = 10.53 µm; 9R(30): λ= 9.22 µm).

#### **2.3 Photoacoustic cell**

54 CO2 Laser – Optimisation and Application

stabilization loop are opened and forced hot air perturbation is introduced, the power instability is 10.2%, a value too large for many applications; when the frequency stabilization loop is closed and the power stabilization loop is opened (no perturbation), the power instability is reduced to 1.06%; when the frequency stabilization loop is closed and the power stabilization loop is opened and forced hot air perturbation is introduced into laser cavity, the power instability increases only a little, to 1.57%; and when both the frequency stabilization loop and the power stabilization loop are closed and forced hot air perturbation is introduced, the power instability is reduced drastically, to 0.28%. If there is no perturbation and the two feedback loops are closed, the power instability is only 0.23%. In conclusion, the power instability was reduced by four times with this supplementary

The tunability of our CO2 laser is presented in Fig. 9. We observed the oscillation of 62 different vibrational-rotational lines in both the 10.4 μm and 9.4 μm bands. In this way, the laser was line tunable between 9.2 μm and 10.8 μm with powers varying between 1 and 6.5 W depending on

the emitted laser transition. More than 20 lines had output powers in excess of 5 W.

Fig. 9. Tunability of the low power CO2 laser with diffraction grating: P(max) = 6.5 W; Tunability: 9R(8) – 9R(34); 9P(8) – 9P(36); 10R(6) – 10R(36); 10P(6) – 10P(40); No. of lines: 62.

9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8

Wavelength (μm)

10P(30)

10P(26)

10P(20)

10P(14)

10P(10)

10P(8)

10P(6)

10R(6)

10R(8) 10R(10)

10R(14)

10R(18)

10R(24)

10R(28)

10R(32)

10R(34)

10R(36)

10P(38)

10P(36)

10P(34) 10P(32)

Fig. 10. Coherent GEM SELECT 50TM CO2 laser in the experimental setup.

feedback loop, from 1% to as low as 0.23% for a period of 2 minutes.

9P(36) 9P(34)

9P(32)

9P(28)

9P(22)

9P(16)

9P(12)

No. 2 **LIR 25 SF**

9R(12)

9R(16)

9R(24)

9R(26)

9R(28)

9R(10)

9R(8)

9R(30)

9R(34)

9R(32)

9P(8)

Power (W)

In the literature the PA cells are often characterized as "nonresonant" or "resonant". This terminology is misleading, because any PA cell can be operated at an acoustic resonance or far from its resonance. Thus, it is preferable to label the system in terms of its nonresonant or resonant mode of operation.

To design an optimum acoustically resonant PA cell to be used in CO2 laser photoacoustic spectroscopy, the following requirements have to be met:


CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 57

Following these guidelines, a PA cell was designed, constructed, and tested. An H-type cylindrical cell designed for resonant photoacoustic spectroscopy in gases is shown in Fig. 12. The longitudinal resonant cell is a cylinder with microphones located at the loop position of the first longitudinal mode (the maximum pressure amplitude). Some general considerations imply that the coherent photoacoustic background signal caused by window heating is decreased if the beam enters the cell at the pressure nodes of the resonance. The advantage of mounting the windows at the pressure nodes is well demonstrated, and the window heating signal is decreased by the *Q* factor. The laser beam enters and exits the cell at the Brewster angle. It is more advantageous to have the beam pass through the windows

Fig. 12. Schematic of the PA cell designed for the first longitudinal resonance mode.

reflection, but also to obtain a noncorrosive surface to withstand aggressive gases.

The influence of scattered light onto the PA background signal can be minimized by using a highly reflecting polished material, with a good thermally conducting substrate. Bijnen et al. (Bijnen et al., 1996) investigated different materials for the resonant tube and found that the background signal decreased for polished stainless steel, polished brass, and polished, goldcoated copper in a ratio of 6:2:1, respectively. In the case of the CO2 laser, the best performance was obtained by employing a copper tube with a polished gold coating as resonator material. Because of the excellent heat-conducting properties, the absorbed heat can be quickly dispersed in the copper tube. The gold coating was used not only to optimize laser radiation

Many polar compounds (e.g. ammonia) are highly adsorptive and produce an error in real time concentration measurements by adhering to the detector surfaces. These molecules interact strongly with most metals and many insulating materials. Ammonia is a good model compound for these molecules as it shows the characteristic adsorptive behavior that is not a health hazard at low concentrations. The rate of ammonia adsorption on the gas handling surfaces depends on the surface material and temperature, and on the mixture concentration, flow rate, and pressure. Comparing the ammonia results with those for ethylene, which interacts weakly with most surfaces, provides a measure of the cell-sample interaction. Beck (Beck, 1985) evaluated the suitability of several surface materials for minimizing sample adsorption loss. Four materials–304 stainless steel, gold, paraffin wax, and Teflon–were tested using ammonia as a sample. The results show that both metals interact strongly with the sample. Teflon coating (thickness <25 μm) was found to provide accurate real time response for ammonia sample flows. Also, no signal decay is observed following flow termination. Additionally, the coatings must not degrade the acoustic response of the cell. The Teflon coating actually increases the cell *Q* by a small amount (1 percent). This is attributed to the smooth slick surface obtained by Teflon coating which

*<sup>B</sup>* is nearly constant over a wide range of wavelengths, and

*<sup>B</sup>* with wavelength can be tolerated since reflectivity increases very slowly for

at the Brewster angle (

small deviations from

θ

variations of

θ*B*), as θ

θ*B*.


Various ways to design (cylindrical geometry, H geometry, T geometry, or using a Helmholtz resonator) and operate (longitudinal, azimuthal, radial, or Helmholtz resonances) resonant PA cells have been studied (Zharov & Letokhov, 1986). Furthermore, PA cells for multipass (Koch & Lahmann, 1978; Nägele & Sigrist, 2000) or intracavity operation (Fung & Lin, 1986; Harren et al., 1990a) were designed. The effect of window heating in the amplitude modulation schemes has been minimized by introducing acoustic baffles (Dewey, 1977), developing windowless cells (Gerlach & Amer, 1980; Miklos & Lörincz, 1989; Angeli et al., 1992), or using tunable air columns (Bijnen et al., 1996). In many cases the window-heating signal can be markedly reduced by positioning the entrance and exit of the light beam at nodes of the mode being excited.

A cylindrical cell operated at a radial resonance and having Brewster windows mounted at the pressure nodes of the first radial mode, as presented by Gerlach and Amer (Gerlach & Amer, 1980), does not fulfill all these requirements. Therefore, an open resonant cell excited in its first longitudinal acoustic mode was developed to fulfill most of these requirements.

The H-type longitudinally resonant cell was chosen to form the core of our measuring instrument. Dividing the PA cell into a central chamber and two buffer chambers adjacent to the Brewster windows, a design which lowered significantly the coherent photoacoustic background noise, was first proposed by Tonelli et al. (Tonelli et al., 1983). The characteristics of this type of PA cell have been discussed by Nodov (Nodov, 1978), Kritchman et al. (Kritchman et al., 1978), and Harren et al. (Harren et al., 1990a). Its main advantages are: (a) stable operation at a relatively low frequency; a quality factor of about 20, i.e., much lower than that of a radial resonator, which makes it less sensitive to environmental changes; the efficient conversion of radial to longitudinal modes and the relatively long wavelength guarantee a sufficiently high photoacoustic amplitude; (b) a longitudinal resonator is not noticeably influenced by the gas flow at the desired flow rate of several L/h; noise by gas flow phenomena is negligible for properly positioned inlet and outlet ports; (c) window noise is minimal if the windows are located at a quarter wavelength from the ends of the resonator tube; (d) the construction is rugged and simple and can be achieved with low adhesion materials.

vi. the electrical noise and the coherent acoustic background noise must be as low as possible; this can be done by using low noise microphones, good acoustic and vibration isolation, low noise electronics, and good electronic isolation (no ground loops, proper shielding); vii. the coherent photoacoustic background signal due to the heating of the walls and windows must be minimized by using optical components of very high quality and

viii. the cell must enable continuous gas flow operation, and consequently not only the cell windows, but also the gas inlets and outlets have to be positioned at pressure nodes of

ix. the cell must have low gas consumption and fast response, and the cell volume has to be sufficiently small to prevent prohibitive dilution when the produced trace gas is

x. the adsorption and desorption rates on the surfaces in direct contact with the sample gas that can influence particularly measurements on sealed-off samples must be minimized by using special cell materials and reducing the surface-to-volume ratio; xi. the effect of the loss mechanisms which we can control must be minimized by an

Various ways to design (cylindrical geometry, H geometry, T geometry, or using a Helmholtz resonator) and operate (longitudinal, azimuthal, radial, or Helmholtz resonances) resonant PA cells have been studied (Zharov & Letokhov, 1986). Furthermore, PA cells for multipass (Koch & Lahmann, 1978; Nägele & Sigrist, 2000) or intracavity operation (Fung & Lin, 1986; Harren et al., 1990a) were designed. The effect of window heating in the amplitude modulation schemes has been minimized by introducing acoustic baffles (Dewey, 1977), developing windowless cells (Gerlach & Amer, 1980; Miklos & Lörincz, 1989; Angeli et al., 1992), or using tunable air columns (Bijnen et al., 1996). In many cases the window-heating signal can be markedly reduced by positioning the entrance and

A cylindrical cell operated at a radial resonance and having Brewster windows mounted at the pressure nodes of the first radial mode, as presented by Gerlach and Amer (Gerlach & Amer, 1980), does not fulfill all these requirements. Therefore, an open resonant cell excited in its first longitudinal acoustic mode was developed to fulfill most of these requirements. The H-type longitudinally resonant cell was chosen to form the core of our measuring instrument. Dividing the PA cell into a central chamber and two buffer chambers adjacent to the Brewster windows, a design which lowered significantly the coherent photoacoustic background noise, was first proposed by Tonelli et al. (Tonelli et al., 1983). The characteristics of this type of PA cell have been discussed by Nodov (Nodov, 1978), Kritchman et al. (Kritchman et al., 1978), and Harren et al. (Harren et al., 1990a). Its main advantages are: (a) stable operation at a relatively low frequency; a quality factor of about 20, i.e., much lower than that of a radial resonator, which makes it less sensitive to environmental changes; the efficient conversion of radial to longitudinal modes and the relatively long wavelength guarantee a sufficiently high photoacoustic amplitude; (b) a longitudinal resonator is not noticeably influenced by the gas flow at the desired flow rate of several L/h; noise by gas flow phenomena is negligible for properly positioned inlet and outlet ports; (c) window noise is minimal if the windows are located at a quarter wavelength from the ends of the resonator tube; (d) the construction is rugged and simple and can be

flowed through the cell volume by a continuous gas stream;

exit of the light beam at nodes of the mode being excited.

introducing acoustic baffles;

appropriate system design.

achieved with low adhesion materials.

the resonance;

Following these guidelines, a PA cell was designed, constructed, and tested. An H-type cylindrical cell designed for resonant photoacoustic spectroscopy in gases is shown in Fig. 12. The longitudinal resonant cell is a cylinder with microphones located at the loop position of the first longitudinal mode (the maximum pressure amplitude). Some general considerations imply that the coherent photoacoustic background signal caused by window heating is decreased if the beam enters the cell at the pressure nodes of the resonance. The advantage of mounting the windows at the pressure nodes is well demonstrated, and the window heating signal is decreased by the *Q* factor. The laser beam enters and exits the cell at the Brewster angle. It is more advantageous to have the beam pass through the windows at the Brewster angle (θ*B*), as θ*<sup>B</sup>* is nearly constant over a wide range of wavelengths, and variations of θ*<sup>B</sup>* with wavelength can be tolerated since reflectivity increases very slowly for small deviations from θ*B*.

Fig. 12. Schematic of the PA cell designed for the first longitudinal resonance mode.

The influence of scattered light onto the PA background signal can be minimized by using a highly reflecting polished material, with a good thermally conducting substrate. Bijnen et al. (Bijnen et al., 1996) investigated different materials for the resonant tube and found that the background signal decreased for polished stainless steel, polished brass, and polished, goldcoated copper in a ratio of 6:2:1, respectively. In the case of the CO2 laser, the best performance was obtained by employing a copper tube with a polished gold coating as resonator material. Because of the excellent heat-conducting properties, the absorbed heat can be quickly dispersed in the copper tube. The gold coating was used not only to optimize laser radiation reflection, but also to obtain a noncorrosive surface to withstand aggressive gases.

Many polar compounds (e.g. ammonia) are highly adsorptive and produce an error in real time concentration measurements by adhering to the detector surfaces. These molecules interact strongly with most metals and many insulating materials. Ammonia is a good model compound for these molecules as it shows the characteristic adsorptive behavior that is not a health hazard at low concentrations. The rate of ammonia adsorption on the gas handling surfaces depends on the surface material and temperature, and on the mixture concentration, flow rate, and pressure. Comparing the ammonia results with those for ethylene, which interacts weakly with most surfaces, provides a measure of the cell-sample interaction. Beck (Beck, 1985) evaluated the suitability of several surface materials for minimizing sample adsorption loss. Four materials–304 stainless steel, gold, paraffin wax, and Teflon–were tested using ammonia as a sample. The results show that both metals interact strongly with the sample. Teflon coating (thickness <25 μm) was found to provide accurate real time response for ammonia sample flows. Also, no signal decay is observed following flow termination. Additionally, the coatings must not degrade the acoustic response of the cell. The Teflon coating actually increases the cell *Q* by a small amount (1 percent). This is attributed to the smooth slick surface obtained by Teflon coating which

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 59

large for optimal operation. A practical radius can be deduced to be *rbuf* ≈ 3*r*. The gas absorption amplitude is barely influenced above this value. A small radius for the resonator of the resonant cell is advantageous as it enhances gas absorption. The limit for the resonator radius is mainly determined by the wings of the gaussian laser beam profile hitting the wall; *r* should roughly be at least three times the radius of the laser beam to

Our PA cell design, based on the above considerations, is shown in Fig. 13 in cross sectional longitudinal view. The PA cell is made of stainless steel and Teflon to reduce the outgassing problems and consists of an acoustic resonator (pipe), windows, gas inlets and outlets, and microphones. It also contains an acoustic filter to suppress the flow and window noise. ZnSe windows at the Brewster angle are glued with epoxy (Torr-Seal) to their respective mounts. The resonant conditions are obtained as longitudinal standing waves in an open tube (resonator) are placed coaxially inside a larger chamber. We use an open end tube type of resonator, excited in its first longitudinal mode. To achieve a larger signal (eqs. 26 and 27, Part I), we chose a long absorption path length (*L* = 300 mm) and an inner diameter of the pipe of 2*r* = 7 mm (*r* ≅ 1.5*w*5, see Fig. 2). The fundamental longitudinal wave, therefore, has a

wavelength is ∼1% longer than the nominal value, in accordance with predictions of Eq. (5, Part I). The two buffer volumes placed near the Brewster windows have a length *Lbuf* = 75

The total cell volume is approximately 1.0 dm3 (total length 450 mm, and inner diameter 57 mm, minus inner mechanical parts). For flowing conditions, however, it is advantageous to reduce the active volume of the cell. Especially if the flow rate is smaller than 1 L/h (16.6

/8) and a diameter 2*rbuf* = 57 mm (*rbuf* ≅ 8*r*). The inner wall of the stainless steel resonator tube is polished. It is centered inside the outer stainless steel tube with Teflon spacers. A massive spacer is positioned at one end to prevent bypassing of gas in the flow system; the other is partially open to avoid the formation of closed volumes. Gas is admitted and exhausted through two ports located near the ends of the resonator tube. The perturbation of the acoustic resonator amplitude by the gas flow noise is thus minimized.

*<sup>s</sup>* = 2*L* = 600 mm (and a resonance frequency *f*0 = 564 Hz). The effective

reduce wall absorption to an acceptable level.

λ

Fig. 13. A resonant photoacoustic cell with buffer volumes.

nominal wavelength

mm (λ

would decrease any surface frictional or scattering loss of acoustic energy. Rooth et al. (Rooth et al., 1990) tested the following wall materials – stainless steel 304, gold (on Nicoated stainless steel), Teflon PTFE, and Teflon PFA – in contact with the gas. Stainless steel proved to be an almost unsaturable reservoir for ammonia at pptV levels. The number of stored molecules exceeded by a factor of 10 or more the number of potential locations on the total geometric surface. Despite its inferior properties in terms of adsorption, Olafsson et al. (Olafsson et al., 1989) used a stainless steel cell for detecting NH3 and found that an operating temperature of 100oC combined with water vapors led to a very significant reduction of NH3 adsorption. Apparently, the water molecules stick to the walls even more efficiently than NH3, and the cell walls are effectively coated with water. Later on, the sample cell was constructed with Teflon as wall material (Olafsson et al., 1992).

Since an open pipe efficiently picks up and amplifies noise from the environment, it should be surrounded by an enclosure. In order to ensure high acoustic reflections at the pipe ends, a sudden change of the cross section is necessary. Therefore, the resonator pipe should open up into a larger volume or to buffers with a much larger cross section. The buffers can be optimized to minimize flow noise and/or window signals. The length of the two buffers accounting for half the resonator length is chosen such as to minimize the acoustic background signal originating from absorption by the ZnSe windows. Open pipes were introduced for PA detection as early as 1977 (Zharov & Letokhov, 1986), and the most sensitive PA detectors currently used are based on open resonant pipes. In resonant cells, window signals can be diminished by using λ/4 buffers next to the windows. These buffers, placed perpendicular to the resonator axis near the windows, are tuned to the resonator frequency and act as interference filters for the window signals (the coupling of the window signals into the resonator is reduced by large buffer volumes that act as interference dampers).

It was found both theoretically and experimentally that the signal amplitude decreases drastically when buffer length *Lbuf* < λ/8 (Bijnen et al., 1996); the resonance frequency and the quality factor, for both the window and gas signals, are not much affected by changing the buffer length. The length of the buffer is optimal for window signal suppression when *L* = 2*Lbuf* (*L* >> *r*) (*L* and *r* stand for resonator length and radius). The dependence of the gas absorption *pg* and window absorption pressure *pw* on the ratio of the buffer and resonator radii is:

$$p\_s \approx \frac{\sqrt{L}}{r} \left(1 - \frac{r^2}{r\_{buf}^2}\right) \tag{1}$$

$$p\_w \approx \frac{r}{r\_{bw}\sqrt{L}} \,\tag{2}$$

The ratio between the gas absorption signal and window signal then becomes:

$$\frac{p\_g}{p\_w} \approx \left(\frac{r\_{bw}}{r}\right)^2 L. \tag{3}$$

The optimal buffer length, resulting in an optimal suppression of the photoacoustic background signal, is λ/4. Choosing a buffer length of λ/8 has the advantage of a shorter cell, and a good, though not optimal, suppression of the window signal is still possible in this case. If the volume and overall size of the buffers pose no problem, their radii have to be

would decrease any surface frictional or scattering loss of acoustic energy. Rooth et al. (Rooth et al., 1990) tested the following wall materials – stainless steel 304, gold (on Nicoated stainless steel), Teflon PTFE, and Teflon PFA – in contact with the gas. Stainless steel proved to be an almost unsaturable reservoir for ammonia at pptV levels. The number of stored molecules exceeded by a factor of 10 or more the number of potential locations on the total geometric surface. Despite its inferior properties in terms of adsorption, Olafsson et al. (Olafsson et al., 1989) used a stainless steel cell for detecting NH3 and found that an operating temperature of 100oC combined with water vapors led to a very significant reduction of NH3 adsorption. Apparently, the water molecules stick to the walls even more efficiently than NH3, and the cell walls are effectively coated with water. Later on, the

Since an open pipe efficiently picks up and amplifies noise from the environment, it should be surrounded by an enclosure. In order to ensure high acoustic reflections at the pipe ends, a sudden change of the cross section is necessary. Therefore, the resonator pipe should open up into a larger volume or to buffers with a much larger cross section. The buffers can be optimized to minimize flow noise and/or window signals. The length of the two buffers accounting for half the resonator length is chosen such as to minimize the acoustic background signal originating from absorption by the ZnSe windows. Open pipes were introduced for PA detection as early as 1977 (Zharov & Letokhov, 1986), and the most sensitive PA detectors currently used are based on open resonant pipes. In resonant cells,

λ

placed perpendicular to the resonator axis near the windows, are tuned to the resonator frequency and act as interference filters for the window signals (the coupling of the window signals into the resonator is reduced by large buffer volumes that act as interference dampers). It was found both theoretically and experimentally that the signal amplitude decreases

quality factor, for both the window and gas signals, are not much affected by changing the buffer length. The length of the buffer is optimal for window signal suppression when *L* = 2*Lbuf* (*L* >> *r*) (*L* and *r* stand for resonator length and radius). The dependence of the gas absorption

<sup>2</sup> 1 *<sup>g</sup>*

*L r*

*r r* ∝ − 

> *buf r*

*g buf*

*p r <sup>L</sup> p r* <sup>∝</sup> 

The optimal buffer length, resulting in an optimal suppression of the photoacoustic

cell, and a good, though not optimal, suppression of the window signal is still possible in this case. If the volume and overall size of the buffers pose no problem, their radii have to be

2

*buf*

2

λ

*pg* and window absorption pressure *pw* on the ratio of the buffer and resonator radii is:

*w*

The ratio between the gas absorption signal and window signal then becomes:

*w*

/4. Choosing a buffer length of

/4 buffers next to the windows. These buffers,

, (1)

. (3)

/8 has the advantage of a shorter

/8 (Bijnen et al., 1996); the resonance frequency and the

*<sup>p</sup> r L* <sup>∝</sup> . (2)

sample cell was constructed with Teflon as wall material (Olafsson et al., 1992).

λ

*p*

window signals can be diminished by using

drastically when buffer length *Lbuf* <

background signal, is

λ

large for optimal operation. A practical radius can be deduced to be *rbuf* ≈ 3*r*. The gas absorption amplitude is barely influenced above this value. A small radius for the resonator of the resonant cell is advantageous as it enhances gas absorption. The limit for the resonator radius is mainly determined by the wings of the gaussian laser beam profile hitting the wall; *r* should roughly be at least three times the radius of the laser beam to reduce wall absorption to an acceptable level.

Our PA cell design, based on the above considerations, is shown in Fig. 13 in cross sectional longitudinal view. The PA cell is made of stainless steel and Teflon to reduce the outgassing problems and consists of an acoustic resonator (pipe), windows, gas inlets and outlets, and microphones. It also contains an acoustic filter to suppress the flow and window noise. ZnSe windows at the Brewster angle are glued with epoxy (Torr-Seal) to their respective mounts. The resonant conditions are obtained as longitudinal standing waves in an open tube (resonator) are placed coaxially inside a larger chamber. We use an open end tube type of resonator, excited in its first longitudinal mode. To achieve a larger signal (eqs. 26 and 27, Part I), we chose a long absorption path length (*L* = 300 mm) and an inner diameter of the pipe of 2*r* = 7 mm (*r* ≅ 1.5*w*5, see Fig. 2). The fundamental longitudinal wave, therefore, has a nominal wavelength λ*<sup>s</sup>* = 2*L* = 600 mm (and a resonance frequency *f*0 = 564 Hz). The effective wavelength is ∼1% longer than the nominal value, in accordance with predictions of Eq. (5, Part I). The two buffer volumes placed near the Brewster windows have a length *Lbuf* = 75 mm (λ/8) and a diameter 2*rbuf* = 57 mm (*rbuf* ≅ 8*r*). The inner wall of the stainless steel resonator tube is polished. It is centered inside the outer stainless steel tube with Teflon spacers. A massive spacer is positioned at one end to prevent bypassing of gas in the flow system; the other is partially open to avoid the formation of closed volumes. Gas is admitted and exhausted through two ports located near the ends of the resonator tube. The perturbation of the acoustic resonator amplitude by the gas flow noise is thus minimized.

Fig. 13. A resonant photoacoustic cell with buffer volumes.

The total cell volume is approximately 1.0 dm3 (total length 450 mm, and inner diameter 57 mm, minus inner mechanical parts). For flowing conditions, however, it is advantageous to reduce the active volume of the cell. Especially if the flow rate is smaller than 1 L/h (16.6

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 61

frequency of the laser modulation or the cell resonance itself were to shift by a few hertz. PA cells exhibiting narrow resonances (as in the case of excitation of the radial modes) require tight control of both temperature and laser modulation frequency to avoid responsivity

9 Cell 2

547 582

564

The acoustic resonator is characterized by the quality factor *Q*, which is defined as the ratio of the resonance frequency to the frequency bandwidth between half power points. The amplitude of the microphone signal is 1/ 2 of the maximum amplitude at these points, because the energy of the standing wave is proportional to the square of the induced pressure. The quality factor was measured by filling the PA cell with 1 ppmV of ethylene buffered in nitrogen at a total pressure of 1 atm and by tuning the modulation frequency in 10 Hz increments (2 Hz increments near the top of the curve) across the resonance profile to estimate the half width, as described above. For this PA cell, the profile width at half intensity was 35 Hz, yielding a quality factor *Q* = 16.1 (Eq. 15, Part I) at a resonance frequency *f*0 = 564 Hz. The experimentally determined resonance is not completely symmetric, as the curve rises steeply on one side and becomes less steep on the other side of the maximum. This asymmetry is caused by a coherent superposition of the standing

500 520 540 560 580 600 620 640 660

Chopper frequency *f* (Hz)

acoustic waves in the detection region of the microphones (Karbach & Hess, 1985).

ν

The calibration of the PA system is usually performed with a reference gas. We calibrated our PA cell with the widely used reference gas ethylene, whose absorption coefficients are accurately known at CO2-laser wavelengths. Ethylene is well suited for this purpose, since it interacts only weakly with common cell surface materials. Ethylene is chemically inert, has the same molecular weight as nitrogen and possesses no permanent dipole moment which means negligible adsorption on the cell walls. Furthermore, its spectrum within the CO2 laser wavelength range is highly structured. In particular it exhibits a characteristic absorption peak at the 10P(14) laser transition at 949.49 cm-1 which is caused by the

commercially prepared, certified mixture containing 0.96 ppmV C2H4 in pure nitrogen throughout our investigations. For calibration we examined this reference mixture at a total pressure *p* of approximately 1013 mbar and a temperature *T* ≅ 23oC and using the commonly accepted value of the absorption coefficient of 30.4 cm-1atm-1 at the 10P(14) line of the 12C16O2 laser. For shorter time intervals (by changing the calibration gas mixture after a careful vacuum cleaning of the PA cell), the variation of the cell constant was smaller than

7 vibration of C2H4 centered at 948.7715 cm-1. We used a

Fig. 15. Resonance curve for the first longitudinal mode of the PA cell.

PA signal *V* (mV)

losses during the experiment.

proximity of the Q branch of the

sccm - standard cubic centimeters per minute), the replenish time for the 1.0 dm3 cell becomes impractical. The buffer volume at the entrance port of the cell affects the renewal time τ considerably. The buffer volume is approximately 200 cm3, yielding a time constant of 12 min (τ = *V*/*Rflow* = (200 cm3)/(16.6 cm3/min) = 12 min). By reducing the buffer volume to 24 cm3, with *rbuf* ≅ 3*r* (diameter 20 mm, length 75 mm), a τ of 1.5 min is obtained. However, an increased acoustical noise level was observed, due to the gas flow.

In photoacoustic measurements in the gas phase, microphones are usually employed as sensing elements of the acoustic waves generated by the heat deposition of the absorbing molecules. Although high-quality condenser microphones offer the best noise performance, they are rarely used in photoacoustic gas detection because of their large size, lower robustness, and relatively high price. The most common microphones employed are miniature electret devices originally developed as hearing aids. The choice of a miniature microphone is particularly advantageous since it can be readily incorporated in the resonant cavity without significantly degrading the *Q* of the resonance. The frequency response of electret microphones extends beyond 10 kHz, and the response to incident pressure waves is linear over many orders of magnitude.

In our PA cells there are four Knowles electret EK-3033 or EK-23024 miniature microphones in series (sensitivity 20 mV/Pa each at 564 Hz) mounted flush with the wall. They are situated at the loops of the standing wave pattern, at an angle of 90o to one another. The microphones are coupled to the resonator by holes (1 mm diameter) positioned on the central perimeter of the resonator. The battery-powered microphones are mounted in a Teflon ring pulled over the resonator tube (Fig. 14). It is of significant importance to prevent gas leakage from inside the resonator tube along the Teflon microphone holder, since minute spacing between the holder and resonator tube produces a dramatic decrease of the microphone signal and the *Q* value. The electrical output from these microphones is summed and the signal is selectively amplified by a two-phase lock-in amplifier tuned to the chopper frequency.

Fig. 14. Teflon rings used to mount the microphones flush with the tube wall.

The resonance curve of our PA cell (cell response in rms volts) was recorded as a function of laser beam chopping frequency and the results are plotted in Fig. 15. An accurate method is to construct the resonance curve point by point. In this case, the acoustic signal is measured at different fixed frequencies thus avoiding potential problems arising from the slow formation of a steady state standing wave in the resonator and the finite time resolution of the lock-in amplifier. It is evident from these data that the cell resonance curve is fairly broad, implying that the absorption measurements would not be considerably affected if the

sccm - standard cubic centimeters per minute), the replenish time for the 1.0 dm3 cell becomes impractical. The buffer volume at the entrance port of the cell affects the renewal

In photoacoustic measurements in the gas phase, microphones are usually employed as sensing elements of the acoustic waves generated by the heat deposition of the absorbing molecules. Although high-quality condenser microphones offer the best noise performance, they are rarely used in photoacoustic gas detection because of their large size, lower robustness, and relatively high price. The most common microphones employed are miniature electret devices originally developed as hearing aids. The choice of a miniature microphone is particularly advantageous since it can be readily incorporated in the resonant cavity without significantly degrading the *Q* of the resonance. The frequency response of electret microphones extends beyond 10 kHz, and the response to incident pressure waves is

In our PA cells there are four Knowles electret EK-3033 or EK-23024 miniature microphones in series (sensitivity 20 mV/Pa each at 564 Hz) mounted flush with the wall. They are situated at the loops of the standing wave pattern, at an angle of 90o to one another. The microphones are coupled to the resonator by holes (1 mm diameter) positioned on the central perimeter of the resonator. The battery-powered microphones are mounted in a Teflon ring pulled over the resonator tube (Fig. 14). It is of significant importance to prevent gas leakage from inside the resonator tube along the Teflon microphone holder, since minute spacing between the holder and resonator tube produces a dramatic decrease of the microphone signal and the *Q* value. The electrical output from these microphones is summed and the signal is selectively amplified by a two-phase lock-in amplifier tuned to the

Fig. 14. Teflon rings used to mount the microphones flush with the tube wall.

The resonance curve of our PA cell (cell response in rms volts) was recorded as a function of laser beam chopping frequency and the results are plotted in Fig. 15. An accurate method is to construct the resonance curve point by point. In this case, the acoustic signal is measured at different fixed frequencies thus avoiding potential problems arising from the slow formation of a steady state standing wave in the resonator and the finite time resolution of the lock-in amplifier. It is evident from these data that the cell resonance curve is fairly broad, implying that the absorption measurements would not be considerably affected if the

24 cm3, with *rbuf* ≅ 3*r* (diameter 20 mm, length 75 mm), a

linear over many orders of magnitude.

an increased acoustical noise level was observed, due to the gas flow.

considerably. The buffer volume is approximately 200 cm3, yielding a time constant of

= *V*/*Rflow* = (200 cm3)/(16.6 cm3/min) = 12 min). By reducing the buffer volume to

τ

of 1.5 min is obtained. However,

time τ

12 min (

τ

chopper frequency.

frequency of the laser modulation or the cell resonance itself were to shift by a few hertz. PA cells exhibiting narrow resonances (as in the case of excitation of the radial modes) require tight control of both temperature and laser modulation frequency to avoid responsivity losses during the experiment.

Fig. 15. Resonance curve for the first longitudinal mode of the PA cell.

The acoustic resonator is characterized by the quality factor *Q*, which is defined as the ratio of the resonance frequency to the frequency bandwidth between half power points. The amplitude of the microphone signal is 1/ 2 of the maximum amplitude at these points, because the energy of the standing wave is proportional to the square of the induced pressure. The quality factor was measured by filling the PA cell with 1 ppmV of ethylene buffered in nitrogen at a total pressure of 1 atm and by tuning the modulation frequency in 10 Hz increments (2 Hz increments near the top of the curve) across the resonance profile to estimate the half width, as described above. For this PA cell, the profile width at half intensity was 35 Hz, yielding a quality factor *Q* = 16.1 (Eq. 15, Part I) at a resonance frequency *f*0 = 564 Hz. The experimentally determined resonance is not completely symmetric, as the curve rises steeply on one side and becomes less steep on the other side of the maximum. This asymmetry is caused by a coherent superposition of the standing acoustic waves in the detection region of the microphones (Karbach & Hess, 1985).

The calibration of the PA system is usually performed with a reference gas. We calibrated our PA cell with the widely used reference gas ethylene, whose absorption coefficients are accurately known at CO2-laser wavelengths. Ethylene is well suited for this purpose, since it interacts only weakly with common cell surface materials. Ethylene is chemically inert, has the same molecular weight as nitrogen and possesses no permanent dipole moment which means negligible adsorption on the cell walls. Furthermore, its spectrum within the CO2 laser wavelength range is highly structured. In particular it exhibits a characteristic absorption peak at the 10P(14) laser transition at 949.49 cm-1 which is caused by the proximity of the Q branch of the ν7 vibration of C2H4 centered at 948.7715 cm-1. We used a commercially prepared, certified mixture containing 0.96 ppmV C2H4 in pure nitrogen throughout our investigations. For calibration we examined this reference mixture at a total pressure *p* of approximately 1013 mbar and a temperature *T* ≅ 23oC and using the commonly accepted value of the absorption coefficient of 30.4 cm-1atm-1 at the 10P(14) line of the 12C16O2 laser. For shorter time intervals (by changing the calibration gas mixture after a careful vacuum cleaning of the PA cell), the variation of the cell constant was smaller than

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 63

mV/Pa, *Q* = 340

mV/Pa, *Q* = 40

mV/Pa, *Q* = 43

mV/Pa, *Q* = 32

mV/Pa, *Q* = 70

a The value of 50 V cm/W reported for a rms signal of 162 mV was corrected for a peak-to-peak signal

b In brackets are the values we deduced using the authors' specifications for microphone responsivity. c These authors calculated the cell constant by using a PA signal 2 rms instead of a 2 2 x rms signal; as a result, their cell constant (and responsivity) value is half the one

Based on the measured noises, background signals, and cell responsivity, all parameters characterizing the PA instrument can be evaluated (see Table 2). Some of them depend on the CO2 laser and the PA cell, while others are determined by either the coherent acoustic

Several factors influence the lowest levels at which selected compounds can be detected by CO2 laser spectroscopic techniques, within prescribed confidence limits, in a multicomponent mixture. These factors, some of which are interdependent, include (1) the sensitivity or

*f*<sup>0</sup> = 1986 Hz,

4.18x16 cm2, *f*<sup>0</sup> = 2.65 kHz, 1 microphone, *SM* = 12.5

4.18x16 cm2, *f*<sup>0</sup> = 2.86 kHz, 2 microphones, *SM* = 25 mV/Pa, *Q* = 168

*L* = 15 cm, *f*<sup>0</sup> = 1030 Hz, 1 microphone, *SM* = 1000

*L* = 45 cm, *f*<sup>0</sup> = 555 Hz, 1 microphone, *SM* = 1000

*L* = 10 cm, *f*<sup>0</sup> = 1600 Hz, 3 microphones, *SM* = 60

Cell volume = 1 cm3,

5x12 cm2, *f*<sup>0</sup> = 1250 Hz, 16 microphones, *SM* = 160

*f*<sup>0</sup> = 1915 Hz, 1 microphone,

*<sup>f</sup>*= 1600 Hz 1.45

1 microphone, *SM* = 26 mV/Pa (52) 2000

*SM* = 22 mV/Pa, *Q* = 49.7 (71.5) 3250c

*min* (cm-1) of the particular CO2 laser detection technique

**(V cm/W)** 

3.5 (280)

1.72 (69)

(2000) 2000

(1.64) 1640

(270) 4500

260 (1625)

*C*

**(Pa cm/W)** 

**Authors Excitation mode PA cell characteristics** *<sup>R</sup>*

(Meyer & Sigrist,

(Thöny & Sigrist,

(Fink et al., 1996)

(Harren et al.,

(Harren et al.,

(Henningsen & Melander, 1997)

(Nägele & Sigrist,

(Pushkarsky et al., 2002)

1997)

1997)

2000)

of 402 mV.

(Bijnen *et al*., 1996)

1995)

1990) First radial mode

Resonance in vicinity of the first radial mode

mode

mode (intracavity operation)

Second

mode

PA cell

mode

we obtained by our methodology of calculus.

minimum detectable absorptivity

First longitudinal

First longitudinal

longitudinal mode

First longitudinal

First longitudinal mode in a

multipass resonant

First longitudinal

Table 1. Comparison of our results with different PA cells.

background noise or the coherent photoacoustic background signal.

α

Nonresonant operation, pulsed excitation

2%. The calibration also depends to some extent on the modulation waveform, since only the fundamental Fourier component of that waveform is resonant with, and hence significantly excites, the first longitudinal mode.

Using this PA cell and an optimized experimental arrangement we measured a cell responsivity *R* = 280 V cm/W. With the total responsivity of the four microphones *SM tot* = 80 mV/Pa (20 mV/Pa each) (Eq. 30, Part I), a cell constant *C* = 3500 Pa cm/W can be calculated (Eq. 28, Part I). A comparison of these PA cell parameters with other results reported in the literature is presented in Table 1. Different photoacoustic resonator designs such as longitudinal organ pipe resonators excited in the first longitudinal mode, closed longitudinal resonators excited in the second longitudinal mode, and cylindrical resonators excited in the first radial mode (Fig. 16) were used by various authors. As can be noticed from the table, the cell responsivity we obtained is one of the best values that have been reported up to now.


2%. The calibration also depends to some extent on the modulation waveform, since only the fundamental Fourier component of that waveform is resonant with, and hence

Using this PA cell and an optimized experimental arrangement we measured a cell responsivity *R* = 280 V cm/W. With the total responsivity of the four microphones *SM tot* = 80 mV/Pa (20 mV/Pa each) (Eq. 30, Part I), a cell constant *C* = 3500 Pa cm/W can be calculated (Eq. 28, Part I). A comparison of these PA cell parameters with other results reported in the literature is presented in Table 1. Different photoacoustic resonator designs such as longitudinal organ pipe resonators excited in the first longitudinal mode, closed longitudinal resonators excited in the second longitudinal mode, and cylindrical resonators excited in the first radial mode (Fig. 16) were used by various authors. As can be noticed from the table, the cell responsivity we obtained is one of the best values that have been

> *L* = 30 cm, *f*<sup>0</sup> = 564 Hz, 4 microphones, *SM* = 80 mV/Pa, *Q* = 16.1

*L* = 20 cm, *f* = 33.3 Hz,

*L* = 20 cm, *f* = 695 Hz,

*L* = 30 cm, *f*<sup>0</sup> = 695 Hz,

*L* = 15 cm, 2*r* = 1.5 cm,

*L* = 60 cm, *f*<sup>0</sup> = 555 Hz,

*L* = 10 cm, *f*<sup>0</sup> = 1608 Hz,

*L* = 30 cm, *f*<sup>0</sup> = 556 Hz,

*L* = 30 cm, *f*<sup>0</sup> = 560 Hz, 4 microphones, *SM* = 40 mV/Pa, *Q* = 16.4

*L* = 30 cm, *f*<sup>0</sup> = 560 Hz, 4 microphones, *SM* = 40

*L* = 10 cm, *f*<sup>0</sup> = 1653 Hz,

1 microphone, *SM* = 10 mV/Pa,

mV/Pa, *Q* = 20

*Q* = 31.8

6.54x15.56 cm2, *f*<sup>0</sup> = 2.7 kHz, 1 microphone, *SM* = 11mV/Pa + preamplif.x10, *Q* = 560

1 microphone 16.3

1 microphone 121a

1 microphone, *Q* = 17.4 <sup>56</sup>

4 microphones <sup>114</sup>

1 microphone, *SM* = 50 mV/Pa 1-10 (20-200)b

1 microphone, *Q* = 52 <sup>1990</sup>

1 microphone, *SM* = 10 mV/Pa (39) <sup>3900</sup>

**(V cm/W)** 

280 3500

26.5 241

(200) 5000

(160) 4000

(37) 3700

*C*

**(Pa cm/W)** 

**Authors Excitation mode PA cell characteristics** *<sup>R</sup>*

First longitudinal

mode

operation

operation

Nonresonant operation

longitudinal mode

First longitudinal

First longitudinal

First longitudinal

First longitudinal

First longitudinal

Second

mode

mode

mode

mode

mode (intracavity operation)

(Crane, 1978) Nonresonant

(Hubert, 1983) Nonresonant

1980) First radial mode

(Ryan et al., 1983) First longitudinal mode

significantly excites, the first longitudinal mode.

reported up to now.

 (Dumitras et al., 2007) - Our results

(Gerlach & Amer,

(Gandurin et al.,

(Bernegger & Sigrist, 1987)

(Sauren et al.,

(Rooth et al., 1990)

(Harren et al., 1990b)

(Harren et al., 1990a)

(Harren et al., 1990a)

1986)

1989)


a The value of 50 V cm/W reported for a rms signal of 162 mV was corrected for a peak-to-peak signal of 402 mV.

b In brackets are the values we deduced using the authors' specifications for microphone responsivity. c These authors calculated the cell constant by using a PA signal 2

 rms instead of a 2 2 x rms signal; as a result, their cell constant (and responsivity) value is half the one we obtained by our methodology of calculus.

Table 1. Comparison of our results with different PA cells.

Based on the measured noises, background signals, and cell responsivity, all parameters characterizing the PA instrument can be evaluated (see Table 2). Some of them depend on the CO2 laser and the PA cell, while others are determined by either the coherent acoustic background noise or the coherent photoacoustic background signal.

Several factors influence the lowest levels at which selected compounds can be detected by CO2 laser spectroscopic techniques, within prescribed confidence limits, in a multicomponent mixture. These factors, some of which are interdependent, include (1) the sensitivity or minimum detectable absorptivity α*min* (cm-1) of the particular CO2 laser detection technique

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 65

the coherent acoustical background noise-equivalent signal *ac VN* , *PL* is the laser excitation power, and Δ*<sup>f</sup>*

g The limiting sensitivity of the system or the microphone noise-limited minimum detectable absorption coefficient (the equivalent bulk absorption coefficient in the gas) is *Ssys* = *Scell*/*PL* (the minimum detectable absorption strength is defined as the strength that gives a SNR at the transducer output equal to one). h The limiting sensitivity of the system gives a limiting measurable concentration of ethylene of *clim* = *Ssys*/

α

 The minimum detectable absorption coefficient or the equivalent absorption coefficient of C2H4 for a minimum detectable concentration (the absorption coefficient corresponding to the synchronous

mThe minimum detectable absorption cross-section per molecule of ethylenedetermined by the synchronous background signal is the ratio between the equivalent absorption coefficient of C2H4 for minimum detectable

n Knowing the cell responsivity, we can determine the sensitivity of the photoacoustic cell (the rms voltage amplitude measured by the lock-in amplifier) to measure 1 ppb of a given gas at a given laser frequency

(a)

(b)

(c) Fig. 16. Different photoacoustic resonator designs: (a) longitudinal organ pipe resonator, excited in the first longitudinal mode; (b) closed longitudinal resonator excited in the second

longitudinal mode; (c) cylindrical resonator excited in the first radial mode.

number of absorbing molecules per cubic centimeter (*Ntot* = 2.5x1019 cm-3 at 1013 mbar and 20oC).

α*PLRc* (α

i The minimum measurable signal in nitrogen, as determined by the coherent photoacoustical

j The minimum detectable peak-to-peak pressure amplitude can be determined by dividing the minimum measurable signal in nitrogen by the responsivity of the microphone: *pmin* = 2 2 *Vmin*/*SM*. k The minimum measurable signal in nitrogen, limited by the synchronous background signal, gives a

*el* α is the absorption coefficient corresponding to

2*PmeasR,* where *Pmeas* is the measured laser power

*min*/*Ntot*, where *Ntot* is the

= 30.4 cm-1 atm-1, *PL* = 1 W, *R* = 280 V cm/W, and

= 2 2 *<sup>b</sup> VN* /*R* (or the ratio between the peak-to-peak value of the

σ*min* = α α.

defined as min / / *el D PL cell* =α Δ = Δ *f S f* , where min

background signal, is *Vmin* = *<sup>b</sup> VN* (nitrogen) x *PL*.

minimum detectable concentration *cmin* = 2 2 *Vmin*/

synchronous background signal and the cell responsivity).

concentration and the number of absorbing molecules per unit volume:

α*min* = *cmin*α

with 1 W of unchopped laser power: 2 2 *Vppb* =

Table 2. PA cell parameters.

is the detection bandwidth).

after chopper: *PL* = 2*Pmeas*.

background signal) is

*c* = 10-9 atm).

l

employed; (2) the absorption coefficients and spectral uniqueness of both the compounds of interest and interferences; (3) the total number of compounds that absorb within the wavelength regions of the CO2 laser output; (4) the wavelengths and number of CO2 laser lines used for monitoring; and (5) the output power of the laser at each of these lines when the photoacoustic technique is employed. The minimum concentrations of various vapors that can be detected under interference-free conditions by the CO2 laser photoacoustic technique are given by the relationship *cmin* = α*min*/α(λ). Here α*min* is the minimum detectable absorptivity value for the photoacoustic detection system in units of cm-1, and α(λ) is the absorption coefficient in units of cm-1atm-1 of the vapor of interest at the CO2 laser monitoring wavelength. In order to determine the concentrations of the various gas mixture components, it is necessary to know the absolute absorption coefficients for every gas component at the laser wavelengths. Our CO2 laser photoacoustic system with a α*min* value of 2.7x10-8 cm-1 should provide interference-free minimum detectable concentrations between 0.9 ppbV and 270 ppbV for vapors with usual absorption coefficients of 30-0.1 cm-1atm-1.


a This quality factor value corresponds to a full bandwidth at the 0.707 amplitude points of Δ*f* = *f*0/*Q* ≅ 35 Hz b The cell responsivity is the signal per unit power per unit absorption coefficient; in our case, the signal per unit power is 11.6 mV/4.0 W = 2.9x10-3 V/W (rms value) or 8.2x10-3 V/W (peak-to-peak value) for 0.96 ppmV of C2H4 (the absorption coefficient α*\** = 30.4 cm-1 atm-1 x 0.96x10-6 atm = 2.92x10-5 cm-1, where α = 30.4 cm-1 atm-1 is the absorption coefficient of C2H4 at 10P(14) line of the CO2 laser), so that *R* = 8.2x10-3 V/W/2.92x10-5 cm-1 ≅ 280 V cm/W; the same responsivity was obtained with the etalon mixture of 10 ppmV of C2H4 in N2: *R* = 8.4x10-2 V/W/3x10-4 cm-1 ≅ 280 V cm/W

c The microphone responsivity is determined from the Knowles data-sheet for the microphone type 3033: 54 dB (≅500) attenuation at 564 Hz from 1 V/0.1 Pa, leading to *SM* ≅ 20 mV/Pa

d The cell constant is the pressure amplitude per unit absorption coefficient per unit power: *C* = *R*/*SM*  e The pressure amplitude response per unit incident power for 1 ppmV of C2H4 is *p*/*PL* = *C*α*\** 

f The limiting sensitivity of the cell is *Scell* = 2 2 / *ac V R <sup>N</sup>* (several authors, e.g., (Harren et al., 1990a) used the rms value of the voltage instead of its peak-to-peak value, resulting in a limiting sensitivity of the cell and of the system and the limiting measurable concentration of ethylene lower by a factor of 2.84; other authors, e.g., (Kosterev et al., 2005), used a parameter named "sensitivity to absorption",

defined as min / / *el D PL cell* =α Δ = Δ *f S f* , where min *el* α is the absorption coefficient corresponding to the coherent acoustical background noise-equivalent signal *ac VN* , *PL* is the laser excitation power, and Δ*<sup>f</sup>* is the detection bandwidth).

g The limiting sensitivity of the system or the microphone noise-limited minimum detectable absorption coefficient (the equivalent bulk absorption coefficient in the gas) is *Ssys* = *Scell*/*PL* (the minimum detectable absorption strength is defined as the strength that gives a SNR at the transducer output equal to one). h The limiting sensitivity of the system gives a limiting measurable concentration of ethylene of *clim* = *Ssys*/α. i The minimum measurable signal in nitrogen, as determined by the coherent photoacoustical background signal, is *Vmin* = *<sup>b</sup> VN* (nitrogen) x *PL*.

j The minimum detectable peak-to-peak pressure amplitude can be determined by dividing the minimum measurable signal in nitrogen by the responsivity of the microphone: *pmin* = 2 2 *Vmin*/*SM*. k The minimum measurable signal in nitrogen, limited by the synchronous background signal, gives a minimum detectable concentration *cmin* = 2 2 *Vmin*/α2*PmeasR,* where *Pmeas* is the measured laser power after chopper: *PL* = 2*Pmeas*.

l The minimum detectable absorption coefficient or the equivalent absorption coefficient of C2H4 for a minimum detectable concentration (the absorption coefficient corresponding to the synchronous background signal) is α*min* = *cmin*α = 2 2 *<sup>b</sup> VN* /*R* (or the ratio between the peak-to-peak value of the synchronous background signal and the cell responsivity).

mThe minimum detectable absorption cross-section per molecule of ethylenedetermined by the synchronous background signal is the ratio between the equivalent absorption coefficient of C2H4 for minimum detectable concentration and the number of absorbing molecules per unit volume: σ*min* = α*min*/*Ntot*, where *Ntot* is the number of absorbing molecules per cubic centimeter (*Ntot* = 2.5x1019 cm-3 at 1013 mbar and 20oC). n Knowing the cell responsivity, we can determine the sensitivity of the photoacoustic cell (the rms voltage

amplitude measured by the lock-in amplifier) to measure 1 ppb of a given gas at a given laser frequency with 1 W of unchopped laser power: 2 2 *Vppb* = α*PLRc* (α = 30.4 cm-1 atm-1, *PL* = 1 W, *R* = 280 V cm/W, and *c* = 10-9 atm).

Table 2. PA cell parameters.

64 CO2 Laser – Optimisation and Application

employed; (2) the absorption coefficients and spectral uniqueness of both the compounds of interest and interferences; (3) the total number of compounds that absorb within the wavelength regions of the CO2 laser output; (4) the wavelengths and number of CO2 laser lines used for monitoring; and (5) the output power of the laser at each of these lines when the photoacoustic technique is employed. The minimum concentrations of various vapors that can be detected under interference-free conditions by the CO2 laser photoacoustic

> α*min*/α(λ). Here α

absorption coefficient in units of cm-1atm-1 of the vapor of interest at the CO2 laser monitoring wavelength. In order to determine the concentrations of the various gas mixture components, it is necessary to know the absolute absorption coefficients for every gas component at the

should provide interference-free minimum detectable concentrations between 0.9 ppbV and

Microphone responsivityc, *SM* (V/Pa) 4 x20x10-3 = 8x10-2

a This quality factor value corresponds to a full bandwidth at the 0.707 amplitude points of Δ*f* = *f*0/*Q* ≅ 35 Hz b The cell responsivity is the signal per unit power per unit absorption coefficient; in our case, the signal per unit power is 11.6 mV/4.0 W = 2.9x10-3 V/W (rms value) or 8.2x10-3 V/W (peak-to-peak value) for

> α*\**

 = 30.4 cm-1 atm-1 is the absorption coefficient of C2H4 at 10P(14) line of the CO2 laser), so that *R* = 8.2x10-3 V/W/2.92x10-5 cm-1 ≅ 280 V cm/W; the same responsivity was obtained with the etalon mixture

c The microphone responsivity is determined from the Knowles data-sheet for the microphone type

d The cell constant is the pressure amplitude per unit absorption coefficient per unit power: *C* = *R*/*SM* 

f The limiting sensitivity of the cell is *Scell* = 2 2 / *ac V R <sup>N</sup>* (several authors, e.g., (Harren et al., 1990a) used the rms value of the voltage instead of its peak-to-peak value, resulting in a limiting sensitivity of the cell and of the system and the limiting measurable concentration of ethylene lower by a factor of 2.84; other authors, e.g., (Kosterev et al., 2005), used a parameter named "sensitivity to absorption",

, *Scell* (W cm-1) 2.6x10-8

, *Vmin* (μV) (root mean square) 12

*min* (cm-1) 2.7x10-8

, *pmin* (Pa) 4.2x10-4

σ

= 30.4 cm-1 atm-1 x 0.96x10-6 atm = 2.92x10-5 cm-1, where

*min* (cm2) 1.1x10-27

3.0

α*\** 

absorptivity value for the photoacoustic detection system in units of cm-1, and

**Parameter/units Value** 

Cell responsivityb, *R* (V cm/W) 280

Cell constantd, *C* (Pa cm/W) 3.5x103 Pressure amplitude responsee, *p*/*PL* (Pa/W) 10-1

Limiting sensitivity of the systemg, *Ssys* (cm-1) (at 4.4 W laser power) 5.9x10-9 Limiting measurable concentration of ethyleneh, *clim* (ppbV) 0.2

Minimum detectable concentrationk, *cmin* (ppbV) 0.89

, α

Cell sensitivity for 1 ppbV of C2H4 at 1 W of unchopped laser powern,

3033: 54 dB (≅500) attenuation at 564 Hz from 1 V/0.1 Pa, leading to *SM* ≅ 20 mV/Pa

e The pressure amplitude response per unit incident power for 1 ppmV of C2H4 is *p*/*PL* = *C*

Minimum detectable absorption cross-section per moleculem,

of 10 ppmV of C2H4 in N2: *R* = 8.4x10-2 V/W/3x10-4 cm-1 ≅ 280 V cm/W

laser wavelengths. Our CO2 laser photoacoustic system with a

270 ppbV for vapors with usual absorption coefficients of 30-0.1 cm-1atm-1.

*min* is the minimum detectable

*min* value of 2.7x10-8 cm-1

564 16.1

α

α(λ) is the

technique are given by the relationship *cmin* =

Resonance frequency, *f*0 (Hz)

Limiting sensitivity of the cellf

Minimum measurable signal in nitrogeni

Minimum detectable pressure amplitudej

0.96 ppmV of C2H4 (the absorption coefficient

Minimum detectable absorptivityl

*Vppb* (μV at 1 ppbV)

α

Quality factora, *Q*

Fig. 16. Different photoacoustic resonator designs: (a) longitudinal organ pipe resonator, excited in the first longitudinal mode; (b) closed longitudinal resonator excited in the second longitudinal mode; (c) cylindrical resonator excited in the first radial mode.

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 67

To keep the flow noise at a sufficiently low level, the flow must be in the laminar regime. Another practical requirement is the time response, which is determined by the gas sample exchange rate in the resonant cell. In addition, a delay occurs because the gas flows from the inlet to the resonant cell first through the acoustic filter. A response time of < 1 s and a delay of < 10 s may occur in the continuous flow mode. Taking into account the largest dimension and the limiting value of the Reynolds number (*Re* ≤ 2300 for laminar flow), the flow velocity should not exceed 1.7 m/s. This value is far too large, since it would give a flow rate of 4.8 L/min (large gas consumption). As an operating value a flow rate of up to 0.5 L/min was used. With this value, the maximum flow velocity was about 15 cm/s, the Reynolds

from the rise time of the PA signal is longer due to gas mixing in the buffer volumes of the cell. Nevertheless, the measured response times are below 10 s for nonadsorbing gases. Adsorption on the PA cell may increase the response time significantly. Note that the adsorption effect can be effectively reduced by using appropriate wall materials and higher wall temperatures. The adsorption effects can prevent accurate determination of the vapor pressure, since even with an *in situ* sample the vapor pressure will equilibrate between the

Let us consider the system to be a cell with constant volume. For an ideal gas, d*T*/d*E* = (*nCv*)-1, so that d*p*/d*E* = *R*/(*CvV*). Here *T* is the temperature, *p* is the pressure, *E* is the absorbed energy, *n* is the number of moles of the gas, *Cv* is the molar heat capacity at constant volume of the gas mixture, *R* is the gas constant, and *V* is the volume of the cell. For a real photoacoustic system the contents of the cell do not completely equilibrate at the modulation frequency; thus the above equations are a simplification. However, they do emphasize the basic constraints for maximizing the photoacoustic signal; (1) the gas mixture in the cell should have the lowest possible molar heat capacity, and (2) the effective volume of the cell should be as small as possible. The latter is also advantageous when the sample amount is limited. The ideal conditions for PA spectroscopy are a gas mixture consisting of a small amount of sample buffered in a large amount of a nonabsorbing gas with a low *Cv*, such as rare gases, inside a cell with the smallest possible volume. Since the laser beam has cylindrical symmetry, the best way to minimize the volume is to use a cylindrically symmetric cell with an internal diameter barely larger than the diameter of the laser beam. Cylindrical cells, without additions, such as baffles, gas valves, sample fingers, or microphone tubes, and having a diameter of less than about 1/4 of wavelength, behave as simple pipes. Since the speed of sound is inversely proportional to the mass density of the gas (see Eq. 6, Part I), the frequency is lower for a more massive gas. The speed of sound is effectively independent of the total buffer gas pressure. Some works suggest that using the heavier noble gases as buffers increases the signal-to-noise level in acoustically resonant PA

Davidson et al. (Davidson et al., 1990) investigated the importance of window noise and the role of acoustic baffles in photoacoustic spectroscopy. Small amounts of dirt or imperfections can cause heating at the windows and thus the production of a photoacoustic background signal. Window absorption is a major problem for intracavity photoacoustic spectroscopy because of the high light intensity inside the cavity. The signature of window noise is that it is laser frequency independent; its intensity tracks the intensity of the exciting radiation. This signal can actually mask the signal of interest (see spectrum D in Fig. 17). It was shown that the window noise should decrease with increasing modulation frequency

τ

< 0.7 s. The response time determined

number *Re* < 200, and the calculated response time

rate of vapor emission and rate of plating out.

spectroscopy (Thomas III et al., 1978).

A comparison of the results we obtained by using an extracavity PA cell and the experimental parameters measured using intracavity PA cells is given in Table 3. If we take into consideration only the parameters determined by the coherent acoustical background noise (SNR = 1), then the minimum detectable absorptivity *Ssys* (cm-1) is much lower (1-2 orders of magnitude) in the intracavity arrangements due to the increased laser power. Unfortunately, only SNR is often considered in the literature, which yields an extrapolated detection limit that may be considerably too small. In reality, other background signals such as window absorption limit the ultimate sensitivity. These background signals must always be taken into consideration, as they can only be reduced, but not eliminated. In real PA instruments, the minimum measurable signal *Vmin* is higher in extracavity PA cells (3 times in our case) and much higher in intracavity PA cells (hundreds or even thousands of times) than the coherent acoustic background noise *ac VN* . From this table it clearly follows that the best sensitivity is obtained with our extracavity PA instrument, with α*min* (cm-1) being better by one or two orders of magnitude than in intracavity arrangements.


a For a bandwidth of 1 Hz.

b The authors claim that they determined a coherent acoustical background noise of 0.1 μV, but their measured *Ssys* and *clim* correspond to *ac VN* = 0.81 μV.

c The value of *Scell* = 1.4x10-8 cm-1, as cited by the authors, was corrected for a peak-to-peak value of the coherent acoustical background noise.

d A factor of 0.78 was introduced either in the absorption coefficient of ethylene or in the intracavity laser power to compensate for the influence of saturation; the value of *Ssys* = 1.8x10-10 cm-1 claimed by the authors was corrected for a peak-to-peak value of the coherent acoustical background noise.

e The value of 6 pptV claimed by authors was corrected for a peak-to-peak value of the coherent acoustical background noise

Table 3. Comparison of our results (extracavity PA cell) with the experimental parameters determined with intracavity PA cells.

A comparison of the results we obtained by using an extracavity PA cell and the experimental parameters measured using intracavity PA cells is given in Table 3. If we take into consideration only the parameters determined by the coherent acoustical background noise (SNR = 1), then the minimum detectable absorptivity *Ssys* (cm-1) is much lower (1-2 orders of magnitude) in the intracavity arrangements due to the increased laser power. Unfortunately, only SNR is often considered in the literature, which yields an extrapolated detection limit that may be considerably too small. In reality, other background signals such as window absorption limit the ultimate sensitivity. These background signals must always be taken into consideration, as they can only be reduced, but not eliminated. In real PA instruments, the minimum measurable signal *Vmin* is higher in extracavity PA cells (3 times in our case) and much higher in intracavity PA cells (hundreds or even thousands of times) than the coherent acoustic background noise *ac VN* . From this table it clearly follows that the

α

**(Dumitras et al., 2007) (Harren et al., 1990a) (Fink et al., 1996)** 

*min* (cm-1) being better

best sensitivity is obtained with our extracavity PA instrument, with

by one or two orders of magnitude than in intracavity arrangements.

*R* (V cm/W) 280 37 52 *SM tot* (mV/Pa) 80 10 26 *C* (Pa cm/W) 3500 3700 2000 *PL* (W) 4.4 100 40 *p*/*PL* (Pa/W) 10-1 1.1x10-1 6x10-2 Parameters determined by the coherent acoustic background noise (SNR = 1) *ac VN* (rms)a (μV) 2.6 0.5 0.81b *Scell* (W cm-1) 2.6x10-8 4.0x10-8 c 4.4x10-8 *Ssys* (cm-1) 5.9x10-9 5.1x10-10 d 1.1x10-9 *clim* (pptV) 200 17e 34 Parameters determined by the coherent photoacoustic background signal (SBR = 1)

*<sup>b</sup> VN* (rms) (μV/W) 2.7 1.5 26 *Vmin* (rms) (μV) 12 117d 1040 *pmin* (Pa) 4.2x10-4 3.3x10-2 1.1x10-1 *cmin* (ppbV) 0.9 3.8 46

*min* (cm-1) 2.7x10-8 1.2x10-7 1.4x10-6

b The authors claim that they determined a coherent acoustical background noise of 0.1 μV, but their

c The value of *Scell* = 1.4x10-8 cm-1, as cited by the authors, was corrected for a peak-to-peak value of the

d A factor of 0.78 was introduced either in the absorption coefficient of ethylene or in the intracavity laser power to compensate for the influence of saturation; the value of *Ssys* = 1.8x10-10 cm-1 claimed by the

Table 3. Comparison of our results (extracavity PA cell) with the experimental parameters

authors was corrected for a peak-to-peak value of the coherent acoustical background noise. e The value of 6 pptV claimed by authors was corrected for a peak-to-peak value of the coherent

**Parameter Our results** 

PA cell and CO2 laser

a For a bandwidth of 1 Hz.

acoustical background noise

measured *Ssys* and *clim* correspond to *ac VN* = 0.81 μV.

coherent acoustical background noise.

determined with intracavity PA cells.

α

To keep the flow noise at a sufficiently low level, the flow must be in the laminar regime. Another practical requirement is the time response, which is determined by the gas sample exchange rate in the resonant cell. In addition, a delay occurs because the gas flows from the inlet to the resonant cell first through the acoustic filter. A response time of < 1 s and a delay of < 10 s may occur in the continuous flow mode. Taking into account the largest dimension and the limiting value of the Reynolds number (*Re* ≤ 2300 for laminar flow), the flow velocity should not exceed 1.7 m/s. This value is far too large, since it would give a flow rate of 4.8 L/min (large gas consumption). As an operating value a flow rate of up to 0.5 L/min was used. With this value, the maximum flow velocity was about 15 cm/s, the Reynolds number *Re* < 200, and the calculated response time τ < 0.7 s. The response time determined from the rise time of the PA signal is longer due to gas mixing in the buffer volumes of the cell. Nevertheless, the measured response times are below 10 s for nonadsorbing gases. Adsorption on the PA cell may increase the response time significantly. Note that the adsorption effect can be effectively reduced by using appropriate wall materials and higher wall temperatures. The adsorption effects can prevent accurate determination of the vapor pressure, since even with an *in situ* sample the vapor pressure will equilibrate between the rate of vapor emission and rate of plating out.

Let us consider the system to be a cell with constant volume. For an ideal gas, d*T*/d*E* = (*nCv*)-1, so that d*p*/d*E* = *R*/(*CvV*). Here *T* is the temperature, *p* is the pressure, *E* is the absorbed energy, *n* is the number of moles of the gas, *Cv* is the molar heat capacity at constant volume of the gas mixture, *R* is the gas constant, and *V* is the volume of the cell. For a real photoacoustic system the contents of the cell do not completely equilibrate at the modulation frequency; thus the above equations are a simplification. However, they do emphasize the basic constraints for maximizing the photoacoustic signal; (1) the gas mixture in the cell should have the lowest possible molar heat capacity, and (2) the effective volume of the cell should be as small as possible. The latter is also advantageous when the sample amount is limited. The ideal conditions for PA spectroscopy are a gas mixture consisting of a small amount of sample buffered in a large amount of a nonabsorbing gas with a low *Cv*, such as rare gases, inside a cell with the smallest possible volume. Since the laser beam has cylindrical symmetry, the best way to minimize the volume is to use a cylindrically symmetric cell with an internal diameter barely larger than the diameter of the laser beam.

Cylindrical cells, without additions, such as baffles, gas valves, sample fingers, or microphone tubes, and having a diameter of less than about 1/4 of wavelength, behave as simple pipes. Since the speed of sound is inversely proportional to the mass density of the gas (see Eq. 6, Part I), the frequency is lower for a more massive gas. The speed of sound is effectively independent of the total buffer gas pressure. Some works suggest that using the heavier noble gases as buffers increases the signal-to-noise level in acoustically resonant PA spectroscopy (Thomas III et al., 1978).

Davidson et al. (Davidson et al., 1990) investigated the importance of window noise and the role of acoustic baffles in photoacoustic spectroscopy. Small amounts of dirt or imperfections can cause heating at the windows and thus the production of a photoacoustic background signal. Window absorption is a major problem for intracavity photoacoustic spectroscopy because of the high light intensity inside the cavity. The signature of window noise is that it is laser frequency independent; its intensity tracks the intensity of the exciting radiation. This signal can actually mask the signal of interest (see spectrum D in Fig. 17). It was shown that the window noise should decrease with increasing modulation frequency

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 69

In an attempt to reduce the effects of microphone noise, the output of two microphones was summed in the low-noise preamplifier. Two microphones seem better than one when observing the noise level, but the difference is not as obvious in the spectra that were taken. However, the absolute signal level does increase with an increasing number of microphones;

High isolation against window absorption may be obtained by introducing acoustic baffles between the windows and the resonator. However, the resonator also introduces additional noise. Pressure fluctuations from turbulence in the gas and acoustic flux reaching the resonator from the surroundings will be amplified along with the signal. Furthermore the amplification provided by a resonator is accompanied by an increased sensitivity to parameters which affect

Besides cleaning the cell windows, a very careful rinsing of the inner walls of the cell is also very important. If the inner of the cell is not properly cleaned before a measurement, a considerable drift of the photoacoustic background signal is observed if the gas flow is interrupted. This fact demonstrates that the desorption of IR-absorbing gases and vapors from the cell walls can make a large contribution to the background signal. That is why no measurement started until after the PA cell had been rinsed with pure nitrogen till the coherent photoacoustical background noise reached the minimum value of 2.7 μV/W.

To distinguish the gas absorption signal from other signals (e.g., from the walls, windows, or interfering gases), one has to switch the CO2 laser to other laser lines. However, repositioning the laser beam to its original wavelength can change the configuration of the laser cavity (deviation in grating position, thermal drift) and result in irreproducible absorption signals if the operation is not carefully conducted. Using a CO2 laser stabilized on the top of the gain curve ensures that both the laser frequency and output power are reestablished with high accuracy when the laser operation is changed from one line to another.

Whenever monitoring is performed by flowing the gas mixture through a cell, a crucial question is whether the measured signal, which represents the trace gas concentration in the interaction region, also reflects the concentration at the source. On their way to the cell, the different components of a gas mixture may react with one another, form clusters or aerosols, and react with or be adsorbed on particles present, or on the sampling line and cell walls. Adsorption problems are particularly severe for polar molecules with large dipole moments, such as water and ammonia, but they can be reduced by a proper choice of materials.

The vacuum/gas handling system is an important element in these measurements owing to its role in ensuring PA cell and gas purity. The Teflon/stainless steel system can perform several functions without necessitating any disconnections. It can be used to pump out the cell, mix gases in the desired proportions, and monitor the total pressure of gases. Whenever possible, the PA cell was employed in the gas flow mode of operation to minimize any tendency for the vapor to stick to the cell walls and the effects of the subsequent outgassing of contaminants, which would otherwise lead to increasing background signals during an

To design an efficient vacuum/gas handling system to be used in LPAS, one must make

when the sample is weakly absorbing, more microphones are an advantage.

the resonance frequency, such as gas composition, temperature, and pressure.

**2.4 Gas handling system** 

experimental run.

sure that the following operations can be carried out:

(Rosengren, 1975), which suggests that a relatively high modulation frequency is advantageous. The approach to this problem is to keep the windows as clean as possible and place acoustic baffles between the windows and the body of the sample cell where the microphones are mounted.

Fig. 17. Photoacoustic spectra: (A) clean windows on baffled cell; (B) clean windows on unbaffled cell; (C) dirty windows on baffled cell; (D) dirty windows on unbaffled cell (Davidson et al., 1990).

The acoustic baffles hinder the propagation of the window noise into the central region of the cell near the microphones. In an attempt to quantify the usefulness of the baffles, four spectra are shown in Fig. 17. These spectra illustrate the microphone signal versus laser frequency. For both the baffled and unbaffled cells, a longitudinal resonance frequency was used. From this figure it is immediately obvious how important it is to have clean windows. If the sample makes it difficult to keep the windows clean, a cell with baffles will perform much better than one without them. Even with clean windows, the baffles give a flatter base line.

The random noise level visible on the base lines of spectra A and B in Fig. 17 is probably due to a combination of the ambient lab noise, noise from the microphones, associated electronics, and the fluctuations of the laser itself. The ultimate limit of a microphone's sensitivity is set by the random thermal fluctuations in the sample and of the microphone diaphragm. In practice, the random fluctuations of the laser do not seem to be critical. Also, the combined electronic noise of the lock-in, preamplifier, and FET amplifier in the microphones totaled about 3 μV. This is at least a factor of 10 less than the noise level observed in the spectra. The noise that is visible in the spectra stems almost exclusively from thermal fluctuations and ambient lab noise. One of the major ambient noise sources is the mechanical chopper. In practice, this seems to set the detection limit. Acoustically isolating the chopper improves the noise, but replacing it with a nonmechanical modulator is better still, as it also speeds up modulation.

In an attempt to reduce the effects of microphone noise, the output of two microphones was summed in the low-noise preamplifier. Two microphones seem better than one when observing the noise level, but the difference is not as obvious in the spectra that were taken. However, the absolute signal level does increase with an increasing number of microphones; when the sample is weakly absorbing, more microphones are an advantage.

High isolation against window absorption may be obtained by introducing acoustic baffles between the windows and the resonator. However, the resonator also introduces additional noise. Pressure fluctuations from turbulence in the gas and acoustic flux reaching the resonator from the surroundings will be amplified along with the signal. Furthermore the amplification provided by a resonator is accompanied by an increased sensitivity to parameters which affect the resonance frequency, such as gas composition, temperature, and pressure.

Besides cleaning the cell windows, a very careful rinsing of the inner walls of the cell is also very important. If the inner of the cell is not properly cleaned before a measurement, a considerable drift of the photoacoustic background signal is observed if the gas flow is interrupted. This fact demonstrates that the desorption of IR-absorbing gases and vapors from the cell walls can make a large contribution to the background signal. That is why no measurement started until after the PA cell had been rinsed with pure nitrogen till the coherent photoacoustical background noise reached the minimum value of 2.7 μV/W.

To distinguish the gas absorption signal from other signals (e.g., from the walls, windows, or interfering gases), one has to switch the CO2 laser to other laser lines. However, repositioning the laser beam to its original wavelength can change the configuration of the laser cavity (deviation in grating position, thermal drift) and result in irreproducible absorption signals if the operation is not carefully conducted. Using a CO2 laser stabilized on the top of the gain curve ensures that both the laser frequency and output power are reestablished with high accuracy when the laser operation is changed from one line to another.

#### **2.4 Gas handling system**

68 CO2 Laser – Optimisation and Application

(Rosengren, 1975), which suggests that a relatively high modulation frequency is advantageous. The approach to this problem is to keep the windows as clean as possible and place acoustic baffles between the windows and the body of the sample cell where the

Fig. 17. Photoacoustic spectra: (A) clean windows on baffled cell; (B) clean windows on unbaffled cell; (C) dirty windows on baffled cell; (D) dirty windows on unbaffled cell

The acoustic baffles hinder the propagation of the window noise into the central region of the cell near the microphones. In an attempt to quantify the usefulness of the baffles, four spectra are shown in Fig. 17. These spectra illustrate the microphone signal versus laser frequency. For both the baffled and unbaffled cells, a longitudinal resonance frequency was used. From this figure it is immediately obvious how important it is to have clean windows. If the sample makes it difficult to keep the windows clean, a cell with baffles will perform much better than one without them. Even with clean windows, the baffles give a flatter base line.

The random noise level visible on the base lines of spectra A and B in Fig. 17 is probably due to a combination of the ambient lab noise, noise from the microphones, associated electronics, and the fluctuations of the laser itself. The ultimate limit of a microphone's sensitivity is set by the random thermal fluctuations in the sample and of the microphone diaphragm. In practice, the random fluctuations of the laser do not seem to be critical. Also, the combined electronic noise of the lock-in, preamplifier, and FET amplifier in the microphones totaled about 3 μV. This is at least a factor of 10 less than the noise level observed in the spectra. The noise that is visible in the spectra stems almost exclusively from thermal fluctuations and ambient lab noise. One of the major ambient noise sources is the mechanical chopper. In practice, this seems to set the detection limit. Acoustically isolating the chopper improves the noise, but replacing it with a nonmechanical modulator is better

microphones are mounted.

(Davidson et al., 1990).

still, as it also speeds up modulation.

Whenever monitoring is performed by flowing the gas mixture through a cell, a crucial question is whether the measured signal, which represents the trace gas concentration in the interaction region, also reflects the concentration at the source. On their way to the cell, the different components of a gas mixture may react with one another, form clusters or aerosols, and react with or be adsorbed on particles present, or on the sampling line and cell walls. Adsorption problems are particularly severe for polar molecules with large dipole moments, such as water and ammonia, but they can be reduced by a proper choice of materials.

The vacuum/gas handling system is an important element in these measurements owing to its role in ensuring PA cell and gas purity. The Teflon/stainless steel system can perform several functions without necessitating any disconnections. It can be used to pump out the cell, mix gases in the desired proportions, and monitor the total pressure of gases. Whenever possible, the PA cell was employed in the gas flow mode of operation to minimize any tendency for the vapor to stick to the cell walls and the effects of the subsequent outgassing of contaminants, which would otherwise lead to increasing background signals during an experimental run.

To design an efficient vacuum/gas handling system to be used in LPAS, one must make sure that the following operations can be carried out:

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 71

The pressure of the gases added to the PA cell was determined by means of three Baratron pressure gauges (MKS Instruments, Inc.): 622A (0-1000 mbar), 122A (0-1000 mbar), and 122A

We use thermal mass flowmeters, or mass flow controllers (MFC), to deliver stable and known gas flows to the PA cell. The most critical processes will require flow measurement accuracies of 1% or better in the range 1000 to 10 sccm (7x10-4 to 7x10-6 mol/sec; 1 sccm (at 0oC) = 7.436x10-7 mol/sec). The digital MFCs sense the mass flow from the temperature difference between two temperature sensors in thermal contact with the gas stream and then process the information digitally with a microcontroller. The analog sensor output is amplified and digitized before it is sent to a microprocessor to compute the final control valve position. The gas flow in our gas handling system is adjusted by two gas flow controllers, MKS 1179A (0 - 1000 sccm) and MKS 2259CC (0 - 200 sccm), which are

By using an adequate scrubber for CO2 filtration, the CO2 interference problem can be resolved. The CO2 trap must neither alter the ethylene concentration level, nor introduce new interfering gases. By using a CO2 trap with a volume of 120 cm3 filled with fresh KOH pellets, we succeeded to reduce the CO2 content in the exhaled breath (mixt expiratory air collection) of a healthy nonsmoking young person from 3.4% (equivalent to an ethylene concentration of 2.35 ppmV) to 156 ppmV (equivalent to an ethylene concentration of 10.8

The water vapors could be additionally filtered by a cryogenic trap filled with liquid nitrogen. Using a simple and small cryogenic trap, we demonstrated the negative influence in our experiments (Dumitras et al., 2008). The liquid nitrogen temperature -196oC (77 K) is bellow the frozen point of the ethylene gas -169.2oC (104 K), so the practical effects is just to frozen both water vapors and ethylene. Introducing in the flow a calibrated mixture of 1 ppm C2H4 in N2, we observed after filling the cell at 1 atm pressure that the maximum ethylene concentration is only 51 ppb, diminished by a factor of 20 from the initial ethylene concentration. The level starts to increase suddenly at the point where we stopped the liquid nitrogen admission in the trap. In conclusion, a simple nitrogen trap is not suited for our experiments involving ethylene, but a special thermocontrolled trap can do the job, setting the working temperature below -78.5oC (194.5K), the freezing point of CO2, but above -

Fig. 19. General view of the gas mixing station.

(0-100 mbar), connected to a digital two-channel unit PDR-C-2C.

connected to a digital four-channel instrument MKS 247C.

ppbV), that is a reduction factor of 218 (see Section 2.7).

169.2oC (104 K), the freezing point of ethylene.


A vacuum/gas handling system to be used in PA experiments was designed and implemented based on these guidelines. The schematic of the gas handling chain is shown in Fig. 18, while a general view of the valves and distribution system is given in Fig. 19.

#### Fig. 18. Gas handling system.

Gas transport lines throughout the gas mixing station were made of Teflon (Swagelok PFA-T6M-1M-30M, 6 mm inner diameter and 1 mm wall thickness) to minimize adsorption and contamination. The toggle valves V1-V17 (Swagelok SS-1GS6mm) and union tees T1-T11 (Swagelok SS-6MO-3) were made of stainless steel. No valve grease was used. The PA cell gas inlet and outlet were connected to the gas handling system with Swagelok fittings (male connectors SS-6MO-1-2RT). Connections to the inlet and outlet valves of the PA cell were made via flexible Teflon tubing so as to minimize the coupling of mechanical vibrations to the PA cell. The flexible lines also make it possible to position the PA cell during optical alignment.

Fig. 19. General view of the gas mixing station.

i. evacuation by the vacuum system of the entire gas handling system, including the PA

ii. controlled introduction of a gas or gas mixture either for rinsing the PA cell and the gas handling system with pure nitrogen or for calibrating the PA spectrometer with a

iv. safe insertion in the gas handling system of a sample cuvette (usually made of Pyrex

v. filtration of certain gases (carbon dioxide and water vapors), which interfere with the

vi. controlled introduction of the trace gas to be measured from the sample cuvette or bag into the PA cell by a nonabsorbing gas (nitrogen or synthetic air) acting as carrier; vii. controlled change of the sample and carrier gas flow rates within a broad range (10-

ix. quick monitoring of the trace gas concentration in the sample gas by ensuring a

A vacuum/gas handling system to be used in PA experiments was designed and implemented based on these guidelines. The schematic of the gas handling chain is shown in Fig. 18, while a general view of the valves and distribution system is given in Fig. 19.

Gas transport lines throughout the gas mixing station were made of Teflon (Swagelok PFA-T6M-1M-30M, 6 mm inner diameter and 1 mm wall thickness) to minimize adsorption and contamination. The toggle valves V1-V17 (Swagelok SS-1GS6mm) and union tees T1-T11 (Swagelok SS-6MO-3) were made of stainless steel. No valve grease was used. The PA cell gas inlet and outlet were connected to the gas handling system with Swagelok fittings (male connectors SS-6MO-1-2RT). Connections to the inlet and outlet valves of the PA cell were made via flexible Teflon tubing so as to minimize the coupling of mechanical vibrations to the PA cell. The flexible lines also make it possible to position the PA cell during optical alignment.

iii. pressure measurement in the PA cell and in different sections of the system;

viii. simultaneous measurement of two sample gases (e.g., ethylene and ammonia);

glass) or aluminum-coated plastic bag with the trace gas sample;

response time on the order of minutes or even seconds.

cell, either totally or in different sections;

certified gas mixture;

trace gas to be measured;

1000 sccm);

Fig. 18. Gas handling system.

The pressure of the gases added to the PA cell was determined by means of three Baratron pressure gauges (MKS Instruments, Inc.): 622A (0-1000 mbar), 122A (0-1000 mbar), and 122A (0-100 mbar), connected to a digital two-channel unit PDR-C-2C.

We use thermal mass flowmeters, or mass flow controllers (MFC), to deliver stable and known gas flows to the PA cell. The most critical processes will require flow measurement accuracies of 1% or better in the range 1000 to 10 sccm (7x10-4 to 7x10-6 mol/sec; 1 sccm (at 0oC) = 7.436x10-7 mol/sec). The digital MFCs sense the mass flow from the temperature difference between two temperature sensors in thermal contact with the gas stream and then process the information digitally with a microcontroller. The analog sensor output is amplified and digitized before it is sent to a microprocessor to compute the final control valve position. The gas flow in our gas handling system is adjusted by two gas flow controllers, MKS 1179A (0 - 1000 sccm) and MKS 2259CC (0 - 200 sccm), which are connected to a digital four-channel instrument MKS 247C.

By using an adequate scrubber for CO2 filtration, the CO2 interference problem can be resolved. The CO2 trap must neither alter the ethylene concentration level, nor introduce new interfering gases. By using a CO2 trap with a volume of 120 cm3 filled with fresh KOH pellets, we succeeded to reduce the CO2 content in the exhaled breath (mixt expiratory air collection) of a healthy nonsmoking young person from 3.4% (equivalent to an ethylene concentration of 2.35 ppmV) to 156 ppmV (equivalent to an ethylene concentration of 10.8 ppbV), that is a reduction factor of 218 (see Section 2.7).

The water vapors could be additionally filtered by a cryogenic trap filled with liquid nitrogen. Using a simple and small cryogenic trap, we demonstrated the negative influence in our experiments (Dumitras et al., 2008). The liquid nitrogen temperature -196oC (77 K) is bellow the frozen point of the ethylene gas -169.2oC (104 K), so the practical effects is just to frozen both water vapors and ethylene. Introducing in the flow a calibrated mixture of 1 ppm C2H4 in N2, we observed after filling the cell at 1 atm pressure that the maximum ethylene concentration is only 51 ppb, diminished by a factor of 20 from the initial ethylene concentration. The level starts to increase suddenly at the point where we stopped the liquid nitrogen admission in the trap. In conclusion, a simple nitrogen trap is not suited for our experiments involving ethylene, but a special thermocontrolled trap can do the job, setting the working temperature below -78.5oC (194.5K), the freezing point of CO2, but above - 169.2oC (104 K), the freezing point of ethylene.

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 73

mouth and trachea), where air does not come into contact with the alveoli of the lungs. The following part of a breath, about 350 mL, is "alveolar" breath, which comes from the lungs, where gaseous exchange between the blood and breath air takes place. Dead space air can be interpreted as essential for the detection, and depends on the type of molecule detected from the breath test. For example, the dead-space is used to quantify the amount of the NO molecules. In the case of an asthmatic patient, if the airways are inflamed, a high-level of NO is released into the airways and into the dead-space air. But for volatile organic compounds (VOCs) exchanged between blood and alveolar air, the dead-space air is a "contaminant" diluting the concentrations of VOCs when breath air is collected. In terms of the origin of the collected breath gases, there are three basic collection approaches: 1. *upper airway collection* for NO test; this means that only dead-space gas is collected (it is only for the NO test); 2. *alveolar collection*; this means that pure alveolar gas is collected (for tests of other inorganic gases and VOCs); 3. *mixed expiratory collection*; this means that total breath air, including dead-space air and alveolar gas is collected (appropriate for tests of special gases and VOCs). Because the mixed expiratory collection method is easy to perform in spontaneously breathing subjects requiring no additional equipment, it has been most frequently used in practical applications. However, concentrations of endogenous substances in alveolar air are two to three times higher than those found in mixed expiratory samples, because there is no dilution by dead-space gas. Collection of breath air can be performed for a single breath or for collection of individual breathes over a certain period of time. If the sample is collected through a single breath, one has to be sure that this single

The rate of change in concentration of a species *i* in a flowing cell is given by:

*t tC*

Fig. 21. Time response of the PA spectrometer for a gas flow rate of 100 sccm.

= *V*/*Rflow* is the renewal time constant.

( ) [ ] ( )*tCF V R*

where *Rflow* is the gas flow rate (liter/min or sccm), *Fi* is the feed concentration of species *i*, and *V* is the cell volume. This equation assumes that the adsorption rate of *i* is zero, and that gas mixing inside the cell is instantaneous. Integrating Eq. (4) with the initial condition that

*<sup>i</sup> flow* <sup>=</sup> <sup>−</sup> <sup>d</sup>

*ii*

<sup>d</sup> , (4)

( ) [ ( ) *V/tRexpFtC* ] *ii* 1 −−= *flow* , (5)

breath is representative.

*Ci*(0) = 0 gives

and τ

The following gases were used throughout the experiments:


The flow rate was usually set at a low value of 30-100 sccm in all experiments in order to eliminate the acoustic noise of the gas flow, and all measurements were carried out with the PA cell at atmospheric pressure. Flow noise increases upwards of 10 L/h (167 sccm) were found to limit the minimum response time of the detector. The flow velocity minimizes the accumulation of the produced gases in the sampling cell. The carrier gas we used was either nitrogen or synthetic air, and its flow rate through the system was monitored by the calibrated flowmeter. Provision is made for bypassing the flowmeter with the gas mixture flow prior to a measurement to equilibrate the feedline surfaces. This ensures that the measured rise times are an exclusive function of the cell characteristics. A measurement is initiated by diverting the gas flow from the bypass through the flowmeter and PA cell and monitoring the photoacoustic signal rise that follows.

As far as the sampling procedure is concerned, we use an extractive method, based on the collection of trace gas samples by some type of container or collecting medium and subsequent analysis in the laboratory. A problem may arise at this point due to some alterations of the gas composition caused by adsorption and desorption processes on the inner surface of the collecting container. The breath samples we analyzed were obtained from volunteers who agreed to provide such samples at certain time intervals. The volunteers were asked to exhale into a sample bag with a normal exhalation flow rate. The breath samples were collected in 0.75-liter aluminum-coated bags (QuinTron, Milwaukee, Wisconsin, USA) equipped with valves that sealed them after filling (Fig. 20). The bags were inserted into the gas handling system, which ensured a better control by means of two independently adjusted flow controllers of the upstream pressure and the flow rate through the sample bag.

Fig. 20. Aluminum-coated plastic bag with sample gas.

The exhaled air is a heterogeneous gas. For a healthy individual, the first part of a exhaled breath, roughly 150 mL, consists of "dead-space" air from the upper airways (such as the



The flow rate was usually set at a low value of 30-100 sccm in all experiments in order to eliminate the acoustic noise of the gas flow, and all measurements were carried out with the PA cell at atmospheric pressure. Flow noise increases upwards of 10 L/h (167 sccm) were found to limit the minimum response time of the detector. The flow velocity minimizes the accumulation of the produced gases in the sampling cell. The carrier gas we used was either nitrogen or synthetic air, and its flow rate through the system was monitored by the calibrated flowmeter. Provision is made for bypassing the flowmeter with the gas mixture flow prior to a measurement to equilibrate the feedline surfaces. This ensures that the measured rise times are an exclusive function of the cell characteristics. A measurement is initiated by diverting the gas flow from the bypass through the flowmeter and PA cell and

As far as the sampling procedure is concerned, we use an extractive method, based on the collection of trace gas samples by some type of container or collecting medium and subsequent analysis in the laboratory. A problem may arise at this point due to some alterations of the gas composition caused by adsorption and desorption processes on the inner surface of the collecting container. The breath samples we analyzed were obtained from volunteers who agreed to provide such samples at certain time intervals. The volunteers were asked to exhale into a sample bag with a normal exhalation flow rate. The breath samples were collected in 0.75-liter aluminum-coated bags (QuinTron, Milwaukee, Wisconsin, USA) equipped with valves that sealed them after filling (Fig. 20). The bags were inserted into the gas handling system, which ensured a better control by means of two independently adjusted flow controllers of the upstream pressure and the flow rate through

The exhaled air is a heterogeneous gas. For a healthy individual, the first part of a exhaled breath, roughly 150 mL, consists of "dead-space" air from the upper airways (such as the

The following gases were used throughout the experiments:

nitrogen 6.0 (purity 99.9999%).

the sample bag.

monitoring the photoacoustic signal rise that follows.

Fig. 20. Aluminum-coated plastic bag with sample gas.

hydrocarbons max. 0.1 ppmV, nitrogen oxides max. 0.1 ppmV);

mouth and trachea), where air does not come into contact with the alveoli of the lungs. The following part of a breath, about 350 mL, is "alveolar" breath, which comes from the lungs, where gaseous exchange between the blood and breath air takes place. Dead space air can be interpreted as essential for the detection, and depends on the type of molecule detected from the breath test. For example, the dead-space is used to quantify the amount of the NO molecules. In the case of an asthmatic patient, if the airways are inflamed, a high-level of NO is released into the airways and into the dead-space air. But for volatile organic compounds (VOCs) exchanged between blood and alveolar air, the dead-space air is a "contaminant" diluting the concentrations of VOCs when breath air is collected. In terms of the origin of the collected breath gases, there are three basic collection approaches: 1. *upper airway collection* for NO test; this means that only dead-space gas is collected (it is only for the NO test); 2. *alveolar collection*; this means that pure alveolar gas is collected (for tests of other inorganic gases and VOCs); 3. *mixed expiratory collection*; this means that total breath air, including dead-space air and alveolar gas is collected (appropriate for tests of special gases and VOCs). Because the mixed expiratory collection method is easy to perform in spontaneously breathing subjects requiring no additional equipment, it has been most frequently used in practical applications. However, concentrations of endogenous substances in alveolar air are two to three times higher than those found in mixed expiratory samples, because there is no dilution by dead-space gas. Collection of breath air can be performed for a single breath or for collection of individual breathes over a certain period of time. If the sample is collected through a single breath, one has to be sure that this single breath is representative.

The rate of change in concentration of a species *i* in a flowing cell is given by:

$$\frac{\text{d}C\_i(t)}{\text{d}t} = \frac{R\_{flow}}{V} [F\_i - C\_i(t)],\tag{4}$$

where *Rflow* is the gas flow rate (liter/min or sccm), *Fi* is the feed concentration of species *i*, and *V* is the cell volume. This equation assumes that the adsorption rate of *i* is zero, and that gas mixing inside the cell is instantaneous. Integrating Eq. (4) with the initial condition that *Ci*(0) = 0 gives

$$C\_{\hat{1}}(t) = F\_{\hat{1}} \left[ 1 - \exp\left(-\mathcal{R}\_{flow} t \;/\; V\right) \right] \tag{5}$$

and τ= *V*/*Rflow* is the renewal time constant.

Fig. 21. Time response of the PA spectrometer for a gas flow rate of 100 sccm.

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 75

The software user interface contains three panels which display in real time the following parameters: CO2 laser power level; PA signal; and trace gas concentration. Another window

All settings and properties are stored to disk from session to session. In addition, a file may be automatically generated when running an experiment, including: a) **Laser power** stores powermeter readings of power incident on the sample as a function of time; b) **PA signal** stores the instantaneous values of the PA signal measured by the lock-in amplifier as a function of time; c) **Trace gas concentration** stores the time evolution of the trace gas

We designed and characterized two experimental set-ups with the PA cell in an external configuration: the first one with a low power CO2 laser where the saturation effects are negligible, and a second one with a high power CO2 laser where the saturation effects are important and have to be taken into consideration. We measured all relevant features and determined all quantities used in literature to compare our findings with the best results reported in the previous published papers. All measurements were done in nitrogen and ethylene with the 10P(14) line of a cw CO2 laser. We succeeded to obtain a minimum detectable concentration better by more than a factor of 10 compared to the best results

To investigate the possibility of using a high power laser in an extracavity configuration, we introduced in the experimental set-up a commercial CO2 laser (Coherent GEM SELECT 50TM laser) with output power till 50 W and tunable on 73 different lines (Dumitras et al., 2010). When this laser is tuned on 10P(14) line, the maximum power delivered after chopper and

To change the laser power inside the PA cell we tried either to modify the input power in the laser (RF power supply) or to introduce a beam splitter in the path of the laser beam. Unfortunately, both methods change significantly the beam path inside the PA cell, thus perturbing unacceptably the results of the measurements. The waveguide laser has a poor beam pointing because it has a short optical resonator and the variation of the transverse RF

The saturation effects at high laser power were investigated by using the method of truncation of a gaussian laser beam. This approach was possible because the laser beam is very close to a gaussian beam (M2 < 1.1). The method consists in passing the beam through an aperture with known diameter (Fig. 23). To avoid deformations owing to heating, we used water cooled metallic diaphragms with diameters between 1.42 mm and 5.03 mm. All

When a gaussian beam of radius *w* is truncated by an aperture of radius *a* (Fig. 24), the power transmitted through the aperture is *T* = *P*(*a*)/*P* = 1 – exp(-2*a*2/*w*2). When 2*a* = 2*w*, *T* ≅ 86%, that is 86% of the laser power is transmitted through the aperture (this is known as 86% criterion). When 2*a* = π*w*, *T* ≅ 99%, that is 99% of the laser power is transmitted through the aperture and we have the 99% criterion. This formula offers a possibility to measure precisely the diameter of the laser beam at the position of the diaphragm. By knowing the radius of the aperture (*a*) and by measuring the laser power before and after the aperture (*P*

diaphragms were placed at a distance of 450 mm from the beam waist of the laser.

(countdown) indicates the number of remaining measurement points.

concentration for a given laser wavelength.

**2.6 Low power vs. high power lasers** 

previously reported in the literature.

excitation modifies the laser gain profile.

focusing lens is 14.5 W.

The solid line in Fig. 21 shows the rise time curve predicted by Eq. (5) for the experimental parameter values: *V* = 1200 cm3 and *Rflow* = 100 sccm. The total renewal time of the gas content in the system (sampling cell, scrubber, and photoacoustic cell) is τ = 12 min (1/*e* time). This τ value is small compared to the time response of certain biological samples (e.g., the C2H4 production of a single flower, 0.02-0.3 nL/g/h) (Harren et al., 1990b).

#### **2.5 Data acquisition and processing**

The acquisition and processing of the recorded data was done with Keithley TestPoint software. TestPoint data acquisition software provides a development environment in which data acquisition applications can be generated. A graphical editor is provided for creating a user interface, or "panel", which the user sees and interacts with as the application executes. A user panel is made of pictorial elements that represent such things as switches, variable controls, numerical, text and selection boxes, bar displays, graphs, and strip charts. In addition, an application editor is provided, which ensures some interactive means of specifying how the visual elements on the user panel interact with the data sources and processing functions to achieve application goals. TestPoint uses an automated textual description of the operations carried out by each user panel element.

We developed a modular software architecture aimed at controlling the experiments, collecting data, and preprocessing information. It helps automate the process of collecting and processing experimental results. The software controls the chopper frequency, transfers powermeter readings, normalizes data, and automatically stores files. It allows the user to set parameters such as the PA cell responsivity (a constant used to normalize raw data), gas absorption coefficient, number of averaged samples at every measurement point, sample acquisition rate, and total number of measurement points. This software interfaces the following instruments:


The software user interface allows the user to set or read input data and instantaneous values for the PA voltage (rms), average laser power after chopper, and trace gas concentration. Users may set experimental parameters for the PA cell responsivity and gas absorption coefficient. They are also provided with a text input to write a description of the experiments or take other notes. The user interface also provides data visualization (Fig. 22).

Fig. 22. Software user interface used to record trace gas concentrations.

The software user interface contains three panels which display in real time the following parameters: CO2 laser power level; PA signal; and trace gas concentration. Another window (countdown) indicates the number of remaining measurement points.

All settings and properties are stored to disk from session to session. In addition, a file may be automatically generated when running an experiment, including: a) **Laser power** stores powermeter readings of power incident on the sample as a function of time; b) **PA signal** stores the instantaneous values of the PA signal measured by the lock-in amplifier as a function of time; c) **Trace gas concentration** stores the time evolution of the trace gas concentration for a given laser wavelength.

#### **2.6 Low power vs. high power lasers**

74 CO2 Laser – Optimisation and Application

The solid line in Fig. 21 shows the rise time curve predicted by Eq. (5) for the experimental parameter values: *V* = 1200 cm3 and *Rflow* = 100 sccm. The total renewal time of the gas

The acquisition and processing of the recorded data was done with Keithley TestPoint software. TestPoint data acquisition software provides a development environment in which data acquisition applications can be generated. A graphical editor is provided for creating a user interface, or "panel", which the user sees and interacts with as the application executes. A user panel is made of pictorial elements that represent such things as switches, variable controls, numerical, text and selection boxes, bar displays, graphs, and strip charts. In addition, an application editor is provided, which ensures some interactive means of specifying how the visual elements on the user panel interact with the data sources and processing functions to achieve application goals. TestPoint uses an automated textual

We developed a modular software architecture aimed at controlling the experiments, collecting data, and preprocessing information. It helps automate the process of collecting and processing experimental results. The software controls the chopper frequency, transfers powermeter readings, normalizes data, and automatically stores files. It allows the user to set parameters such as the PA cell responsivity (a constant used to normalize raw data), gas absorption coefficient, number of averaged samples at every measurement point, sample acquisition rate, and total number of measurement points. This software interfaces the

The software user interface allows the user to set or read input data and instantaneous values for the PA voltage (rms), average laser power after chopper, and trace gas concentration. Users may set experimental parameters for the PA cell responsivity and gas absorption coefficient. They are also provided with a text input to write a description of the experiments or take other notes. The user interface also provides data visualization (Fig. 22).

value is small compared to the time response of certain biological samples (e.g.,

τ

= 12 min (1/*e*

content in the system (sampling cell, scrubber, and photoacoustic cell) is

description of the operations carried out by each user panel element.

Fig. 22. Software user interface used to record trace gas concentrations.

the C2H4 production of a single flower, 0.02-0.3 nL/g/h) (Harren et al., 1990b).

time). This

τ

following instruments: • lock-in amplifier;

• laser powermeter; • gas flowmeter.

• chopper;

**2.5 Data acquisition and processing** 

We designed and characterized two experimental set-ups with the PA cell in an external configuration: the first one with a low power CO2 laser where the saturation effects are negligible, and a second one with a high power CO2 laser where the saturation effects are important and have to be taken into consideration. We measured all relevant features and determined all quantities used in literature to compare our findings with the best results reported in the previous published papers. All measurements were done in nitrogen and ethylene with the 10P(14) line of a cw CO2 laser. We succeeded to obtain a minimum detectable concentration better by more than a factor of 10 compared to the best results previously reported in the literature.

To investigate the possibility of using a high power laser in an extracavity configuration, we introduced in the experimental set-up a commercial CO2 laser (Coherent GEM SELECT 50TM laser) with output power till 50 W and tunable on 73 different lines (Dumitras et al., 2010). When this laser is tuned on 10P(14) line, the maximum power delivered after chopper and focusing lens is 14.5 W.

To change the laser power inside the PA cell we tried either to modify the input power in the laser (RF power supply) or to introduce a beam splitter in the path of the laser beam. Unfortunately, both methods change significantly the beam path inside the PA cell, thus perturbing unacceptably the results of the measurements. The waveguide laser has a poor beam pointing because it has a short optical resonator and the variation of the transverse RF excitation modifies the laser gain profile.

The saturation effects at high laser power were investigated by using the method of truncation of a gaussian laser beam. This approach was possible because the laser beam is very close to a gaussian beam (M2 < 1.1). The method consists in passing the beam through an aperture with known diameter (Fig. 23). To avoid deformations owing to heating, we used water cooled metallic diaphragms with diameters between 1.42 mm and 5.03 mm. All diaphragms were placed at a distance of 450 mm from the beam waist of the laser.

When a gaussian beam of radius *w* is truncated by an aperture of radius *a* (Fig. 24), the power transmitted through the aperture is *T* = *P*(*a*)/*P* = 1 – exp(-2*a*2/*w*2). When 2*a* = 2*w*, *T* ≅ 86%, that is 86% of the laser power is transmitted through the aperture (this is known as 86% criterion). When 2*a* = π*w*, *T* ≅ 99%, that is 99% of the laser power is transmitted through the aperture and we have the 99% criterion. This formula offers a possibility to measure precisely the diameter of the laser beam at the position of the diaphragm. By knowing the radius of the aperture (*a*) and by measuring the laser power before and after the aperture (*P*

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 77

a factor of 6. We can observe that the saturation effects manifest immediately as the laser power is increased more than 2 W. The cause of the saturation is that the collisional relaxation to de-excite the molecules cannot keep up with the excitation rate by the laser beam intensity. By increasing laser intensity, the excitation pumping rate of the molecules grows higher and a molecule is more likely to absorb a nearby photon before it relaxes to the ground state. So, as the number of molecules in the excited state increases, the number of molecules which can absorb laser radiation is reduced. That is why we introduced a supplementary scale in Fig. 27, representing the cell responsivity function on the intensity of the focused beam inside the PA cell. A thorough analysis of the laser beam propagation through the focusing lens and in the PA cell was done (Dumitras et al., 2007). For a lens with a focal length of 400 mm, we got in this case a beam diameter at beam waist of 0.89 mm. It can be remarked that saturation starts at laser intensities greater than 0.5 kW/cm2. This result shows that saturation effects manifest even at low laser intensities. Previously, Harren et al. (Harren et al., 1990a) observed a strong saturation at a much higher intensity (200 kW/cm2; the laser power was ten times higher and the beam area was ten times smaller than in our case at 13 W), when the PA cell was placed intracavity of a waveguide CO2 laser. Our conclusion is that high power lasers could be used in PA systems, but saturation effects should be taken into consideration (by making a correlation between the PA cell

responsivity and the working laser intensity, as in Fig. 27).

Fig. 26. Variation of laser power function on diaphragm aperture size.

on laser power and on laser intensity in the focal spot.

Fig. 27. Saturation effects measured as the dependence of the PA cell responsivity function

An important question is: what happens with the system noises when a diaphragm is introduced in the laser beam path? We proceeded to record the coherent PA background

and *P*(*a*), respectively), we can determine immediately the radius of the laser beam (*w*). As it can be seen in Fig. 25, by using five different diaphragms, the resulting average diameter is 2*w* = (7.09 ± 0.2) mm, with an error of less than 3%.

Fig. 23. Attenuation of a laser beam by a diaphragm.

Fig. 24. Truncation of a gaussian laser beam.

Fig. 25. Measurement of laser beam diameter by the method of truncation.

Figure 26 shows the attenuation of the laser beam when different diaphragms were placed in its path. The solid line is the theoretical curve given by the above equation. By introducing these five diaphragms, the laser power was varied between less than 2 W and near 10 W. In this way, we were able to investigate the laser power range from low power where saturation effects have no significance till high power where saturation effects manifest strongly.

We investigated the influence of saturation by measuring the dependence of the PA cell responsivity function on laser power (Fig. 27). From low laser power regime (under 2 W) where the saturation effects are not important till high power regime (14.5 W, no diaphragm), the PA cell responsivity decreases from 312 V cm/W till 52 V cm/W, that is by

and *P*(*a*), respectively), we can determine immediately the radius of the laser beam (*w*). As it can be seen in Fig. 25, by using five different diaphragms, the resulting average diameter is

2*w* = (7.09 ± 0.2) mm, with an error of less than 3%.

Fig. 23. Attenuation of a laser beam by a diaphragm.

Fig. 24. Truncation of a gaussian laser beam.

manifest strongly.

Fig. 25. Measurement of laser beam diameter by the method of truncation.

Figure 26 shows the attenuation of the laser beam when different diaphragms were placed in its path. The solid line is the theoretical curve given by the above equation. By introducing these five diaphragms, the laser power was varied between less than 2 W and near 10 W. In this way, we were able to investigate the laser power range from low power where saturation effects have no significance till high power where saturation effects

We investigated the influence of saturation by measuring the dependence of the PA cell responsivity function on laser power (Fig. 27). From low laser power regime (under 2 W) where the saturation effects are not important till high power regime (14.5 W, no diaphragm), the PA cell responsivity decreases from 312 V cm/W till 52 V cm/W, that is by a factor of 6. We can observe that the saturation effects manifest immediately as the laser power is increased more than 2 W. The cause of the saturation is that the collisional relaxation to de-excite the molecules cannot keep up with the excitation rate by the laser beam intensity. By increasing laser intensity, the excitation pumping rate of the molecules grows higher and a molecule is more likely to absorb a nearby photon before it relaxes to the ground state. So, as the number of molecules in the excited state increases, the number of molecules which can absorb laser radiation is reduced. That is why we introduced a supplementary scale in Fig. 27, representing the cell responsivity function on the intensity of the focused beam inside the PA cell. A thorough analysis of the laser beam propagation through the focusing lens and in the PA cell was done (Dumitras et al., 2007). For a lens with a focal length of 400 mm, we got in this case a beam diameter at beam waist of 0.89 mm. It can be remarked that saturation starts at laser intensities greater than 0.5 kW/cm2. This result shows that saturation effects manifest even at low laser intensities. Previously, Harren et al. (Harren et al., 1990a) observed a strong saturation at a much higher intensity (200 kW/cm2; the laser power was ten times higher and the beam area was ten times smaller than in our case at 13 W), when the PA cell was placed intracavity of a waveguide CO2 laser. Our conclusion is that high power lasers could be used in PA systems, but saturation effects should be taken into consideration (by making a correlation between the PA cell responsivity and the working laser intensity, as in Fig. 27).

Fig. 26. Variation of laser power function on diaphragm aperture size.

Fig. 27. Saturation effects measured as the dependence of the PA cell responsivity function on laser power and on laser intensity in the focal spot.

An important question is: what happens with the system noises when a diaphragm is introduced in the laser beam path? We proceeded to record the coherent PA background

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 79

of 18 in the second case. In a molecular gas with a high absorption coefficient (e.g. SF6), the

Interference of other absorbing substances may impair the theoretical detection limit in a multicomponent analysis of the real samples. Such interference may be caused by other molecular systems present in the environment or substances that are entrained by the carrier flux. If an interfering species is present in the environment, its effect can be minimized by either the introduction of scrubbers and cryogenic traps or the use of dual beam techniques

The CO2 laser spectral outputs occur in the wavelength region where a large number of compounds possess strong absorption features and where absorptive interferences from water vapors, carbon dioxide, and other major atmospheric gaseous components may

The breath air is a mixture of nitrogen, oxygen, carbon dioxide, water, inert gases, and traces of VOCs (Table 5). The matrix elements in breath air vary widely from person to person, both qualitatively and quantitatively, particularly for VOCs. More than 1000 trace VOCs have been distinguished in human breath air, at concentrations from ppmV to pptV levels. Only a small number of VOCs are common to everyone, including isoprene, acetone, ethane, and methanol, which are products of core metabolic processes. In addition to these VOCs, exhaled NO, H2, NH3, and CO are related to health condition and can reflect a potential disease of the individual or a recent exposure to a drug or an environmental pollutant. **Component Inhaled air (%) Exhaled air (%)** 

> Nitrogen 78.0 78.0 Oxygen 21.0 16.0 Carbon dioxide 0.04 3.0-5.0 Argon 0.93 1.0 Water 2.0 5.0-6.0

> > 0.01

Table 5. Concentration of different components in inhaled and exhaled air.

scrubber filled with a chemical active agent, KOH in our case (Bratu et al., 2011).

A healthy adult human has a respiratory rate of 12-15 breaths/min at rest, inspiring and expiring 6-8 L of air per minute. O2 enters the blood and CO2 is eliminated through the alveoli. When the end-tidal concentration of CO2 in healthy persons is measured, a large change of CO2 concentration is observed between the inhaled air (~ 0.04%) and the exhaled air (~ 4%). The exact amount of exhaled CO2 varies according to the fitness, energy expenditure and diet of a particular person, with regular values of 3-5%. Due to this high concentration of carbon dioxide in the breath and because CO2 laser lines are absorbed by this gas, it is necessary to remove most of the carbon dioxide from the exhaled air by introducing a

Due to the exact coincidence of the CO2 vibrational-rotational transitions with the CO2 laser lines, carbon dioxide at high concentration in comparison with trace gases like C2H4 is

250x10-9 (250 ppb) 6x10-9 (6 ppb)

minimum detectable concentration could be as low as 9 pptV.

**2.7 Removal of interfering gases** 

using two photoacoustic (PA) cells.

Other ammonia ethylene

influence the measurements.

signal on laser power (with and without a diaphragm) and the results are given in Fig. 28. The background signal is huge when a diaphragm is inserted into the system, being of more than 50 times higher than in the case that no diaphragm limits the laser beam. Truncation distorts the intensity pattern of the transmitted beam in both the near-field (Fresnel) and farfield (Fraunhofer) regions. The diffraction effects on an ideal gaussian beam of a sharpedged circular aperture even as large as 2*a* = 2*w* (99% criterion) will cause near-field diffraction ripples with an intensity variation Δ*I*/*I* ≅ ± 17% in the near field, along with a peak intensity reduction of ≅ 17% on axis in the far field (Siegman, 1986). In conclusion, the method of diaphragms used to measure the saturation effects is applicable, but in a laser PA system used in practice an aperture has never to be introduced.

Fig. 28. Dependence of coherent PA background signal on laser power (with and without a diaphragm).



Table 4. Comparison of low vs. high laser power configurations: 10P(14) laser line in N2\* (α *=* 0 cm-1atm-1), C2H4\*\* (α *=* 30.4 cm-1atm-1), and SF6\*\*\* (α *=* 686 cm-1atm-1).

To this date, the minimum detectable concentrations obtained by us in ethylene (0.9 ppbV with a low power laser and 0.21 ppbV with a high power laser) are the best values reported in the literature, improving this parameter by a factor of 4.2 in the first case and by a factor of 18 in the second case. In a molecular gas with a high absorption coefficient (e.g. SF6), the minimum detectable concentration could be as low as 9 pptV.

#### **2.7 Removal of interfering gases**

78 CO2 Laser – Optimisation and Application

signal on laser power (with and without a diaphragm) and the results are given in Fig. 28. The background signal is huge when a diaphragm is inserted into the system, being of more than 50 times higher than in the case that no diaphragm limits the laser beam. Truncation distorts the intensity pattern of the transmitted beam in both the near-field (Fresnel) and farfield (Fraunhofer) regions. The diffraction effects on an ideal gaussian beam of a sharpedged circular aperture even as large as 2*a* = 2*w* (99% criterion) will cause near-field diffraction ripples with an intensity variation Δ*I*/*I* ≅ ± 17% in the near field, along with a peak intensity reduction of ≅ 17% on axis in the far field (Siegman, 1986). In conclusion, the method of diaphragms used to measure the saturation effects is applicable, but in a laser PA

Fig. 28. Dependence of coherent PA background signal on laser power (with and without a

A comparison of low laser power vs. high laser power configurations is presented in Table 4. It seems resonable that high power lasers could be used in PA instruments provided that

**Parameter Low power High power Factor**  Output laser power (W) 5.5 33 > 6.0 Average laser power (at cell exit) (W) 2.2 14.5 > 6.6

Cell responsivity *R* (V cm/W)\*\* 280 312 > 1.1 Signal saturation\*\* Small Very high > 6.0

*min* (ppbV)\*\*

0.9 0.04

α

*min* (cm-1)\*\* 2.7x10-8 0.64x10-8 < 4.3

Better 4.2 x Better 18 x

 *=* 686 cm-1atm-1).

*min* (ppbV)\*\*\*

Table 4. Comparison of low vs. high laser power configurations: 10P(14) laser line in N2\* (

To this date, the minimum detectable concentrations obtained by us in ethylene (0.9 ppbV with a low power laser and 0.21 ppbV with a high power laser) are the best values reported in the literature, improving this parameter by a factor of 4.2 in the first case and by a factor

 *=* 30.4 cm-1atm-1), and SF6\*\*\* (

α

2.7 0.7 < 4.0

0.21 0.009 < 4.3

α

system used in practice an aperture has never to be introduced.

the saturation is considered and compensated.

Coherent photoacoustic background signal

Best value previously reported (Harren et al., 1990)

α

Minimum detectable concentration *c*

 *c*

Minimum detectable absorptivity

*min* = 3.8 ppbV)\*\*

*=* 0 cm-1atm-1), C2H4\*\* (

diaphragm).

(µV/W)\*

(*c*

Interference of other absorbing substances may impair the theoretical detection limit in a multicomponent analysis of the real samples. Such interference may be caused by other molecular systems present in the environment or substances that are entrained by the carrier flux. If an interfering species is present in the environment, its effect can be minimized by either the introduction of scrubbers and cryogenic traps or the use of dual beam techniques using two photoacoustic (PA) cells.

The CO2 laser spectral outputs occur in the wavelength region where a large number of compounds possess strong absorption features and where absorptive interferences from water vapors, carbon dioxide, and other major atmospheric gaseous components may influence the measurements.

The breath air is a mixture of nitrogen, oxygen, carbon dioxide, water, inert gases, and traces of VOCs (Table 5). The matrix elements in breath air vary widely from person to person, both qualitatively and quantitatively, particularly for VOCs. More than 1000 trace VOCs have been distinguished in human breath air, at concentrations from ppmV to pptV levels. Only a small number of VOCs are common to everyone, including isoprene, acetone, ethane, and methanol, which are products of core metabolic processes. In addition to these VOCs, exhaled NO, H2, NH3, and CO are related to health condition and can reflect a potential disease of the individual or a recent exposure to a drug or an environmental pollutant.


Table 5. Concentration of different components in inhaled and exhaled air.

A healthy adult human has a respiratory rate of 12-15 breaths/min at rest, inspiring and expiring 6-8 L of air per minute. O2 enters the blood and CO2 is eliminated through the alveoli. When the end-tidal concentration of CO2 in healthy persons is measured, a large change of CO2 concentration is observed between the inhaled air (~ 0.04%) and the exhaled air (~ 4%). The exact amount of exhaled CO2 varies according to the fitness, energy expenditure and diet of a particular person, with regular values of 3-5%. Due to this high concentration of carbon dioxide in the breath and because CO2 laser lines are absorbed by this gas, it is necessary to remove most of the carbon dioxide from the exhaled air by introducing a scrubber filled with a chemical active agent, KOH in our case (Bratu et al., 2011).

Due to the exact coincidence of the CO2 vibrational-rotational transitions with the CO2 laser lines, carbon dioxide at high concentration in comparison with trace gases like C2H4 is

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 81

solution with very low chloride content. It reacts violently with acid and it is corrosive in moist air toward metals such as zinc, aluminum, tin and lead, forming a combustible, explosive gas. It absorbs rapidly carbon dioxide and water from air. Cautions must be taken when used because the inhaled dust is caustic and irritant, and touching skin or clothes

We have investigated the efficiency of the KOH scrubber using four recipients with different volumes (13 cm3, 45 cm3, 120 cm3, and 213 cm3, respectively), and we found out what type has to be used in order to reduce efficiently the amount of CO2 from the exhaled air sample (Bratu et al., 2011). The KOH scrubber must neither change the ethylene concentration level, nor introduce new interfering gases. The measurements were made each time on the same person (healthy female, 30 years old) and with a new filling of KOH pellets. The gas from the sample bag was transferred into the PA cell at a controlled flow rate of 300 sccm (only for the 13 cm3 trap) or 600 sccm, in order to ensure a sufficient time of flow in the scrubber column and to minimize any tendency for the vapor to stick to the cell walls or any other effects of internal outgassing of contaminants, which would otherwise lead to increase background signals during an experimental run. The typical resulting final pressure inside the PA cell was around 700 mbar and the corresponding responsivity was 170 cmV/W (see

The experimental results without the KOH scrubber showed an equivalent ethylene absorption concentration of 2750 ppbV (with alveolar air collection) and 2350 ppbV (with mixt expiratory air collection), representing mainly the contribution of ethylene, carbon dioxide, water vapors and ammonia to the absorption of 10P(14) CO2 laser line (Fig. 29). We tested the efficiency of traps filled with KOH and having different volumes (between 13 cm3

For the first measurement we used a trap with a small volume of 13 cm3 of KOH scrubber, and we obtained a decrease of the PA signal down to 1-3 mV. The equivalent ethylene concentration was 435 ppb and 240 ppb, respectively (alveolar air collection vs. mixt expiratory air collection), indicating that the CO2 concentration was reduced by factors of 6.3

could lead to less or more severe chemical burnings.

and 213 cm3) in removing CO2 from exhaled air.

Fig. 29. Efficiency of KOH traps for CO2 removal from exhaled air.

Fig. 3, Part I).

inevitably excited by CO2 laser radiation and the related photoacoustic signal may exceed the trace signal by many orders of magnitude. The absorption coefficient increases strongly with temperature, but it is independent of the CO2 concentration over a wide range. Ethylene can be excited by the 10P(14) line of the CO2 laser, where the maximum absorption coefficient α(C2H4) has a value of 30.4 cm-1 atm-1 and ammonia by the 9R(30) line where α(NH3) = 56 cm-1 atm-1 (Dumitras et al., 2011). A 4% concentration of CO2 has an absorption strength comparable to 2760 ppbV of C2H4 (at the 10P(14) laser line, α(CO2) = 2.1x10-3 atm-1cm-1 and *c*(C2H4) = *c*(CO2)α(CO2)/α(C2H4). This equivalent ethylene concentration was found also experimentally (see Fig. 29, measurement without trap). So, the photoacoustic signal is 100 times higher owing to exhaled carbon dioxide in comparison with the usual concentration of ethylene in exhaled air. Similarly, at the 9R(30) line of CO2 laser, the same concentration of CO2 has an absorption coefficient equal to that of 1500 ppbV of NH3. This value is also considerably higher (6 times) compared to the real range of breath concentration which is situated approximately at 250 ppb for ammonia.

Water vapor exhibits a broad continuum with occasional weak lines in the frequency range of the CO2 laser (for H2O at the 10P (14) laser line, α(H2O) = 2.85x10-5 atm-1cm-1). The two dominant peaks are the absorption lines on 10R(20) and the most favorable one for ambient air measurement, the 10P(40) laser transition. A 5% concentration of H2O has an absorption strength comparable to 46.9 ppbV of C2H4, that is the normal concentration of water in exhaled air has approximately the same influence in the photoacoustic signal as the normal concentration of ethylene.

Due to the additive character of the photoacoustic signal under normal pressure conditions, the presence of a large amount of water vapor and carbon dioxide impedes C2H4 detection in the low-concentration range (ppbV). Consequently, some means of selective spectral discrimination is required if ethylene is to be detected interference free in the matrix of absorbing gases. There are several ways to overcome this problem. One way is to remove CO2 from the flowing sample by absorption on a KOH-based scrubber inserted between the sampling cell and the PA cell. Taking into account the nature of the specific chemical reactions involved in the CO2 removal by KOH, a certain amount of water is also absorbed from the sample passing the scrubber. In this way, concentrations below 1 ppmV CO2 (equivalent to a concentration of 0.07 ppbV of C2H4) can be achieved without influencing the C2H4 or NH3 concentration.

Before entering the photoacoustic cell, the gas mixture passes through a KOH scrubber (Fig. 18), which retains most of the interfering carbon dioxide. The removal of CO2 is limited to the absorbent surface of the pellets. Hence, the larger the surface area or the more porous the granular solid, the larger the capacity of the system to absorb CO2. At the same time, the flow resistance varies inversely proportional to the particle size. Large particles offer less resistance, but have the disadvantage of providing a smaller total area for reaction. The granules of KOH that we used were typically Merck KOH pellets GR for analysis, with approximate dimensions of 10x7x2 mm. When residence time (time of contact between CO2 and absorbent) is less than 1 second, CO2 absorption capacity is greatly reduced, so we introduced flow controllers in order to ensure this pre-requisite.

Potassiun hydroxide is a caustic compound of strong alkaline chemical, dissolving readily in water, giving off much heat and forming a caustic solution. It is a white deliquescent solid in the form of pellets obtained by concentration of purified electrolytic potassium hydroxide

inevitably excited by CO2 laser radiation and the related photoacoustic signal may exceed the trace signal by many orders of magnitude. The absorption coefficient increases strongly with temperature, but it is independent of the CO2 concentration over a wide range. Ethylene can be excited by the 10P(14) line of the CO2 laser, where the maximum absorption

(NH3) = 56 cm-1 atm-1 (Dumitras et al., 2011). A 4% concentration of CO2 has an absorption

found also experimentally (see Fig. 29, measurement without trap). So, the photoacoustic signal is 100 times higher owing to exhaled carbon dioxide in comparison with the usual concentration of ethylene in exhaled air. Similarly, at the 9R(30) line of CO2 laser, the same concentration of CO2 has an absorption coefficient equal to that of 1500 ppbV of NH3. This value is also considerably higher (6 times) compared to the real range of breath

Water vapor exhibits a broad continuum with occasional weak lines in the frequency range

dominant peaks are the absorption lines on 10R(20) and the most favorable one for ambient air measurement, the 10P(40) laser transition. A 5% concentration of H2O has an absorption strength comparable to 46.9 ppbV of C2H4, that is the normal concentration of water in exhaled air has approximately the same influence in the photoacoustic signal as the normal

Due to the additive character of the photoacoustic signal under normal pressure conditions, the presence of a large amount of water vapor and carbon dioxide impedes C2H4 detection in the low-concentration range (ppbV). Consequently, some means of selective spectral discrimination is required if ethylene is to be detected interference free in the matrix of absorbing gases. There are several ways to overcome this problem. One way is to remove CO2 from the flowing sample by absorption on a KOH-based scrubber inserted between the sampling cell and the PA cell. Taking into account the nature of the specific chemical reactions involved in the CO2 removal by KOH, a certain amount of water is also absorbed from the sample passing the scrubber. In this way, concentrations below 1 ppmV CO2 (equivalent to a concentration of 0.07 ppbV of C2H4) can be achieved without influencing the

Before entering the photoacoustic cell, the gas mixture passes through a KOH scrubber (Fig. 18), which retains most of the interfering carbon dioxide. The removal of CO2 is limited to the absorbent surface of the pellets. Hence, the larger the surface area or the more porous the granular solid, the larger the capacity of the system to absorb CO2. At the same time, the flow resistance varies inversely proportional to the particle size. Large particles offer less resistance, but have the disadvantage of providing a smaller total area for reaction. The granules of KOH that we used were typically Merck KOH pellets GR for analysis, with approximate dimensions of 10x7x2 mm. When residence time (time of contact between CO2 and absorbent) is less than 1 second, CO2 absorption capacity is greatly reduced, so we

Potassiun hydroxide is a caustic compound of strong alkaline chemical, dissolving readily in water, giving off much heat and forming a caustic solution. It is a white deliquescent solid in the form of pellets obtained by concentration of purified electrolytic potassium hydroxide

introduced flow controllers in order to ensure this pre-requisite.

strength comparable to 2760 ppbV of C2H4 (at the 10P(14) laser line,

concentration which is situated approximately at 250 ppb for ammonia.

α(CO2)/α

of the CO2 laser (for H2O at the 10P (14) laser line,

(C2H4) has a value of 30.4 cm-1 atm-1 and ammonia by the 9R(30) line where

α

α

(H2O) = 2.85x10-5 atm-1cm-1). The two

(C2H4). This equivalent ethylene concentration was

(CO2) = 2.1x10-3 atm-

coefficient

α

α

1cm-1 and *c*(C2H4) = *c*(CO2)

concentration of ethylene.

C2H4 or NH3 concentration.

solution with very low chloride content. It reacts violently with acid and it is corrosive in moist air toward metals such as zinc, aluminum, tin and lead, forming a combustible, explosive gas. It absorbs rapidly carbon dioxide and water from air. Cautions must be taken when used because the inhaled dust is caustic and irritant, and touching skin or clothes could lead to less or more severe chemical burnings.

We have investigated the efficiency of the KOH scrubber using four recipients with different volumes (13 cm3, 45 cm3, 120 cm3, and 213 cm3, respectively), and we found out what type has to be used in order to reduce efficiently the amount of CO2 from the exhaled air sample (Bratu et al., 2011). The KOH scrubber must neither change the ethylene concentration level, nor introduce new interfering gases. The measurements were made each time on the same person (healthy female, 30 years old) and with a new filling of KOH pellets. The gas from the sample bag was transferred into the PA cell at a controlled flow rate of 300 sccm (only for the 13 cm3 trap) or 600 sccm, in order to ensure a sufficient time of flow in the scrubber column and to minimize any tendency for the vapor to stick to the cell walls or any other effects of internal outgassing of contaminants, which would otherwise lead to increase background signals during an experimental run. The typical resulting final pressure inside the PA cell was around 700 mbar and the corresponding responsivity was 170 cmV/W (see Fig. 3, Part I).

The experimental results without the KOH scrubber showed an equivalent ethylene absorption concentration of 2750 ppbV (with alveolar air collection) and 2350 ppbV (with mixt expiratory air collection), representing mainly the contribution of ethylene, carbon dioxide, water vapors and ammonia to the absorption of 10P(14) CO2 laser line (Fig. 29). We tested the efficiency of traps filled with KOH and having different volumes (between 13 cm3 and 213 cm3) in removing CO2 from exhaled air.

Fig. 29. Efficiency of KOH traps for CO2 removal from exhaled air.

For the first measurement we used a trap with a small volume of 13 cm3 of KOH scrubber, and we obtained a decrease of the PA signal down to 1-3 mV. The equivalent ethylene concentration was 435 ppb and 240 ppb, respectively (alveolar air collection vs. mixt expiratory air collection), indicating that the CO2 concentration was reduced by factors of 6.3

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 83

Fig. 30. Decrease of KOH trap efficiency when the same fill was used for multiple

The nonlinearity of the CO2 removal could be explained by the mechanism of the chemical reactions. First, the CO2 combines with the water vapors present in the exhaled air in the

 CO2 + H2O H2CO3. (6) Further, the last one combines with the KOH, creating potassium carbonate and water, and

 H2CO3 + 2KOH K2CO3 + 2H2O + Energy. (7) In the same time, K2CO3 is a highly hygroscopic compound with a retaining capacity of 0.2 g

The water is of high importance in limiting the rate of CO2 absorption. High CO2 concentrations entering the KOH absorber generates large quantities of water, because the reaction (7) is producing water. We know that the absorption rate is greater thanks to the film of moisture coating the pellets, but the same film impedes the access to the active potassium hydroxide pellet volume. More dedicated studies should be made in order to

In conclusion, we determined experimentally that in the process of CO2 removal from the breath air samples, a quantity of minimum 120 cm3 KOH pellets should be used for a sampling bag of 750 mL in order to keep the detection of ethylene and ammonia traces free of CO2 interference. It should be mentioned that this volume of 120 cm3 must be reconsidered for sample bags with a greater volume (> 750 mL) or when the gas transfer rate

Based on our experience, we summarize a list of actions to obtain a minimum detectable

H2O/1 g K2CO3, so the generated water will be only partially returned in the circuit.

establish the moisture content for an optimum rate of absorption.

from the bag to the PA cell is larger (> 600 sccm).

concentration (*cmin*) as low as possible (Dumitras et al., 2010):

**2.8 Recipe for an optimum PA system** 

measurements.

form of carbonic acid:

releasing a small amount of heat:

and 9.8, respectively. Only in the case of this trap we observed a peculiar behaviour. Even if the laser power is constant, the PA signal and consequently the equivalent ethylene concentration increases in time after transfering the gas sample in PA cell. The increase of concentration starts from 50 ppbV and continues until it stabilizes at a level of 435/240 ppbV (after 10-15 minutes). It is known that C2H4 (28.05 g/mol molar mass) is lighter than CO2 (44.0099 g/mol molar mass). Because of that, we can say that after passing the KOH scrubber, first C2H4 enters in the PA cell and then CO2 when the trap is no longer effective. So, at the beginning, we measured only the C2H4 concentration and then CO2 starts to strongly interfere in absorption. It is possible that due to the geometry of the cell, a longer time is required in order to attain the total homogeneity of the molecules inside the resonant tube of the cell, but this is not advantageous for repeated measurements.

Larger KOH traps proved to be more efficient in removal of CO2 from the exhaled air. For the traps with volumes of 45 cm3, 120 cm3, and 213 cm3, respectively, the measured equivalent ethylene concentrations were 41.5/23.6 ppbV, 30/10.8 ppbV, and 26.8/9.1 ppbV, respectively. For larger traps (120 cm3 and 213 cm3), approximately same results were obtained, indicating that most of the CO2 was removed. By using larger traps, a higher transfer rate of the gas mixture in the PA cell is possible, doubling the flow rate to 600 sccm.

For the two largest volumes, we succeeded to reduce the CO2 content from the exhaled air at a level influencing no more the C2H4 and NH3 concentration values, fact proved by the constant evolution in time of all parameters. Therefore, the trap is effective only for a enough large amount of KOH pellets. We found that a minimum volume of 120 cm3 of KOH scrubber and a transfer rate of 600 sccm were optimum to insure the required efficiency.

Analyzing the four cases when we inserted the scrubber, the dependence between the removed content of CO2 and the used KOH quantity proved to be nonlinear, as one could expect. If we consider the content of the sample totally free of CO2 after passing through the 213 cm3 and 120 cm3 KOH traps, we calculated a residual content of CO2 in alveolar collection of 0.58% (5800 ppm) for the 13 cm3 trap and of 0.016% (160 ppm) for the 45 cm3 trap (less than half of the CO2 concentration in the inhaled air).

We measured also the efficiency of the KOH scrubber when it is used for multiple measurements (Fig. 30). A clear saturation effect is evident: the KOH scrubber is not anymore efficient when the same fill is used for multiple runs (it cannot absorb completely the CO2 from the gas mixture). In the case of alveolar collection, the equivalent ethylene concentration increases by 2.3 times for the second run, by 2.6 times for the third run and by 3.4 times for the fourth run. When we measured the mixed expiratory collection, this saturation effect is even larger: the equivalent ethylene concentration increases by 2.4 times for the second run, by 8.5 times for the third run and by 20.2 times for the fourth run. The conclusion is that a new fill of KOH scrubber must be introduced after each measurement.

The lungs and airways are always moist, and inspired gas is rapidly saturated with water vapor in the upper segments of the respiratory system. The temperature in the airways and lungs is most identical with deep body temperature (approximately 37oC); at this temperature water vapor has a partial pressure of 47 torr (~6.2%). The increased saturation found at the third and fourth run for mixed expiratory collection is explained by a higher quantity of water vapors in exhaled breath (originating both from lungs and from upper segments of the respiratory system).

and 9.8, respectively. Only in the case of this trap we observed a peculiar behaviour. Even if the laser power is constant, the PA signal and consequently the equivalent ethylene concentration increases in time after transfering the gas sample in PA cell. The increase of concentration starts from 50 ppbV and continues until it stabilizes at a level of 435/240 ppbV (after 10-15 minutes). It is known that C2H4 (28.05 g/mol molar mass) is lighter than CO2 (44.0099 g/mol molar mass). Because of that, we can say that after passing the KOH scrubber, first C2H4 enters in the PA cell and then CO2 when the trap is no longer effective. So, at the beginning, we measured only the C2H4 concentration and then CO2 starts to strongly interfere in absorption. It is possible that due to the geometry of the cell, a longer time is required in order to attain the total homogeneity of the molecules inside the resonant

Larger KOH traps proved to be more efficient in removal of CO2 from the exhaled air. For the traps with volumes of 45 cm3, 120 cm3, and 213 cm3, respectively, the measured equivalent ethylene concentrations were 41.5/23.6 ppbV, 30/10.8 ppbV, and 26.8/9.1 ppbV, respectively. For larger traps (120 cm3 and 213 cm3), approximately same results were obtained, indicating that most of the CO2 was removed. By using larger traps, a higher transfer rate of the gas mixture in the PA cell is possible, doubling the flow rate to 600 sccm. For the two largest volumes, we succeeded to reduce the CO2 content from the exhaled air at a level influencing no more the C2H4 and NH3 concentration values, fact proved by the constant evolution in time of all parameters. Therefore, the trap is effective only for a enough large amount of KOH pellets. We found that a minimum volume of 120 cm3 of KOH scrubber and a transfer rate of 600 sccm were optimum to insure the required efficiency.

Analyzing the four cases when we inserted the scrubber, the dependence between the removed content of CO2 and the used KOH quantity proved to be nonlinear, as one could expect. If we consider the content of the sample totally free of CO2 after passing through the 213 cm3 and 120 cm3 KOH traps, we calculated a residual content of CO2 in alveolar collection of 0.58% (5800 ppm) for the 13 cm3 trap and of 0.016% (160 ppm) for the 45 cm3

We measured also the efficiency of the KOH scrubber when it is used for multiple measurements (Fig. 30). A clear saturation effect is evident: the KOH scrubber is not anymore efficient when the same fill is used for multiple runs (it cannot absorb completely the CO2 from the gas mixture). In the case of alveolar collection, the equivalent ethylene concentration increases by 2.3 times for the second run, by 2.6 times for the third run and by 3.4 times for the fourth run. When we measured the mixed expiratory collection, this saturation effect is even larger: the equivalent ethylene concentration increases by 2.4 times for the second run, by 8.5 times for the third run and by 20.2 times for the fourth run. The conclusion is that a new fill of KOH scrubber must be introduced after each measurement. The lungs and airways are always moist, and inspired gas is rapidly saturated with water vapor in the upper segments of the respiratory system. The temperature in the airways and lungs is most identical with deep body temperature (approximately 37oC); at this temperature water vapor has a partial pressure of 47 torr (~6.2%). The increased saturation found at the third and fourth run for mixed expiratory collection is explained by a higher quantity of water vapors in exhaled breath (originating both from lungs and from upper

tube of the cell, but this is not advantageous for repeated measurements.

trap (less than half of the CO2 concentration in the inhaled air).

segments of the respiratory system).

Fig. 30. Decrease of KOH trap efficiency when the same fill was used for multiple measurements.

The nonlinearity of the CO2 removal could be explained by the mechanism of the chemical reactions. First, the CO2 combines with the water vapors present in the exhaled air in the form of carbonic acid:

$$\text{CO} \star \text{H}\_2\text{O} \Leftrightarrow \text{H}\_2\text{CO} \tag{6}$$

Further, the last one combines with the KOH, creating potassium carbonate and water, and releasing a small amount of heat:

$$\text{H}\_2\text{CO}\_3 + 2\text{KOH} \Leftrightarrow \text{K}\_2\text{CO}\_3 + 2\text{H}\_2\text{O} + \text{Energy.} \tag{7}$$

In the same time, K2CO3 is a highly hygroscopic compound with a retaining capacity of 0.2 g H2O/1 g K2CO3, so the generated water will be only partially returned in the circuit.

The water is of high importance in limiting the rate of CO2 absorption. High CO2 concentrations entering the KOH absorber generates large quantities of water, because the reaction (7) is producing water. We know that the absorption rate is greater thanks to the film of moisture coating the pellets, but the same film impedes the access to the active potassium hydroxide pellet volume. More dedicated studies should be made in order to establish the moisture content for an optimum rate of absorption.

In conclusion, we determined experimentally that in the process of CO2 removal from the breath air samples, a quantity of minimum 120 cm3 KOH pellets should be used for a sampling bag of 750 mL in order to keep the detection of ethylene and ammonia traces free of CO2 interference. It should be mentioned that this volume of 120 cm3 must be reconsidered for sample bags with a greater volume (> 750 mL) or when the gas transfer rate from the bag to the PA cell is larger (> 600 sccm).

#### **2.8 Recipe for an optimum PA system**

Based on our experience, we summarize a list of actions to obtain a minimum detectable concentration (*cmin*) as low as possible (Dumitras et al., 2010):

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 85

The recipe presented above applied on an extracavity laser PA configuration allowed us to achieve one of the most sensitive PA system with a detection limit of 2.7x10-8 cm-1 for a low power laser or even 0.64x10-8 cm-1 for a high power laser. In this way, the method based on laser photoacoustic spectroscopy became a powerful tool for measurement of trace gases

We have measured precisely the absorption coefficients of ethylene (Dumitras et al., 2007)

The ethylene absorption coefficients for various CO2 laser transitions have been measured in various experiments. Discrepancies as high as ~15% have been found in the absolute IR values observed at many laser transitions. Such discrepancies are typical of many other gases and are partially associated with the difficulty of producing proper gas samples with known concentration levels. Unfortunately, large discrepancies are also found between measurements of the relative spectral signatures (the ratio between absorption coefficients at different wavelengths). Knowledge of the relative spectral signatures rather than absolute ones is sufficient for trace gas identification. We also note that it is rather problematic to obtain highly accurate measurements of the absolute values of the absorption coefficients of gases using the photoacoustic effect. The reason for this is the need of an absolute calibration of the cell. The calibrations cited in the literature are all based on *a priori*  knowledge of the absorption coefficient of a gas at some selected wavelength. However, in

Photoacoustics is emerging as a standard technique for measuring extremely low absorptions independent of the path length and offers a degree of parameter control that cannot be attained by other methods. Radiation absorption by the gas creates a pressure signal which is sensed by the microphone. The resulting signal, processed by a phase sensitive detector, is directly proportional to the absorption coefficient and laser power (or laser power absorbed per unit volume). The sensitivity of the technique is such that absorptions of <10-7 cm-1 can be measured over path lengths of a few tens of centimeters. The small volume of the chamber makes it possible to accurately control the gas parameters,

α

gas or vapor and at a common concentration is called the optoacoustic absorption spectrum or signature and is unique to a combination of vapor and laser. These signatures or "fingerprints" are absolute entities, unique only to the laser frequency and species, which provide the specifics of instrument performance in terms of detection limit and interference

To improve the measurement of ethylene absorption coefficients, a special procedure was followed. Prior to each run, the gas mixture was flowed at 100 sccm for several minutes to stabilize the boundary layer on the cell walls, since a certain amount of adsorption would occur and possibly influence background signals; after this conditioning period, the cell was closed off and used in measurement. For every gas fill with 0.96 ppmV ethylene buffered in pure nitrogen, the responsivity of the cell was determined supposing an absorption

, for all laser wavelengths, for a particular

all cases the absorption coefficient was actually known only to a few percent.

and the system can be operated with static fills or in continuous gas flow mode.

(Dumitras et al., 1996a).

**3.1 Measurement of absorption coefficients** 

The set of values of the absorption coefficients

rejection (Cristescu et al., 2000b).

and ammonia (Dumitras et al., 2011) at CO2 laser wavelengths.

**3. Applications** 


The recipe presented above applied on an extracavity laser PA configuration allowed us to achieve one of the most sensitive PA system with a detection limit of 2.7x10-8 cm-1 for a low power laser or even 0.64x10-8 cm-1 for a high power laser. In this way, the method based on laser photoacoustic spectroscopy became a powerful tool for measurement of trace gases (Dumitras et al., 1996a).

### **3. Applications**

84 CO2 Laser – Optimisation and Application






d. Minimize the coherent acoustic background noise, *ac VN* (caused by the modulation process):








cryogenic trap, respectively, between the sampling cell and the PA cell;

g. Increase the laser power while maintaining the noises at lower values:

intracavity configuration (smaller cavity transmission coefficient);

τ--1/2).



a. Increase the cell constant, *C*:

small diameter (*C* ∝ *r* -1).

amplified by the quality factor, *Q*;

b. Increase the microphone responsivity:

microphones connected in series. c. Minimize the electrical noise, *<sup>e</sup> VN* : - use state-of-the-art lock-in amplifiers; - use longer time averaging ( *<sup>e</sup> VN* ∝


possible polished surfaces);


of the laser beam;

unknown trace gases);

of ethylene).

acoustic band-stop filters (buffer volumes);

reduction less than 2% is obtained if Δ*T* ≤ 4oC);

e. Minimize the coherent PA background signal, *<sup>b</sup> VN* :



#### **3.1 Measurement of absorption coefficients**

We have measured precisely the absorption coefficients of ethylene (Dumitras et al., 2007) and ammonia (Dumitras et al., 2011) at CO2 laser wavelengths.

The ethylene absorption coefficients for various CO2 laser transitions have been measured in various experiments. Discrepancies as high as ~15% have been found in the absolute IR values observed at many laser transitions. Such discrepancies are typical of many other gases and are partially associated with the difficulty of producing proper gas samples with known concentration levels. Unfortunately, large discrepancies are also found between measurements of the relative spectral signatures (the ratio between absorption coefficients at different wavelengths). Knowledge of the relative spectral signatures rather than absolute ones is sufficient for trace gas identification. We also note that it is rather problematic to obtain highly accurate measurements of the absolute values of the absorption coefficients of gases using the photoacoustic effect. The reason for this is the need of an absolute calibration of the cell. The calibrations cited in the literature are all based on *a priori*  knowledge of the absorption coefficient of a gas at some selected wavelength. However, in all cases the absorption coefficient was actually known only to a few percent.

Photoacoustics is emerging as a standard technique for measuring extremely low absorptions independent of the path length and offers a degree of parameter control that cannot be attained by other methods. Radiation absorption by the gas creates a pressure signal which is sensed by the microphone. The resulting signal, processed by a phase sensitive detector, is directly proportional to the absorption coefficient and laser power (or laser power absorbed per unit volume). The sensitivity of the technique is such that absorptions of <10-7 cm-1 can be measured over path lengths of a few tens of centimeters. The small volume of the chamber makes it possible to accurately control the gas parameters, and the system can be operated with static fills or in continuous gas flow mode.

The set of values of the absorption coefficients α, for all laser wavelengths, for a particular gas or vapor and at a common concentration is called the optoacoustic absorption spectrum or signature and is unique to a combination of vapor and laser. These signatures or "fingerprints" are absolute entities, unique only to the laser frequency and species, which provide the specifics of instrument performance in terms of detection limit and interference rejection (Cristescu et al., 2000b).

To improve the measurement of ethylene absorption coefficients, a special procedure was followed. Prior to each run, the gas mixture was flowed at 100 sccm for several minutes to stabilize the boundary layer on the cell walls, since a certain amount of adsorption would occur and possibly influence background signals; after this conditioning period, the cell was closed off and used in measurement. For every gas fill with 0.96 ppmV ethylene buffered in pure nitrogen, the responsivity of the cell was determined supposing an absorption

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 87

Fig. 31. Absorption coefficients of ethylene at CO2 laser wavelengths. The inset shows an

largest discrepancies are recorded for the 9R(28), 9R(30), and 9R(22) laser lines).

5 from other reported data in the case of the CO2 laser 9R lines.

absorption coefficients can also be displayed.

There is general agreement with the results of Brewer et al. (Brewer et al., 1982) for the 0001- 1000 band. The difference between our results and those obtained by the above mentioned authors is less than 10% for the majority of the investigated lines while only for five lines the discrepancy is higher, between 10% and 20%. By contrast, the values determined in the present work are consistently higher in the 0001-0200 band. The difference is larger by 10- 50% for the P branch, while our values in the R branch are higher by a factor of 1.5-5.5 (the

λ(μm)

9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8

10R(34)

9P(30) 9P(34)

10R(24)

10P(36)

10P(24)

10R(6)

10P(6)

10P(14)

C2H4

9.2 9.4 9.6 9.8

9P(10)

9P(18)

9R(10)

9R(18)

9R(30)

The present work was carried out using a methodology which gave the best possible control over the ethylene partial pressure and background signals. The background levels and calibration of the PA cell were checked before and after every experimental run. The present study is considered reliable, particularly in view of the careful attention that was paid to controlling the gas composition and noise signals. No apparent fault could be found with either the apparatus or methodology that would account for the discrepancy by factors of 2-

For the measurement of the absorption coefficients of ammonia (Dumitras et al., 2011), the software user interface allows to record the laser power, the PA signal and the calculated absorption coefficients on different panels**.** The evolution in time of the measurement of the

The gas mixture was flowed at 100 sccm for several minutes to stabilize the boundary layer on the cell walls, since a certain amount of adsorption would occur and possibly influence background signals; after this conditioning period, the cell was closed off and used in measurement. For every gas fill with 10 ppm ammonia buffered in pure nitrogen, the responsivity of the cell was determined supposing an absorption coefficient of 57.12 cm-1atm-1 at 9R(30) laser transition. This is in accordance both to the measurements reported by Brewer & Bruce (Brewer & Bruce, 1978) and by our tests, when the responsivity of the PA system was checked by measuring the well known absorption coefficient of ethylene at 10P(14) line of the CO2 laser. After measurements at all laser lines, the cell responsivity was checked again, to eliminate any possibility of gas desorption during the measurement. The

values at each laser line were obtained by using the measured PA signal and laser power and by knowing precisely the ammonia concentration (10.6 ppm) and the responsivity of the

α

enlarged view of the measurements for the 9-μm band.

α

(cm-1atm-1)

0

1

2

coefficient of 30.4 cm-1atm-1 at 10P(14) laser transition. After measurements at all laser lines, the cell responsivity was checked again, to eliminate any possibility of gas desorption during the measurement. The partial pressure of ethylene was enough to have significant PA signals for all laser lines and low enough to be far away from the saturation regime (observations were only made at a C2H4 concentration of 100 ppmV). The α values at each laser line were obtained from Eq. (29, Part I) using the measured PA signal and laser power (the cell responsivity and ethylene concentration were known). An average over several independent measurements at each line was used to improve the overall accuracy of the results. The values to be presented are thought to be the best published to date.

The absolute magnitudes of the absorption coefficients were calculated as mean values of several independent measurements. An absorption coefficient corresponding to each CO2 laser transition was determined from two sets of 50 different measurements. Every set of measurements was initiated by the frequency stabilization of a given line of the CO2 laser. From one set of measurements to another, the closed loop of the frequency stabilization circuit was interrupted, the laser was tuned again to the top of the gain curve, and then the frequency stabilization was set and checked by watching the long term stability. Inside one set, 50 independent measurements were made at a rate of one per second to assess reproducibility. From one measurement to the next, the error measurement of the absorption coefficient was calculated as the ratio between the maximum difference (maximum value minus minimum value) and the average value. The final value of the ethylene absorption coefficient is given by the arithmetic mean of the two sets of measurements, while the absorption coefficient error is chosen as the larger value of the two sets. The same procedure was applied for every absorption coefficient of ethylene.

To measure the absorption coefficients of ethylene, the software user interface was modified to allow that the laser power, PA signal, and calculated absorption coefficients function on time (or number of measurements) be recorded on different panels.

The results of our measurements for ethylene are given in Fig. 31. Because of the large spacing between laser transitions (1.2-2 cm-1 apart), strong differences of absorption occur. Our results are compared to those of Brewer *et al*. (Brewer et al., 1982) that were also obtained by a photoacoustic method. The difference between the two spectral patterns suggests problems in the measurement techniques (for example, frequency deviation from the laser line center, gas calibration, system purity, linearity, precision) and/or data analysis. The different temperatures and atmospheric pressures at which the measurements were made cannot account for the discrepancies, because Persson *et al*. (Persson et al., 1980) measured a change in absorption coefficient of only 5% at the 10P(14) line for a temperature change of 30oC (negative temperature coefficient), while the changes caused by a pressure difference of 40 Torr are <5% for all CO2 laser wavelengths.

The random coincidence between the emission and absorption lines will be such that some laser lines will lie close to the centers of the absorbing lines and others will be far away in the wings. The result is a spectral representation unique to that molecule. As a consequence of the superposition of different pressure-broadened C2H4 transitions (ν7 vibration), a strong absorption is obtained at the 10P(14) laser line (absorption coefficient of 30.4 cm-1atm-1 at 949.479 cm-1). C2H4 has weaker absorption coefficients at the 10P(12) and 10P(16) CO2 laser transitions (4.36 cm-1atm-1 at 951.192 cm-1 and 5.10 cm-1atm-1 at 947.742 cm-1, respectively). Also, in Fig. 31 ethylene is seen to possess moderately strong absorption profiles within the 9.4-μm band.

coefficient of 30.4 cm-1atm-1 at 10P(14) laser transition. After measurements at all laser lines, the cell responsivity was checked again, to eliminate any possibility of gas desorption during the measurement. The partial pressure of ethylene was enough to have significant PA signals for all laser lines and low enough to be far away from the saturation regime

laser line were obtained from Eq. (29, Part I) using the measured PA signal and laser power (the cell responsivity and ethylene concentration were known). An average over several independent measurements at each line was used to improve the overall accuracy of the

The absolute magnitudes of the absorption coefficients were calculated as mean values of several independent measurements. An absorption coefficient corresponding to each CO2 laser transition was determined from two sets of 50 different measurements. Every set of measurements was initiated by the frequency stabilization of a given line of the CO2 laser. From one set of measurements to another, the closed loop of the frequency stabilization circuit was interrupted, the laser was tuned again to the top of the gain curve, and then the frequency stabilization was set and checked by watching the long term stability. Inside one set, 50 independent measurements were made at a rate of one per second to assess reproducibility. From one measurement to the next, the error measurement of the absorption coefficient was calculated as the ratio between the maximum difference (maximum value minus minimum value) and the average value. The final value of the ethylene absorption coefficient is given by the arithmetic mean of the two sets of measurements, while the absorption coefficient error is chosen as the larger value of the two

α

values at each

(observations were only made at a C2H4 concentration of 100 ppmV). The

results. The values to be presented are thought to be the best published to date.

sets. The same procedure was applied for every absorption coefficient of ethylene.

time (or number of measurements) be recorded on different panels.

difference of 40 Torr are <5% for all CO2 laser wavelengths.

of the superposition of different pressure-broadened C2H4 transitions (

To measure the absorption coefficients of ethylene, the software user interface was modified to allow that the laser power, PA signal, and calculated absorption coefficients function on

The results of our measurements for ethylene are given in Fig. 31. Because of the large spacing between laser transitions (1.2-2 cm-1 apart), strong differences of absorption occur. Our results are compared to those of Brewer *et al*. (Brewer et al., 1982) that were also obtained by a photoacoustic method. The difference between the two spectral patterns suggests problems in the measurement techniques (for example, frequency deviation from the laser line center, gas calibration, system purity, linearity, precision) and/or data analysis. The different temperatures and atmospheric pressures at which the measurements were made cannot account for the discrepancies, because Persson *et al*. (Persson et al., 1980) measured a change in absorption coefficient of only 5% at the 10P(14) line for a temperature change of 30oC (negative temperature coefficient), while the changes caused by a pressure

The random coincidence between the emission and absorption lines will be such that some laser lines will lie close to the centers of the absorbing lines and others will be far away in the wings. The result is a spectral representation unique to that molecule. As a consequence

absorption is obtained at the 10P(14) laser line (absorption coefficient of 30.4 cm-1atm-1 at 949.479 cm-1). C2H4 has weaker absorption coefficients at the 10P(12) and 10P(16) CO2 laser transitions (4.36 cm-1atm-1 at 951.192 cm-1 and 5.10 cm-1atm-1 at 947.742 cm-1, respectively). Also, in Fig. 31 ethylene is seen to possess moderately strong absorption profiles within the 9.4-μm band.

ν

7 vibration), a strong

Fig. 31. Absorption coefficients of ethylene at CO2 laser wavelengths. The inset shows an enlarged view of the measurements for the 9-μm band.

There is general agreement with the results of Brewer et al. (Brewer et al., 1982) for the 0001- 1000 band. The difference between our results and those obtained by the above mentioned authors is less than 10% for the majority of the investigated lines while only for five lines the discrepancy is higher, between 10% and 20%. By contrast, the values determined in the present work are consistently higher in the 0001-0200 band. The difference is larger by 10- 50% for the P branch, while our values in the R branch are higher by a factor of 1.5-5.5 (the largest discrepancies are recorded for the 9R(28), 9R(30), and 9R(22) laser lines).

The present work was carried out using a methodology which gave the best possible control over the ethylene partial pressure and background signals. The background levels and calibration of the PA cell were checked before and after every experimental run. The present study is considered reliable, particularly in view of the careful attention that was paid to controlling the gas composition and noise signals. No apparent fault could be found with either the apparatus or methodology that would account for the discrepancy by factors of 2- 5 from other reported data in the case of the CO2 laser 9R lines.

For the measurement of the absorption coefficients of ammonia (Dumitras et al., 2011), the software user interface allows to record the laser power, the PA signal and the calculated absorption coefficients on different panels**.** The evolution in time of the measurement of the absorption coefficients can also be displayed.

The gas mixture was flowed at 100 sccm for several minutes to stabilize the boundary layer on the cell walls, since a certain amount of adsorption would occur and possibly influence background signals; after this conditioning period, the cell was closed off and used in measurement. For every gas fill with 10 ppm ammonia buffered in pure nitrogen, the responsivity of the cell was determined supposing an absorption coefficient of 57.12 cm-1atm-1 at 9R(30) laser transition. This is in accordance both to the measurements reported by Brewer & Bruce (Brewer & Bruce, 1978) and by our tests, when the responsivity of the PA system was checked by measuring the well known absorption coefficient of ethylene at 10P(14) line of the CO2 laser. After measurements at all laser lines, the cell responsivity was checked again, to eliminate any possibility of gas desorption during the measurement. The α values at each laser line were obtained by using the measured PA signal and laser power and by knowing precisely the ammonia concentration (10.6 ppm) and the responsivity of the

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 89

texture of the fruit), aging and senescence of leaves and flowers and finally, the abscission of

The ethylene biosynthesis process in plants follows the MSAE pathway: L-methionine (amino acid) – SAM (S-adenosyl methionine) – ACC (aminocyclopropane-1-carboxylic acid) – C2H4. Ethylene, or its precursor ACC, stimulates seed germination of many species at concentrations as low as 0.2 ppb. During germination, a complex cross-talking between

Tomato is an useful model plant for studying ethylene action. Three tomato mutants altered in ripening process affects different steps in ethylene synthesis and perception, resulting in a delay of fruit maturation and pigmentation: Never ripe (*Nr*) is mutated in an ethylene receptor and exhibits delayed and incomplete fruit maturation; ripening inhibitor (*rin*) is a delayed gene that causes the block of ripening before the respiratory burst; and non ripening (*nor*) shows pleiotropic effects analogue to *rin.* The aim of our study was to investigate the ethylene emission during seed germination of these 3 mutants, correlation with their germination ability and analysis of ethylene role on the loss of germinability during seed senescence.

The ethylene production per seed measured during seed germination and seedling elongation is presented in Fig. 33. In these genes, ethylene influences not only fruit ripening, but also the seed germination. The germination index and the percentage of germination of the 5-years-old seeds of the mutants are higher in respect to the control (Ny – New Yorker), in spite of the lower ethylene production of germinating seeds. Conversely to other species, in 5-years-old tomato seeds an inverse correlation between ethylene production and percentage of germination exists. During seed senescence, ethylene accumulation occurs and some processes, triggered during germination, result altered. Further analysis is required to clarify

the interaction between ethylene and other hormones like auxin, ABA and cytochinin.

Fig. 33. Ethylene production (ppt/seed) measured during seed germination and seedling

Climacteric fruits show a respiratory rise during ripening (tomato, pear, fig, mango, banana), while others belong to nonclimacteric fruits (cherry, strawberry, lemon). Fruit ripening (yellowing, softening, respiration, autocatalytic ethylene production) and abscission are regulated by ethylene. During ripening, tomatoes show a strong increase in ethylene production coinciding with the climacteric rise in respiration (CO2 production). Ethylene is also involved in the postmaturation processes, playing an important role in fruit ripening. Storage and shipping of fruits in terms of wounding effects, temperature, composition of atmospheric gases, postharvest pathogens or seal-packing conditions are

leaves and fruits (Cristescu et al., 1998; Cristescu et al., 1999; Dumitras et al., 2004).

several plant hormones exists.

elongation.

PA cell (312 V cm/W for high power laser). An average over several independent measurements at each line was used to improve the overall accuracy of the results.

The results of our measurements for ammonia are given in Fig. 32. The experimental results show a spectral representation unique to the ammonia molecule. As it can be seen from Fig. 32, ammonia has weaker absorption coefficients at other CO2 laser transitions; some other significant values for the absorption coefficient were found for 9R and 9P bands: 9R(16) α = 11.29 cm-1atm-1 (error ± 1.4%), 9P(20) α = 2.10 cm-1atm-1 (error ± 2%) and 9P(34) α = 3.99 cm-1atm-1 (error ± 0.62%). In the 10R band the measurements gave: 10R(14) α = 6.17 cm-1atm-1 (error ± 1.5%), 10R(8) α = 20.08 cm-1atm-1 (error ± 1.3%), 10R(6) α = 26.2 cm-1atm-1 (error ± 1.7%), and for the 10P band: 10P(32) α = 12.45 cm-1atm-1 (error ± 2.9%), 10P(34) α = 14.07 cm-1atm-1 (error ± 0.48%) and 10P(36) α = 7.39 cm-1atm-1 (error ± 0.83%). Compared to the other values reported previously in the literature (Brewer & Bruce, 1978), our measurements indicate a general good agreement.

Fig. 32. Absorption coefficients of ammonia at CO2 laser wavelengths.

#### **3.2 Applications in plant physiology**

Ethylene acts as a vegetal hormone produced by all plant tissues. It is transported by diffusion through plant tissues and increases the plasmatic membrane permeability. It has multiple effects on the cell metabolism: increases the oxidative processes, the transport inside the cells and the biodegradation of the organic acids and chlorophyll. Ethylene plays a major role in many metabolic processes: seed and bud dormancy, seed germination promotion, roots induction, development of plantlets (inhibitor of elongation and promotion of lateral shoots), grown promotion, leaf expansion, epinasty (downward curvature of leaves due to the growth of cells on the upper side of the petiole), flowering, wilting of flowers, fruit ripening (ethylene induces some biochemical modifications which produce polyalcohols, hydrocarbons and different oxygenated combinations responsible for the taste, aroma and

PA cell (312 V cm/W for high power laser). An average over several independent

The results of our measurements for ammonia are given in Fig. 32. The experimental results show a spectral representation unique to the ammonia molecule. As it can be seen from Fig. 32, ammonia has weaker absorption coefficients at other CO2 laser transitions; some other significant values for the absorption coefficient were found for 9R and 9P bands: 9R(16) -

α

= 3.99 cm-1atm-1 (error ± 0.62%). In the 10R band the measurements gave: 10R(14) -

Compared to the other values reported previously in the literature (Brewer & Bruce, 1978),

α

= 2.10 cm-1atm-1 (error ± 2%) and 9P(34) -

= 12.45 cm-1atm-1 (error ± 2.9%),

= 7.39 cm-1atm-1 (error ± 0.83%).

α= 26.2

= 20.08 cm-1atm-1 (error ± 1.3%), 10R(6) -

α

α

measurements at each line was used to improve the overall accuracy of the results.

= 11.29 cm-1atm-1 (error ± 1.4%), 9P(20) -

cm-1atm-1 (error ± 1.7%), and for the 10P band: 10P(32) -

our measurements indicate a general good agreement.

= 14.07 cm-1atm-1 (error ± 0.48%) and 10P(36) -

Fig. 32. Absorption coefficients of ammonia at CO2 laser wavelengths.

Ethylene acts as a vegetal hormone produced by all plant tissues. It is transported by diffusion through plant tissues and increases the plasmatic membrane permeability. It has multiple effects on the cell metabolism: increases the oxidative processes, the transport inside the cells and the biodegradation of the organic acids and chlorophyll. Ethylene plays a major role in many metabolic processes: seed and bud dormancy, seed germination promotion, roots induction, development of plantlets (inhibitor of elongation and promotion of lateral shoots), grown promotion, leaf expansion, epinasty (downward curvature of leaves due to the growth of cells on the upper side of the petiole), flowering, wilting of flowers, fruit ripening (ethylene induces some biochemical modifications which produce polyalcohols, hydrocarbons and different oxygenated combinations responsible for the taste, aroma and

**3.2 Applications in plant physiology** 

= 6.17 cm-1atm-1 (error ± 1.5%), 10R(8) -

α

α

α

10P(34) -

α

texture of the fruit), aging and senescence of leaves and flowers and finally, the abscission of leaves and fruits (Cristescu et al., 1998; Cristescu et al., 1999; Dumitras et al., 2004).

The ethylene biosynthesis process in plants follows the MSAE pathway: L-methionine (amino acid) – SAM (S-adenosyl methionine) – ACC (aminocyclopropane-1-carboxylic acid) – C2H4. Ethylene, or its precursor ACC, stimulates seed germination of many species at concentrations as low as 0.2 ppb. During germination, a complex cross-talking between several plant hormones exists.

Tomato is an useful model plant for studying ethylene action. Three tomato mutants altered in ripening process affects different steps in ethylene synthesis and perception, resulting in a delay of fruit maturation and pigmentation: Never ripe (*Nr*) is mutated in an ethylene receptor and exhibits delayed and incomplete fruit maturation; ripening inhibitor (*rin*) is a delayed gene that causes the block of ripening before the respiratory burst; and non ripening (*nor*) shows pleiotropic effects analogue to *rin.* The aim of our study was to investigate the ethylene emission during seed germination of these 3 mutants, correlation with their germination ability and analysis of ethylene role on the loss of germinability during seed senescence.

The ethylene production per seed measured during seed germination and seedling elongation is presented in Fig. 33. In these genes, ethylene influences not only fruit ripening, but also the seed germination. The germination index and the percentage of germination of the 5-years-old seeds of the mutants are higher in respect to the control (Ny – New Yorker), in spite of the lower ethylene production of germinating seeds. Conversely to other species, in 5-years-old tomato seeds an inverse correlation between ethylene production and percentage of germination exists. During seed senescence, ethylene accumulation occurs and some processes, triggered during germination, result altered. Further analysis is required to clarify the interaction between ethylene and other hormones like auxin, ABA and cytochinin.

Fig. 33. Ethylene production (ppt/seed) measured during seed germination and seedling elongation.

Climacteric fruits show a respiratory rise during ripening (tomato, pear, fig, mango, banana), while others belong to nonclimacteric fruits (cherry, strawberry, lemon). Fruit ripening (yellowing, softening, respiration, autocatalytic ethylene production) and abscission are regulated by ethylene. During ripening, tomatoes show a strong increase in ethylene production coinciding with the climacteric rise in respiration (CO2 production). Ethylene is also involved in the postmaturation processes, playing an important role in fruit ripening. Storage and shipping of fruits in terms of wounding effects, temperature, composition of atmospheric gases, postharvest pathogens or seal-packing conditions are

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 91

1.2-1.4 ppb for dead cells, both after 5 hours and 24 hours from the treatment. The increase of ethylene content clearly demonstrates that lipid peroxidation took place owing to the toxic effect of heavy metals (Fig. 34). The measurements were performed on 10P(14) line of the CO2 laser by means of a nitrogen flow-through system (25 sccm). The CO2 laser, tuned off resonance on the 10P(20) line from time to time, causes a clear drop in the observed signal.

The radiation damage in living matter develops along complex chains of events that follow the absorption of energy: a) physical stage: the energy transfer from the radiation to the matter leads mainly to molecular excitations and ionization; b) chemical stage: the primary reactive species (free atoms and radicals, that are usually extremely unstable), undergo secondary single reactions or a succession of reactions among each other and with their environment, causing damage to molecules of biological importance; c) biological stage: molecular changes occurring in a living organism may cause alterations in the system organization, which become macroscopically observable as biological effects. A substantial part of the total ionising radiation effect concerns water radiolysis, water being a major component of living tissues present in all biological systems. Many water ions and radicals are generated inside tissues as primary reactive species. Aqueous free radicals are very reactive and induce oxidative degradation of phospholipids in cell membranes (lipid peroxidation). The aim of our investigation was to measure the X-ray induced ethylene emission in mice breath and to analyse breath exhaled from patients under external X-ray beam therapy for cancer treatment. For the purpose of verifying the radioinduced effect, living mice (B6C3F1 and C57B1/6J male mice, between 3 and 6 months old) have been exposed to the total body action of a 250 kV X-ray apparatus GILARDONI model CHF-320-G. At 250 kV voltage and 15 mA current by using a 0.5 mm Cu filter, the measured dose rate was 90.1 cGy/min at 68.4 cm from the source. The value of the X-ray dose given to the treated mice (9 Gy per total body) is comparable, as order of magnitude, to the therapeutic doses given to a human patient in the course of cancer treatment by radiotherapy. The mice were divided in treated and control groups. Each treated mouse received a substantial amount of X-rays in the whole body, while the control mouse received a zero dose. Samples of the breathing air have been collected before and after irradiation. The breathing air has been concentrated on active coal absorbing pellets for a time as long as 1.5 hours, successively expanded into 0.5 liters sample bags, and then transferred into the photoacoustic cell in order to perform the analysis of ethylene content. The PA analysis of ethylene content, by using the above described

Fig. 34. Toxic effect of Cd on Jurkat cells.

important factors to establish the optimal environment necessary for their long term conservation. The aim of our experiments was to monitor the ethylene emission in plants and fruits at low temperature, together with the effect of the temperature at different ripening stages (important for optimization of different stages in agricultural procedures) and to study the effects of mechanical wounding of fruits.

Ethylene emission was monitored from plantlets at different temperatures and it saturates after about 20 min (Lai et al., 2003). The temperature effect is evident in the emission intensity, which increases almost a factor four from 15o to 25oC. There is a remarkable decrease in the lag time for the gas emission at the optimum temperature for biosynthesis of ethylene (25oC). At temperatures lower than 22oC, this lag time is about 6 min, while drops to less than 2 min at 25oC. Temperature does not influence the ethylene emission of immature fruits (0.004 ppb/g and 0.005 ppb/g for 15oC and 25oC, respectively), while it becomes important when the ripening process is triggered in a maturated fruit (0.012 ppb/g and 1.56 ppb/g for 15oC and 25oC, respectively). The same result is obtained for plantlets. Temperature is important for ACC oxidase activity (decreased at low temperatures). Mechanical wounding exerts its effect at the step where SAM is converted to ACC, the direct precursor of ethylene; this step, regulated by the enzyme ACC synthase is rate limiting in the cascade of events leading to an increase of ethylene production.

#### **3.3 Investigation of lipid peroxidation**

The oxidative modification of biological molecules is an essential part of the normal biological activity in the human organism. An excess in some oxidant activities does cause injury to cells and tissues. Particular attention is devoted to the oxidant activity of free radicals. An increased free radical formation in the organism is involved in the pathophysiology of several diseases. One of the events generated by free radicals interaction with biomolecules is the oxidative degradation of fatty acids. Oxidative stress is the origin or cause of lipid peroxidation and, as a consequence, of a wide variety of pathophysiological processes. Lipid peroxidation is the free-radical-induced oxidative degradation of polyunsaturated fatty acids. Biomembranes and cells are thereby disrupted, causing cell damage and cell death. As a marker of free-radical-mediated damage in the human body, the measurement of the exhaled volatile hydrocarbons, such as ethylene, is a good noninvasive method to monitor lipid peroxidation.

We have studied lipid peroxidation as a consequence of ionising radiation and heavy metals in living cells (Dumitras et al., 2004). Most heavy metals have a toxic action on human cells and may induce lipid peroxidation. Cadmium is a toxic agent which is supposed to affect the transport of ion through the cell membrane. Cadmium and calcium ionic radii are similar, so Cd can be picked up through the Ca transport mechanism. On the other hand, the Cd permeability through the calcium channel is very poor, so Cd can be considered as a blocker of the calcium channel as well. We tried to determine the extent of the toxic action of Cd *in vitro* by monitoring the ethylene concentration in the breathing air of human cells cultured in a liquid medium to which cadmium chloride was added. Cells of the human leukemic T cell line (Jurkat) were kept in a culture in RPMI 1640 medium containing 10% FBS, 1% L-glutamine and 1% penicillin streptomycin at 37oC in a humidified incubator with 5% CO2 and 95% air.

The measurement of ethylene before and after treatment of the culture of human cells with CdCl2 has shown that the concentration has increased from 0.5 ppb for control (live cells) to 1.2-1.4 ppb for dead cells, both after 5 hours and 24 hours from the treatment. The increase of ethylene content clearly demonstrates that lipid peroxidation took place owing to the toxic effect of heavy metals (Fig. 34). The measurements were performed on 10P(14) line of the CO2 laser by means of a nitrogen flow-through system (25 sccm). The CO2 laser, tuned off resonance on the 10P(20) line from time to time, causes a clear drop in the observed signal.

Fig. 34. Toxic effect of Cd on Jurkat cells.

90 CO2 Laser – Optimisation and Application

important factors to establish the optimal environment necessary for their long term conservation. The aim of our experiments was to monitor the ethylene emission in plants and fruits at low temperature, together with the effect of the temperature at different ripening stages (important for optimization of different stages in agricultural procedures)

Ethylene emission was monitored from plantlets at different temperatures and it saturates after about 20 min (Lai et al., 2003). The temperature effect is evident in the emission intensity, which increases almost a factor four from 15o to 25oC. There is a remarkable decrease in the lag time for the gas emission at the optimum temperature for biosynthesis of ethylene (25oC). At temperatures lower than 22oC, this lag time is about 6 min, while drops to less than 2 min at 25oC. Temperature does not influence the ethylene emission of immature fruits (0.004 ppb/g and 0.005 ppb/g for 15oC and 25oC, respectively), while it becomes important when the ripening process is triggered in a maturated fruit (0.012 ppb/g and 1.56 ppb/g for 15oC and 25oC, respectively). The same result is obtained for plantlets. Temperature is important for ACC oxidase activity (decreased at low temperatures). Mechanical wounding exerts its effect at the step where SAM is converted to ACC, the direct precursor of ethylene; this step, regulated by the enzyme ACC synthase is rate limiting in

The oxidative modification of biological molecules is an essential part of the normal biological activity in the human organism. An excess in some oxidant activities does cause injury to cells and tissues. Particular attention is devoted to the oxidant activity of free radicals. An increased free radical formation in the organism is involved in the pathophysiology of several diseases. One of the events generated by free radicals interaction with biomolecules is the oxidative degradation of fatty acids. Oxidative stress is the origin or cause of lipid peroxidation and, as a consequence, of a wide variety of pathophysiological processes. Lipid peroxidation is the free-radical-induced oxidative degradation of polyunsaturated fatty acids. Biomembranes and cells are thereby disrupted, causing cell damage and cell death. As a marker of free-radical-mediated damage in the human body, the measurement of the exhaled volatile hydrocarbons, such as ethylene, is a good

We have studied lipid peroxidation as a consequence of ionising radiation and heavy metals in living cells (Dumitras et al., 2004). Most heavy metals have a toxic action on human cells and may induce lipid peroxidation. Cadmium is a toxic agent which is supposed to affect the transport of ion through the cell membrane. Cadmium and calcium ionic radii are similar, so Cd can be picked up through the Ca transport mechanism. On the other hand, the Cd permeability through the calcium channel is very poor, so Cd can be considered as a blocker of the calcium channel as well. We tried to determine the extent of the toxic action of Cd *in vitro* by monitoring the ethylene concentration in the breathing air of human cells cultured in a liquid medium to which cadmium chloride was added. Cells of the human leukemic T cell line (Jurkat) were kept in a culture in RPMI 1640 medium containing 10% FBS, 1% L-glutamine and 1% penicillin streptomycin at 37oC in a humidified

The measurement of ethylene before and after treatment of the culture of human cells with CdCl2 has shown that the concentration has increased from 0.5 ppb for control (live cells) to

and to study the effects of mechanical wounding of fruits.

the cascade of events leading to an increase of ethylene production.

**3.3 Investigation of lipid peroxidation** 

noninvasive method to monitor lipid peroxidation.

incubator with 5% CO2 and 95% air.

The radiation damage in living matter develops along complex chains of events that follow the absorption of energy: a) physical stage: the energy transfer from the radiation to the matter leads mainly to molecular excitations and ionization; b) chemical stage: the primary reactive species (free atoms and radicals, that are usually extremely unstable), undergo secondary single reactions or a succession of reactions among each other and with their environment, causing damage to molecules of biological importance; c) biological stage: molecular changes occurring in a living organism may cause alterations in the system organization, which become macroscopically observable as biological effects. A substantial part of the total ionising radiation effect concerns water radiolysis, water being a major component of living tissues present in all biological systems. Many water ions and radicals are generated inside tissues as primary reactive species. Aqueous free radicals are very reactive and induce oxidative degradation of phospholipids in cell membranes (lipid peroxidation). The aim of our investigation was to measure the X-ray induced ethylene emission in mice breath and to analyse breath exhaled from patients under external X-ray beam therapy for cancer treatment.

For the purpose of verifying the radioinduced effect, living mice (B6C3F1 and C57B1/6J male mice, between 3 and 6 months old) have been exposed to the total body action of a 250 kV X-ray apparatus GILARDONI model CHF-320-G. At 250 kV voltage and 15 mA current by using a 0.5 mm Cu filter, the measured dose rate was 90.1 cGy/min at 68.4 cm from the source. The value of the X-ray dose given to the treated mice (9 Gy per total body) is comparable, as order of magnitude, to the therapeutic doses given to a human patient in the course of cancer treatment by radiotherapy. The mice were divided in treated and control groups. Each treated mouse received a substantial amount of X-rays in the whole body, while the control mouse received a zero dose. Samples of the breathing air have been collected before and after irradiation. The breathing air has been concentrated on active coal absorbing pellets for a time as long as 1.5 hours, successively expanded into 0.5 liters sample bags, and then transferred into the photoacoustic cell in order to perform the analysis of ethylene content. The PA analysis of ethylene content, by using the above described

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 93

Free radicals come from two major sources: endogenous and exogenous. Endogenous free radicals are produced in the body by different mechanisms whereas exogenous sources of free radicals include air pollution, ionizing radiation, cigarette smoke, inflammation etc. The ultimate step in the peroxidative chain reaction is the formation of different hydrocarbons molecules, depending on the molecular arrangement of the fatty acid involved. In the human body, the fatty acids inside the membrane lipids are mainly linoleic acid and arachidonic acid. The peroxidation of these fatty acids produces two volatile alkanes: ethylene and pentane, respectively. Both of them are considered in literature to be good biomarkers of free radical induced lipid peroxidation in humans. The fact that ethylene is highly volatile, not significantly metabolized by the body and not soluble in body fat, means that this diffuses rapidly into bloodstream after generation and it is transported to the lungs. In

Generally speaking, exhaled breath analysis (called breath test) can be represented as follows: production of the biomarker during a particular biochemical reaction or a complex metabolic process; diffusion of biomarker through tissues and input into haematic flow; possible intermediate accumulation (buffering); possible trapping of biomarker by utilization and assimilation systems or natural chemical transformation; transport to the lungs; transmembrane diffusion to the air space of lungs; diffusion of biomarker and their mixing with inhaled air in the alveolar space of lungs; release of biomarker in the breathing air; collection of a breath sample and assessment of the biomarker in the breath sample.

To get an efficient breath air sample, we used aluminized multi-patient collection bags (750 mL aluminum-coated bags-QuinTron), composed of a disposable mouthpiece and a teemouthpiece assembly (it includes a plastic tee and a removable one-way flutter valve). Multi-patient collection bags (Fig. 35) are designed to collect multiple samples from patients

Mouthpiece and tee-connector 0.75 L aluminum-coated bag 0.40 L discard bag

How is properly collected a breath sample? After an approximately normal inspiration (avoiding filling the lungs at maximum), the subject places the mouthpiece in his/her mouth, forming a tight seal around it with the lips. A normal expiration is then made through the mouth, in order to empty the lungs of as much air as required to provide the alveolar sample. The first portion of the expired air goes out, after which the valve is opened the tee-piece, the remaining expired air being redirected into the collection bag. When a

After the alveolar air sample is collected, the sample gas is transferred into the PA cell and can be analyzed immediately or later. In either case, it is recommendable to seal the large port with the collection bag port cap furnished with the collection bag. The use of the port

suitable sample is collected, the patient stops exhaling and removes the mouthpiece.

the lungs, the gas is excreted in the expired breath and then is collected.

and hold a sample for maximum 6 hours.

Fig. 35. Breath sample collection system.

procedure, takes only few minutes and, after calibration, allows for immediate data release. The radioinduced production of ethylene in the animal appears to be at clearly detectable levels, since the exhaled ethylene increases more than 4 times in the mouse breath after the irradiation (12.4 ppb for control mice before exposure, compared to 55.9 ppb for irradiated mice, after exposure) (Giubileo et al., 2003).

The cigarette smoke contains many toxic components (heavy metals, free radicals, chemicals) that may induce ethylene formation by lipid peroxidation in the lung epithelium (Dumitras et al., 2008; Giubileo et al., 2004). In order to monitor the damages caused by the inhaled smoke, we performed a breath test which gives us information about the volatile compounds under normal and stress circumstances. The exhaled air from the subject being tested was collected inside aluminized bags and then the sample gas was transferred into the measurement PA cell. In all experiments, a high value of ethylene concentration was found immediately after smoking, followed by a slower decrease. A total concentration of 4040 ppb of ethylene was measured in cigarette smoke. In the exhaled breath of a smoker, we found an ethylene concentration of 39 ppb immediately after smoking and even 1.4 ppb at half an hour from smoking a single cigarette, compared to 0.6 ppb as base (before smoking). Ethylene is dangerous for smokers because ethylene oxide is a chemical product that induces cancer in the lungs. For the moment, it is difficult to separate the exogenous and endogenous origin of the ethylene in the smoker's breath.

#### **3.4 Measurement of human biomarkers**

The application of laser photoacoustic spectroscopy for fast and precise measurements of breath biomarkers has opened up new promises for monitoring and diagnostics in recent years, especially because breath test is a non-invasive method, safe, rapid and acceptable to patients.

The detection of biomarkers in the human breath for the purpose of diagnosis has a long history. Ancient Greek physicians already knew that the aroma of human breath could provide clues to diagnosis. The perceptive clinician was alert for the sweet, fruity odor of acetone in patients with uncontrolled diabetes; the musty, fishy reek of advanced liver disease; the urine-like smell that accompanies failing kidneys; and the putrid stench of a lung abscess. Modern breath analysis is a noninvasive medical diagnostic method that distinguishes among more than 1000 compounds in exhaled breath.

Human breath includes hundreds of VOCs in low concentrations even though fewer than fifty of these are found in the majority of normal human's breath. Some of these VOCs (ethane, n-pentane, butane, ethanol, acetone) have been identified as biomarkers to some specific pathologies, including lipid peroxidation, heart failure, asthma, cystic fibrosis, diabetic ketoacidosis, alcohol intoxication, renal failure, and others. However, due to the low concentrations and presence of a large number of chemical species in exhaled air, breath analysis requires high sensitive and selective instrumentation to detect and identify the atypical concentrations of specific biomarkers (Cernat et al., 2010; Popa et al., 2011a). In order to assess the physiological meaning and the diagnostic potential of these substances, the biochemical pathways of generation have to be known.

Ethylene from the human breath is a marker of oxidant stress (in patients on hemodialisys, in acute myocardial infarction, in inflammatory diseases and ultraviolet radiation damage of human skin) and can be directly attributed to biochemical events surrounding lipid peroxidation (Dumitras et al., 2005).

procedure, takes only few minutes and, after calibration, allows for immediate data release. The radioinduced production of ethylene in the animal appears to be at clearly detectable levels, since the exhaled ethylene increases more than 4 times in the mouse breath after the irradiation (12.4 ppb for control mice before exposure, compared to 55.9 ppb for irradiated

The cigarette smoke contains many toxic components (heavy metals, free radicals, chemicals) that may induce ethylene formation by lipid peroxidation in the lung epithelium (Dumitras et al., 2008; Giubileo et al., 2004). In order to monitor the damages caused by the inhaled smoke, we performed a breath test which gives us information about the volatile compounds under normal and stress circumstances. The exhaled air from the subject being tested was collected inside aluminized bags and then the sample gas was transferred into the measurement PA cell. In all experiments, a high value of ethylene concentration was found immediately after smoking, followed by a slower decrease. A total concentration of 4040 ppb of ethylene was measured in cigarette smoke. In the exhaled breath of a smoker, we found an ethylene concentration of 39 ppb immediately after smoking and even 1.4 ppb at half an hour from smoking a single cigarette, compared to 0.6 ppb as base (before smoking). Ethylene is dangerous for smokers because ethylene oxide is a chemical product that induces cancer in the lungs. For the moment, it is difficult to separate the exogenous

The application of laser photoacoustic spectroscopy for fast and precise measurements of breath biomarkers has opened up new promises for monitoring and diagnostics in recent years, especially because breath test is a non-invasive method, safe, rapid and acceptable to patients. The detection of biomarkers in the human breath for the purpose of diagnosis has a long history. Ancient Greek physicians already knew that the aroma of human breath could provide clues to diagnosis. The perceptive clinician was alert for the sweet, fruity odor of acetone in patients with uncontrolled diabetes; the musty, fishy reek of advanced liver disease; the urine-like smell that accompanies failing kidneys; and the putrid stench of a lung abscess. Modern breath analysis is a noninvasive medical diagnostic method that

Human breath includes hundreds of VOCs in low concentrations even though fewer than fifty of these are found in the majority of normal human's breath. Some of these VOCs (ethane, n-pentane, butane, ethanol, acetone) have been identified as biomarkers to some specific pathologies, including lipid peroxidation, heart failure, asthma, cystic fibrosis, diabetic ketoacidosis, alcohol intoxication, renal failure, and others. However, due to the low concentrations and presence of a large number of chemical species in exhaled air, breath analysis requires high sensitive and selective instrumentation to detect and identify the atypical concentrations of specific biomarkers (Cernat et al., 2010; Popa et al., 2011a). In order to assess the physiological meaning and the diagnostic potential of these substances,

Ethylene from the human breath is a marker of oxidant stress (in patients on hemodialisys, in acute myocardial infarction, in inflammatory diseases and ultraviolet radiation damage of human skin) and can be directly attributed to biochemical events surrounding lipid

mice, after exposure) (Giubileo et al., 2003).

**3.4 Measurement of human biomarkers** 

and endogenous origin of the ethylene in the smoker's breath.

distinguishes among more than 1000 compounds in exhaled breath.

the biochemical pathways of generation have to be known.

peroxidation (Dumitras et al., 2005).

Free radicals come from two major sources: endogenous and exogenous. Endogenous free radicals are produced in the body by different mechanisms whereas exogenous sources of free radicals include air pollution, ionizing radiation, cigarette smoke, inflammation etc. The ultimate step in the peroxidative chain reaction is the formation of different hydrocarbons molecules, depending on the molecular arrangement of the fatty acid involved. In the human body, the fatty acids inside the membrane lipids are mainly linoleic acid and arachidonic acid. The peroxidation of these fatty acids produces two volatile alkanes: ethylene and pentane, respectively. Both of them are considered in literature to be good biomarkers of free radical induced lipid peroxidation in humans. The fact that ethylene is highly volatile, not significantly metabolized by the body and not soluble in body fat, means that this diffuses rapidly into bloodstream after generation and it is transported to the lungs. In the lungs, the gas is excreted in the expired breath and then is collected.

Generally speaking, exhaled breath analysis (called breath test) can be represented as follows: production of the biomarker during a particular biochemical reaction or a complex metabolic process; diffusion of biomarker through tissues and input into haematic flow; possible intermediate accumulation (buffering); possible trapping of biomarker by utilization and assimilation systems or natural chemical transformation; transport to the lungs; transmembrane diffusion to the air space of lungs; diffusion of biomarker and their mixing with inhaled air in the alveolar space of lungs; release of biomarker in the breathing air; collection of a breath sample and assessment of the biomarker in the breath sample.

To get an efficient breath air sample, we used aluminized multi-patient collection bags (750 mL aluminum-coated bags-QuinTron), composed of a disposable mouthpiece and a teemouthpiece assembly (it includes a plastic tee and a removable one-way flutter valve). Multi-patient collection bags (Fig. 35) are designed to collect multiple samples from patients and hold a sample for maximum 6 hours.

Mouthpiece and tee-connector 0.75 L aluminum-coated bag 0.40 L discard bag

Fig. 35. Breath sample collection system.

How is properly collected a breath sample? After an approximately normal inspiration (avoiding filling the lungs at maximum), the subject places the mouthpiece in his/her mouth, forming a tight seal around it with the lips. A normal expiration is then made through the mouth, in order to empty the lungs of as much air as required to provide the alveolar sample. The first portion of the expired air goes out, after which the valve is opened the tee-piece, the remaining expired air being redirected into the collection bag. When a suitable sample is collected, the patient stops exhaling and removes the mouthpiece.

After the alveolar air sample is collected, the sample gas is transferred into the PA cell and can be analyzed immediately or later. In either case, it is recommendable to seal the large port with the collection bag port cap furnished with the collection bag. The use of the port

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 95

for the maintenance of the normal pH balance necessary to sustain life. Ammonia is processed in the liver, kidneys and skeletal muscles. Typically, ammonia and ammonium ions (in a healthy individual) are converted into urea in the liver through the urea cycle (Krebs-Henseileit cycle). The urea is then transported through the blood-stream to be excreted into urine by the kidneys. The reversibility of the process requires an equilibrium concentration of ammonia related to the blood urea nitrogen (BUN) loading of the blood. As small molecules, ammonia and ammonium ions can penetrate the blood-lung barrier, and appear in exhaled breath. In the case of kidney dysfunction, urea is unable to be excreted, causing an excessive build up of ammonia in the blood. People with kidney failure have a marked odor of ammonia ("fishy") on their breath, which can be an indicator of this disease. Volunteer participants (Table 6) were recruited from patients receiving HD treatment at the renal dialysis clinics at the IHS Fundeni (International Healthcare Systems), Bucharest. Subjects were dialyzed 3 times per week, with a 4 h dialysis session. They were instructed to use antiseptic mouthwash before each breath sampling, to avoid oral bacteria (over 700 species of bacteria live in our mouths and can interfere with our molecules of interest). HD was accomplished with BAXTER dialysis machines using DICEA (and XENIUM) high performance cellulose diacetate hollow fibre dialyser-gamma series (DICEA 170G) with following characteristics: surface area of 1.7 m2, ultrafiltration rate 12.5 mL/hr/mmHg,

inner diameter of 200 microns and membrane thickness of 15 microns.

**UpostHD (mg/dl)**

Table 6. The particular data of patients and the experimental measurements of breath

A special mention should be made: NH3 is a highly adsorbing compound and the results of successive measurements are often altered by the molecules previously adsorbed on the pathway and cell walls. To ensure the quality of each measurement, an intensive cycle of N2 washing was performed between samples, in order to have a maximum increase of 10% for the background photoacoustic signal. It has to be underlined that the measured photoacoustic signal is due mainly to the absorption of ammonia and ethylene, respectively, but some traces of CO2, H2O, ethanol, etc., influence the measurements (overall contribution is less than 10%). Experimental measurements in order to detect traces of ethylene and ammonia were performed for a healthy volunteer (C. A. male, 26 years old) and for 6 patients with renal failure. Particular data of patients are summarized in Table 6. The exhaled air samples were collected before, during (about 1 hour after the start of HD) and immediately after the HD procedure. Analysis of pre-dialysis urea level and post-dialysis urea level (normal limit in the range of 19 - 43 mg/dL) was made at MedCenter, Bucharest (VITROS 51). The results are

before HD

P1 Male 67 2005 147 37 0.03 0.13 0.52 4.63 3.58 2.39 P2 Male 80 2004 131 39 0.23 0.51 0.93 4.28 2.82 1.53 P3 Male 79 2008 136 22 0.17 0.31 0.91 2.89 2.06 0.67 P4 Male 22 2010 135 21 0.14 0.19 0.84 5.71 4.08 3.24 P5 Male 54 2010 174 48 0.18 0.43 0.89 4.79 3.07 1.5 P6 Male 66 2005 147 66 - - - 2.8 2.01 1.66

during HD

**C2H4 (ppm) NH3 (ppm)**

before HD

during HD

after HD

after HD

**UpreHD (mg/dl)**

**since**

ethylene and ammonia concentrations (± 10% data error).

**Patient Gender Age HD** 

also presented in Table 6.

cap assures that the sample volume will not be lost due to a leak. Its use also avoids the contamination of the sample by gas diffusion through the one-way valve in the large port, if the sample is stored for a long period of time prior to its analysis.

Radiation therapy (also called radiotherapy, X-ray therapy, or irradiation) is the use of certain type of energy (called ionizing radiation) to kill cancer cells and shrink tumors. Radiation therapy injures or destroys cells in the area being treated by damaging their genetic material, making it impossible for these cells to continue grow and divide. Although radiation damages both cancer cells and normal cells, most normal cells can recover from the effects of radiation and function properly. The goal of radiotherapy is to damage as many cancer cells as possible, while limiting harm to nearby healthy tissue.

The effect of ionizing radiation on living cells is supposed to modify the oxidative stress status in the human body through an increase in the peroxidation processes started by the free water radicals generated by indirect radiation effect in living tissue. Important events of the peroxidation take place in the cell membranes determining the release of small linear hydrocarbon molecules through the lipid peroxidation pathways. A fraction of the hydrocarbon molecules generated in the tissue (one among them is the ethylene) will be transported to the lungs by the blood and release in the exhaled breath.

We have analyzed exhaled air from 6 patients between 32 and 77 years old receiving radiation treatment based on X-ray external beam after malign tumor surgery (Dumitras et al., 2008). Breath samples were taken from volunteers at certain time intervals (before, immediately after and at 15 minutes after the X-ray therapy). The patients received fractional doses as high as 2 to 8 Gy depending on the type of cancer. For this experiment patients were asked to exhale into sample bags at a normal exhalation flow rate.

The exhaled air sample was transferred in the PA cell and analyzed in the continuous nitrogen flux. The KOH trap inserted in the gas circuit is used to remove as much as possible the high quantity of CO2 from the exhaled air. To subtract from the final results any influence of the interfering gases (CO2, H2O vapors) we applied the changing lines method, using 3 lines: 10P(14), 10P(16), and 10P(26).

We have measured the following levels of ethylene for a patient (female, 77 years old) with mammary cancer treated by X-ray therapy with a dose of 8 Gy: a) before X-ray therapy: c = 18.6 ppbV; b) Immediately after X-ray therapy: c = 23.17 ppbV; c) 15 min after the X-ray therapy: c = 10.83 ppbV. As a first observation of our measurement we see that, indeed, after the X-ray irradiation the ethylene concentration rises, showing that lipid peroxidation took place. So, it is possible to detect the process in the very first minute after irradiation. The effect of lipid peroxidation is more powerful on the cancer cells, while the healthy cells even affected have higher recovery ability. A surprising decrease in the level of ethylene concentration was observed in the exhaled air after 15 minutes, the level being even lower than the normal level of the patient (e.g. the level measured before any irradiation). This could be explained as a body reaction to the increased level of peroxidic attack: higher the rate of damage, higher the self-defense response of the human organism. Further work is required in order to verify this hypothesis.

In separate studies (Popa et al., 2011b; Popa et al., 2011c), we investigated the breath ethylene and the breath ammonia levels in patients with renal failure receiving haemodialysis (HD) treatment. Human bodies use ammonia in a number of ways, including

cap assures that the sample volume will not be lost due to a leak. Its use also avoids the contamination of the sample by gas diffusion through the one-way valve in the large port, if

Radiation therapy (also called radiotherapy, X-ray therapy, or irradiation) is the use of certain type of energy (called ionizing radiation) to kill cancer cells and shrink tumors. Radiation therapy injures or destroys cells in the area being treated by damaging their genetic material, making it impossible for these cells to continue grow and divide. Although radiation damages both cancer cells and normal cells, most normal cells can recover from the effects of radiation and function properly. The goal of radiotherapy is to damage as

The effect of ionizing radiation on living cells is supposed to modify the oxidative stress status in the human body through an increase in the peroxidation processes started by the free water radicals generated by indirect radiation effect in living tissue. Important events of the peroxidation take place in the cell membranes determining the release of small linear hydrocarbon molecules through the lipid peroxidation pathways. A fraction of the hydrocarbon molecules generated in the tissue (one among them is the ethylene) will be

We have analyzed exhaled air from 6 patients between 32 and 77 years old receiving radiation treatment based on X-ray external beam after malign tumor surgery (Dumitras et al., 2008). Breath samples were taken from volunteers at certain time intervals (before, immediately after and at 15 minutes after the X-ray therapy). The patients received fractional doses as high as 2 to 8 Gy depending on the type of cancer. For this experiment

The exhaled air sample was transferred in the PA cell and analyzed in the continuous nitrogen flux. The KOH trap inserted in the gas circuit is used to remove as much as possible the high quantity of CO2 from the exhaled air. To subtract from the final results any influence of the interfering gases (CO2, H2O vapors) we applied the changing lines method,

We have measured the following levels of ethylene for a patient (female, 77 years old) with mammary cancer treated by X-ray therapy with a dose of 8 Gy: a) before X-ray therapy: c = 18.6 ppbV; b) Immediately after X-ray therapy: c = 23.17 ppbV; c) 15 min after the X-ray therapy: c = 10.83 ppbV. As a first observation of our measurement we see that, indeed, after the X-ray irradiation the ethylene concentration rises, showing that lipid peroxidation took place. So, it is possible to detect the process in the very first minute after irradiation. The effect of lipid peroxidation is more powerful on the cancer cells, while the healthy cells even affected have higher recovery ability. A surprising decrease in the level of ethylene concentration was observed in the exhaled air after 15 minutes, the level being even lower than the normal level of the patient (e.g. the level measured before any irradiation). This could be explained as a body reaction to the increased level of peroxidic attack: higher the rate of damage, higher the self-defense response of the human organism. Further work is

In separate studies (Popa et al., 2011b; Popa et al., 2011c), we investigated the breath ethylene and the breath ammonia levels in patients with renal failure receiving haemodialysis (HD) treatment. Human bodies use ammonia in a number of ways, including

the sample is stored for a long period of time prior to its analysis.

many cancer cells as possible, while limiting harm to nearby healthy tissue.

transported to the lungs by the blood and release in the exhaled breath.

using 3 lines: 10P(14), 10P(16), and 10P(26).

required in order to verify this hypothesis.

patients were asked to exhale into sample bags at a normal exhalation flow rate.

for the maintenance of the normal pH balance necessary to sustain life. Ammonia is processed in the liver, kidneys and skeletal muscles. Typically, ammonia and ammonium ions (in a healthy individual) are converted into urea in the liver through the urea cycle (Krebs-Henseileit cycle). The urea is then transported through the blood-stream to be excreted into urine by the kidneys. The reversibility of the process requires an equilibrium concentration of ammonia related to the blood urea nitrogen (BUN) loading of the blood. As small molecules, ammonia and ammonium ions can penetrate the blood-lung barrier, and appear in exhaled breath. In the case of kidney dysfunction, urea is unable to be excreted, causing an excessive build up of ammonia in the blood. People with kidney failure have a marked odor of ammonia ("fishy") on their breath, which can be an indicator of this disease.

Volunteer participants (Table 6) were recruited from patients receiving HD treatment at the renal dialysis clinics at the IHS Fundeni (International Healthcare Systems), Bucharest. Subjects were dialyzed 3 times per week, with a 4 h dialysis session. They were instructed to use antiseptic mouthwash before each breath sampling, to avoid oral bacteria (over 700 species of bacteria live in our mouths and can interfere with our molecules of interest). HD was accomplished with BAXTER dialysis machines using DICEA (and XENIUM) high performance cellulose diacetate hollow fibre dialyser-gamma series (DICEA 170G) with following characteristics: surface area of 1.7 m2, ultrafiltration rate 12.5 mL/hr/mmHg, inner diameter of 200 microns and membrane thickness of 15 microns.


Table 6. The particular data of patients and the experimental measurements of breath ethylene and ammonia concentrations (± 10% data error).

A special mention should be made: NH3 is a highly adsorbing compound and the results of successive measurements are often altered by the molecules previously adsorbed on the pathway and cell walls. To ensure the quality of each measurement, an intensive cycle of N2 washing was performed between samples, in order to have a maximum increase of 10% for the background photoacoustic signal. It has to be underlined that the measured photoacoustic signal is due mainly to the absorption of ammonia and ethylene, respectively, but some traces of CO2, H2O, ethanol, etc., influence the measurements (overall contribution is less than 10%).

Experimental measurements in order to detect traces of ethylene and ammonia were performed for a healthy volunteer (C. A. male, 26 years old) and for 6 patients with renal failure. Particular data of patients are summarized in Table 6. The exhaled air samples were collected before, during (about 1 hour after the start of HD) and immediately after the HD procedure. Analysis of pre-dialysis urea level and post-dialysis urea level (normal limit in the range of 19 - 43 mg/dL) was made at MedCenter, Bucharest (VITROS 51). The results are also presented in Table 6.

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 97

The most important result is the correlation found between urea data (measured by blood analysis) and the individual breath ammonia and ethylene concentrations (measured by

This analysis demonstrates that HD determines simultaneously a large increase of the ethylene concentration in the exhaled breath (owing to the oxidative stress) and a reduction

Laser photoacoustic spectroscopy technique demonstrated that it will play an important role in the future of exhaled breath analysis. The key attributes of this technique is sensitivity,

The applications of resonant PA spectroscopy include concentration measurements and trace gas analysis, accurate determinations of thermophysical properties, detections of dynamic processes such as gas mixing or chemical reactions, relaxation processes (determinations of collisional lifetimes of specified quantum states and routes of energy exchange in polyatomic molecules), spectroscopic experiments, studies of aerosols, etc. Trace-gas sensing is a rapidly developing field, in demand for applications such as process and air-quality measurements, atmospheric monitoring, breath diagnostics, biology and

More than 250 different volatile organic compounds including air pollutants originating from the burning of fossil fuels, traffic, or natural sources can be identified and measured with a CO2 laser based PA instrument. Such studies are prompted by the growing public concern about serious environmental problems such as acid rain, photochemical smog,

Breath analysis is a noninvasive medical diagnostic method that distinguishes among more than 1000 compounds in exhaled breath. Many of these compounds, if measured accurately at very low concentration levels, typically in the range of few ppbV, can be used to identify particular medical conditions. Measuring human biomarkers in exhaled breath is expected to revolutionize diagnosis and management of many diseases and may soon lead to rapid, improved, lower-cost diagnosis, which will in turn ensure expanded life spans and an improved quality of life. For example, ammonia levels in the breath can be used to determine the exact time necessary for an optimal degree of dialysis for a patient with end-

Trace-gas detection techniques based on PA spectroscopy make it possible to discover and control plant physiology mechanisms such as those responsible for germination, blossoming, senescence, ripening, wounding effects, post anaerobic injury, etc. Many agriculturally interesting gases (ethylene, methane, water vapor concentration, carbon dioxide, ammonia, ozone) can be measured *in situ* and in real time with CO2 and CO laser

In chemistry, PA spectroscopy is useful in the monitoring of chemical processes (reaction rates, equilibrium constants, enthalpies), identification of different compounds (even

The techniques of PA spectroscopy can be extended to the detection of a wide variety of industrial gases, including benzene, hydrogen cyanide, acetylene, carbon monoxide, and carbon

photoacoustic technique), shown in Figs. 36 (b) and 36 (d) for six patients.

of the ammonia concentration, correlated to the level of blood urea nitrogen.

selectivity, fast and real time response and ease to use.

agriculture, chemistry, and security and workplace surveillance.

stratospheric ozone depletion, and global climatic changes.

isomers and radicals), and dimerization of fatty acid vapors**.**

stage renal disease at every session.

based photoacoustic spectrometers.

**4. Conclusions** 

Experimental measurements of breath ethylene and ammonia concentrations for the patients (P1-P6) with renal failure and for the healthy subject (P0) were performed and the results are presented in Fig. 36. The control P0 values are 0.006 ppm ethylene and 0.25 ppm ammonia. All measurements were made at 10P(14) CO2 laser line (10.53 μm), where the ethylene absorption coefficient has the largest value (30.4 cm-1atm-1), and at 9R(30) CO2 laser line (9.22 μm), where the ammonia absorption coefficient has the maximum value of 57 cm-1atm-1.

Fig. 36. Ethylene and ammonia concentrations in exhaled breath of patients under HD treatment: (a) ethylene concentrations; (b) breath ethylene concentration correlation with urea level; (c) ammonia concentrations; (d) breath ethylene concentration correlation with urea level.

As a first observation of our measurements (shown in Fig. 36a), we see that, immediately after HD treatment, the ethylene concentration increases, proving the presence of lipid peroxidation. Oxidative stress is a persistent manifestation at patients with renal failure, showing an imbalance between oxidant and antioxidant systems. HD is associated with increased oxidative stress and all treated patients are exposed to this stress. This situation appears to be due to an increased production of free radicals during HD and immediately after HD and a net reduction of many antioxidants.

In Fig. 36 (c) we can observe, as expected, a reduction of ammonia concentration in exhaled breath at patients under HD treatment, which means that ammonia detection in human breath using LPAS system can be used for determining the exact time necessary at every session for the desired state of HD for a patient with end stage renal disease and, in the same time, could serve as a broad noninvasive screen for incipient renal disease.

The most important result is the correlation found between urea data (measured by blood analysis) and the individual breath ammonia and ethylene concentrations (measured by photoacoustic technique), shown in Figs. 36 (b) and 36 (d) for six patients.

This analysis demonstrates that HD determines simultaneously a large increase of the ethylene concentration in the exhaled breath (owing to the oxidative stress) and a reduction of the ammonia concentration, correlated to the level of blood urea nitrogen.

Laser photoacoustic spectroscopy technique demonstrated that it will play an important role in the future of exhaled breath analysis. The key attributes of this technique is sensitivity, selectivity, fast and real time response and ease to use.

#### **4. Conclusions**

96 CO2 Laser – Optimisation and Application

Experimental measurements of breath ethylene and ammonia concentrations for the patients (P1-P6) with renal failure and for the healthy subject (P0) were performed and the results are presented in Fig. 36. The control P0 values are 0.006 ppm ethylene and 0.25 ppm ammonia. All measurements were made at 10P(14) CO2 laser line (10.53 μm), where the ethylene absorption coefficient has the largest value (30.4 cm-1atm-1), and at 9R(30) CO2 laser line (9.22 μm), where the ammonia absorption coefficient has the maximum value of 57 cm-1atm-1.

(a) (b)

(c) (d)

Fig. 36. Ethylene and ammonia concentrations in exhaled breath of patients under HD treatment: (a) ethylene concentrations; (b) breath ethylene concentration correlation with urea level; (c) ammonia concentrations; (d) breath ethylene concentration correlation with urea level.

As a first observation of our measurements (shown in Fig. 36a), we see that, immediately after HD treatment, the ethylene concentration increases, proving the presence of lipid peroxidation. Oxidative stress is a persistent manifestation at patients with renal failure, showing an imbalance between oxidant and antioxidant systems. HD is associated with increased oxidative stress and all treated patients are exposed to this stress. This situation appears to be due to an increased production of free radicals during HD and immediately

In Fig. 36 (c) we can observe, as expected, a reduction of ammonia concentration in exhaled breath at patients under HD treatment, which means that ammonia detection in human breath using LPAS system can be used for determining the exact time necessary at every session for the desired state of HD for a patient with end stage renal disease and, in the

same time, could serve as a broad noninvasive screen for incipient renal disease.

after HD and a net reduction of many antioxidants.

The applications of resonant PA spectroscopy include concentration measurements and trace gas analysis, accurate determinations of thermophysical properties, detections of dynamic processes such as gas mixing or chemical reactions, relaxation processes (determinations of collisional lifetimes of specified quantum states and routes of energy exchange in polyatomic molecules), spectroscopic experiments, studies of aerosols, etc. Trace-gas sensing is a rapidly developing field, in demand for applications such as process and air-quality measurements, atmospheric monitoring, breath diagnostics, biology and agriculture, chemistry, and security and workplace surveillance.

More than 250 different volatile organic compounds including air pollutants originating from the burning of fossil fuels, traffic, or natural sources can be identified and measured with a CO2 laser based PA instrument. Such studies are prompted by the growing public concern about serious environmental problems such as acid rain, photochemical smog, stratospheric ozone depletion, and global climatic changes.

Breath analysis is a noninvasive medical diagnostic method that distinguishes among more than 1000 compounds in exhaled breath. Many of these compounds, if measured accurately at very low concentration levels, typically in the range of few ppbV, can be used to identify particular medical conditions. Measuring human biomarkers in exhaled breath is expected to revolutionize diagnosis and management of many diseases and may soon lead to rapid, improved, lower-cost diagnosis, which will in turn ensure expanded life spans and an improved quality of life. For example, ammonia levels in the breath can be used to determine the exact time necessary for an optimal degree of dialysis for a patient with endstage renal disease at every session.

Trace-gas detection techniques based on PA spectroscopy make it possible to discover and control plant physiology mechanisms such as those responsible for germination, blossoming, senescence, ripening, wounding effects, post anaerobic injury, etc. Many agriculturally interesting gases (ethylene, methane, water vapor concentration, carbon dioxide, ammonia, ozone) can be measured *in situ* and in real time with CO2 and CO laser based photoacoustic spectrometers.

In chemistry, PA spectroscopy is useful in the monitoring of chemical processes (reaction rates, equilibrium constants, enthalpies), identification of different compounds (even isomers and radicals), and dimerization of fatty acid vapors**.**

The techniques of PA spectroscopy can be extended to the detection of a wide variety of industrial gases, including benzene, hydrogen cyanide, acetylene, carbon monoxide, and carbon

CO2 Laser Photoacoustic Spectroscopy: II. Instrumentation and Applications 99

American Institute of Physics, ISBN 978-1-563-96805-3, Melville, NY, USA Cristescu, S.; Dumitras, D.C. & Duţu, D.C.A. (1998). Photoacoustic Detection of Ethylene

Cristescu, S.; Dumitras, D.C. & Dutu, D.C.A. (2000a). Characterization of a Resonant Cell

Cristescu, S.; Dumitras, D.C. & Dutu, D.C.A. (2000b). Ammonia and Ethene Absorption

Cristescu, S.; Dumitras, D.C.; Dutu, D.C.A. & Mujat, C. (1997). Real-Time Detection System

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Dumitras, D.C.; Banita, S.; Bratu, A.M.; Cernat, R.; Dutu, D.C.A.; Matei, C.; Patachia, M.;

Dumitras, D.C.; Dutu, D.C.; Comaniciu, N. & Draganescu, V. (1976). Sealed-Off CO2 Lasers.

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Released by Biological Samples under Stress Conditions. *Proc. SPIE ROMOPTO '97: Fifth Conference on Optics,* Vol.3405, V.I. Vlad, D.C. Dumitras (Eds.), pp. 627-631,

Using the Acoustic Transmission Line Model. *Proc. SPIE SIOEL '99: Sixth Symposium on Optoelectronics,* Vol.4068, T. Necsoiu, M. Robu, D.C. Dumitras (Eds.),

Measurements with a Tunable CO2 Laser-Based Photoacoustic Trace Gas Detector. *Proc. SPIE ALT '99 International Conference on Advanced Laser Technologies,* Vol.4070, V.I. Pustovoy, V.I. Konov (Eds.), pp. 457-464, SPIE, ISBN 978-0-819-43707-5,

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dioxide, as well as a broad range of chemical warfare agents, including nerve gases (Sarin, Soman, Tabun), blistering agents (phosgene, mustard gas), and poisonous gases (hydrogen cyanide), explosives (TNT, PETN), and harmful drugs (heroin, morphine, narcotine).

Our previous research on LPAS (Dumitras et al., 1993; Dutu et al., 1994a; Dutu et al., 1994b; Dumitras et al., 1996a; Dumitras et al., 1996b; Cristescu et al., 1997; Cristescu et al., 2000a) has led to the development of new applications in plant physiology (seed germination, ripening of climacteric fruits, plant response to pathogen infection) (Cristescu et al., 1998; Cristescu et al., 1999; Lai et al., 2003), measurement of gas absorption coefficients (ethylene, ammonia) (Cristescu et al., 2000b; Dumitras et al., 2007; Dumitras et al., 2011), and medicine (cultures of human cells doped with heavy metals, ionizing radiation damage in living organisms, lipid peroxidation in lung epithelium following the inhalation of cigarette smoke, exhaled breath from patients treated by anti-tumor radioisotope therapy and patients under HD treatment) (Giubileo et al., 2003; Dumitras et al., 2004; Giubileo et al., 2004; Dumitras et al., 2005; Cernat et al., 2010; Popa et al., 2011a; Popa et al., 2011b; Popa et al., 2011c; Popa & Matei, 2011).

Extensions of various aspects of this work are currently being pursued in our laboratory.

#### **5. References**


dioxide, as well as a broad range of chemical warfare agents, including nerve gases (Sarin, Soman, Tabun), blistering agents (phosgene, mustard gas), and poisonous gases (hydrogen

Our previous research on LPAS (Dumitras et al., 1993; Dutu et al., 1994a; Dutu et al., 1994b; Dumitras et al., 1996a; Dumitras et al., 1996b; Cristescu et al., 1997; Cristescu et al., 2000a) has led to the development of new applications in plant physiology (seed germination, ripening of climacteric fruits, plant response to pathogen infection) (Cristescu et al., 1998; Cristescu et al., 1999; Lai et al., 2003), measurement of gas absorption coefficients (ethylene, ammonia) (Cristescu et al., 2000b; Dumitras et al., 2007; Dumitras et al., 2011), and medicine (cultures of human cells doped with heavy metals, ionizing radiation damage in living organisms, lipid peroxidation in lung epithelium following the inhalation of cigarette smoke, exhaled breath from patients treated by anti-tumor radioisotope therapy and patients under HD treatment) (Giubileo et al., 2003; Dumitras et al., 2004; Giubileo et al., 2004; Dumitras et al., 2005; Cernat et

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**3** 

*Belarus* 

**CO2 Lasing on Non-Traditional Bands** 

Construction of powerful and efficient laser sources, lasing in various IR ranges, is of importance for further development of a number of trends, e.g., spectroscopy, laser chemistry, sounding of the atmosphere, and metrology. The most natural way to solve this problem is to use unconventional (nontraditional) transitions to produce lasing in commonly used CO2 lasers. The spectral range of CO2 lasers is greatly increased in lasing on transitions of the so-called "hot" band 0111-1110, whose P-branch is in the range of 10.9-11.3 µm*.*  Thorough investigations of gain, vibrational temperatures (*T1, T2, T3*), and output parameters on lines of the hot band made it possible to achieve efficient lasing both for pulse

In studying the lasing spectrum of hot transitions in TEA CO2 lasers some lines not belonging to the 0111-1110 band. We suggested, that these lasing lines belong to higher level transitions, e.g., 1001-2000 (0400), which were called "doubly hot," i.e., transitions in which compared to hot transitions two deformation quanta or one symmetric quantum rather than one

In the present work lasing in both a TEA laser and a low-pressure laser with longitudinal discharge on some transitions of the CO2 molecule in the range of 11.0-11.6 µm is reported. The rather high resolution of the spectral equipment used and calculation of transition frequencies on the basis of recent spectroscopic constants made it possible to identify definitively the lasing lines obtained as belonging to the doubly hot bands 0221-1220 and 100l-2000 and the sequence hot band 0112-1111. To find optimum conditions for lasing on the aforementioned bands experimental studies of vibrational temperatures in active media of a

Earlier the lasing on the 0200(1000)-0110 band of the CO2 molecule has been obtained in the specific systems at cryogenic temperatures under the lowest efficiency. The optimization of the active medium and its electrical discharge pumping conditions based on the original technique of the temperature model allowed to obtain in the simple TE CO2 laser with UV preionization the powerful lasing on the 0200-0110 band at room temperature. The dependencies of the output and spectral performances of the 16 (14) micrometers lasing vs. a content of the active

To increase the power performances of the 16 (14) microns CO2 laser the possibility of lasing on the 0201(1001)-0111 band have been experimentally and theoretically investigated under the combined (electrical + optical) excitation of the active medium. The conditions for

deformation quantum is added both to the upper and to the lower energy level.

TEA CO2 laser and a low-pressure laser with longitudinal discharge were carried out.

medium, pumping parameters and cavity characteristics have been carried out.

**1. Introduction** 

TEA and for cw longitudinal-discharge CO2 lasers.

*Institute of Physics of National Academy of Sciences of Belarus* 

Vladimir Petukhov and Vadim Gorobets


## **CO2 Lasing on Non-Traditional Bands**

Vladimir Petukhov and Vadim Gorobets

*Institute of Physics of National Academy of Sciences of Belarus Belarus* 

#### **1. Introduction**

102 CO2 Laser – Optimisation and Application

Olafsson, A.; Hammerich, M. & Henningsen, J. (1992). Photoacoustic Spectroscopy of C2H4

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Ryan, J.S.; Hubert, M.H. & Crane, R.A. (1983). Water Vapor Absorption at Isotopic CO2 Laser Wavelengths. *Appl. Opt.,* Vol.22, No.5, (March 1975), pp. 711-717, ISSN 0003-6935 Sauren, H.; Bicanic, D.; Jelink, H. & Reuss, J. (1989). High-Sensitivity, Interference-Free,

Siegman, A.E. (1986). *Lasers*, University Science Books, ISBN 978-0-935-70211-3, Sausalito,

Sigrist, M.W.; Bernegger, S. & Meyer, P.L. (1989). Atmospheric and Exhaust Air Monitoring

Thomas III, L.J.; Kelly, M.J. & Amer, N.M. (1978). The Role of Buffer Gases in Optoacoustic

Thöny, A. & Sigrist, M.W. (1995). New Developments in CO2-Laser Photoacoustic

Tonelli, M.; Minguzzi, P. & Di Lieto, A. (1983). Intermodulated Optoacoustic Spectroscopy.

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*Phys. B,* Vol.105, No.3, (November 2011), pp. 669-674, ISSN 0946-2171 Pushkarsky, M.B.; Weber, M.E.; Baghdassarian, O.; Narasimhan, L.R. & Patel, C.K.N. (2002).

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ISSN 0003-6935

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CA, USA

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978-3-540-11795-4, Berlin, Germany

with a Tunable CO2 Laser. *Appl. Opt.,* Vol.31, No.15, (May 1992), pp. 2657-2668,

Dependence of NH3 and C2H4 Absorption Cross Sections at CO2 Laser Wavelengths. *Appl. Opt.,* Vol.19, No.10, (May 1980), pp.1711-1715, ISSN 0003-6935 Popa, C. & Matei, C. (2011). Photoacoustic Assessment of Oxidative Stress in Dialysis and

Radiotherapy by LPAS System. *Optoelectron. Adv. Mater. – Rapid Commun.*, Vol. 5,

Studies of Ethylene and Ammonia as Biomarkers at Patients with Different Medical Disorders. *U. P. B. Sci. Bull., Series A,* Vol.73, No.2, pp. 167-174, ISSN 1223-7027 Popa, C.; Bratu, A.M.; Matei, C.; Cernat, R.; Popescu, A. & Dumitras, D.C. (2011b).

Qualitative and Quantitative Determination of Human Biomarkers by Laser Photoacoustic Spectroscopy Methods. *Laser Phys.,* Vol.21, No.7, (July 2011), pp.

Measurements from the Patients Breath with Renal Failure via LPAS Method. *Appl.* 

Laser-Based Photoacoustic Ammonia Sensors for Industrial Applications. *Appl.* 

Ammonia in the Atmosphere: Influence of Water Vapor and Carbon Dioxide. *Appl.* 

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*J. Physique (Colloque C6),* Vol.44, No.10, (October 1983), pp. 553-557, ISSN 0449-1947

Construction of powerful and efficient laser sources, lasing in various IR ranges, is of importance for further development of a number of trends, e.g., spectroscopy, laser chemistry, sounding of the atmosphere, and metrology. The most natural way to solve this problem is to use unconventional (nontraditional) transitions to produce lasing in commonly used CO2 lasers. The spectral range of CO2 lasers is greatly increased in lasing on transitions of the so-called "hot" band 0111-1110, whose P-branch is in the range of 10.9-11.3 µm*.*  Thorough investigations of gain, vibrational temperatures (*T1, T2, T3*), and output parameters on lines of the hot band made it possible to achieve efficient lasing both for pulse TEA and for cw longitudinal-discharge CO2 lasers.

In studying the lasing spectrum of hot transitions in TEA CO2 lasers some lines not belonging to the 0111-1110 band. We suggested, that these lasing lines belong to higher level transitions, e.g., 1001-2000 (0400), which were called "doubly hot," i.e., transitions in which compared to hot transitions two deformation quanta or one symmetric quantum rather than one deformation quantum is added both to the upper and to the lower energy level.

In the present work lasing in both a TEA laser and a low-pressure laser with longitudinal discharge on some transitions of the CO2 molecule in the range of 11.0-11.6 µm is reported. The rather high resolution of the spectral equipment used and calculation of transition frequencies on the basis of recent spectroscopic constants made it possible to identify definitively the lasing lines obtained as belonging to the doubly hot bands 0221-1220 and 100l-2000 and the sequence hot band 0112-1111. To find optimum conditions for lasing on the aforementioned bands experimental studies of vibrational temperatures in active media of a TEA CO2 laser and a low-pressure laser with longitudinal discharge were carried out.

Earlier the lasing on the 0200(1000)-0110 band of the CO2 molecule has been obtained in the specific systems at cryogenic temperatures under the lowest efficiency. The optimization of the active medium and its electrical discharge pumping conditions based on the original technique of the temperature model allowed to obtain in the simple TE CO2 laser with UV preionization the powerful lasing on the 0200-0110 band at room temperature. The dependencies of the output and spectral performances of the 16 (14) micrometers lasing vs. a content of the active medium, pumping parameters and cavity characteristics have been carried out.

To increase the power performances of the 16 (14) microns CO2 laser the possibility of lasing on the 0201(1001)-0111 band have been experimentally and theoretically investigated under the combined (electrical + optical) excitation of the active medium. The conditions for

CO2 Lasing on Non-Traditional Bands 105

where Kr *,* Ks*,* Kh are measured small signal gains of the corresponding regular, sequence and hot band lines; T is the translational temperature determined from the gain distribution over the regular band lines (Petukhov et. al.., 1985). The lock-in amplifier and box-car integrator used in the recording system allowed us to achieve a better than 2% measurement

> *10.4* µ*m*

*m 16.4* 

*m 9.3* 

Fig. 1. Simplified diagram of lower vibrational levels of the CO2 molecule.

µ*m* 

*m 14* 

addition, an increased specific energy input is also required.

The first step was optimization of active medium composition and pressure *P* and of discharge current. The measurement of the small signal gain Kh has shown that the optimum mixture for the hot band is CO2:N2:He = 1:1.4:3.5 at a total pressure *P* = 11 Torr *(I* = 15 mA) in which on the strong lines *Kh* = 0.08m-1. It is important that this mixture contains less He and has a large partial content of CO2 as compared with the mixture 1:1.6:6.5 (*P* = 15 Torr, *I =* 10 mA) optimum for the regular band 0001-1000(0200). The theoretical and experimental investigations of vibrational temperatures of a CO2 molecule has shown that to obtain considerable hot band gain *Kh* of a CO2 molecule it is necessary to heat up the *v2(v1)*  mode characterized by vibrational temperature *T2* along with the excitation of the *v3* mode (temperature *T3).* For the conventional values of *T3* ≈1600 – 2200 K realized in an electric discharge the Kh gain is shown to achieve its maximum if T2~l/3*T3* (Bertel et. al.., 1983). Such a relationship between *T2* and *T3* can be reached in gas mixtures with greater CO2 and lesser He contents, as compared to those optimal for the regular band oscillation. In

02<sup>0</sup> 0

031 0

µ*m* 

> *10.4* µ*m*

01<sup>1</sup> 1

µ*m* 

020 1 *9.4* µ*m* 

> *9.4* µ*m*

011 0

*16* µ 00<sup>0</sup> 1

000 0

00<sup>0</sup> 2

gain accuracy for all bands.

E, cm-1

1000

2000

3000

4000

100 0

111 0

10<sup>0</sup> 1

> *14.1* µ

*10.8* µ

obtaining effective lasing at the rotational-vibrational transitions of the 0201-0111 (λ = 16.4 µm) and 1001-0111 (λ = 14.1 µm) bands of the CO2 molecule are examined. To obtain population inversion in the indicated channels one should initially populate the 0002 vibrational level, considerable population of which can be accomplished comparatively simply, for example, in an electric discharge. Then a powerful two-frequency radiation resonant with the 0002-0201 (1001) and 0111-1110(0310) transitions acts on the medium excited in such a way. We will discuss by what means such a scheme of lasing in one active medium can be accomplished.

The lidar complex of equipment based on CO2 laser specially designed for atmospheric sensing, with tuning on generation lines in the spectral ranges 9-11.3 and 4.5-5.6 µm will be described. Considerable extension of the spectral range to the short-wave region is attained due to effective CO2 laser second harmonic generation in nonlinear crystals. Taking into the real potentialities of the lidar complex in hand, using a package of spectroscopic data HITRAN, computer simulation of atmospheric transmission has been made. On this basis, by the method of differential absorption a method has been elaborated for measuring of small concentrations of a number of gases.

#### **2. Effective oscillation of a cw CO2 laser in the range of 11** μ**m (01<sup>1</sup> 1-11<sup>1</sup> 0 band)**

The CO2 laser oscillation spectrum expansion to the long-wave region is of interest for various scientific and practical applications, for example, for spectroscopy, atmosphere monitoring, etc. From this point of view, the use of the P-branch of the hot 0111- 1110 band (10.9—11.4 µm) ( see Fig. 1) has considerable promise. Weak hot band lasing was registered in the middle of the 60s in specific long tube (2—4 m) laser systems. The problem of obtaining the hot band oscillation in commercially available cw CO2 lasers is associated with the low gain realized under conventional conditions. Therefore, the effective hot band cw CO2 laser oscillation demands, first of all, as in the pulsed TEA CO2 system, comprehensive study of excitation and active medium composition effects on the hot band gain.

In this work we present experimental results of searching for optimal conditions of the hot band line lasing in a cw CO2 laser with a commercial 1.2 m sealed-off tube. The hot band gain and output optimization was carried out depending on the active medium composition as well as on the discharge current.

The gain in the active medium was measured by small signal probing using the compensation method. We used as a probing laser a specially developed cw stabilized CO2 laser tunable over many of the hot band, sequence 0002-1001(0201) band and regular 0001- 1000(0200) band lines.

Analysis of the results obtained was carried out on the basis of the universally accepted CO2-molecule vibrational temperature model (Petukhov et. al.., 1985). The vibrational temperatures of the asymmetric (ν3) and bound symmetric-bend (2ν2≈ν1) mode, *T3* and *T2,*  respectively, have been determined from the following expressions (Petukhov et. al.., 1985):

$$T\_3 = -\frac{3380}{\ln \frac{K\_s}{2.1 \cdot K\_t} - \frac{36}{T}} , T\_2 = -\frac{960}{\ln \frac{K\_h}{K\_t} - \frac{18}{T}} ,\tag{1}$$

obtaining effective lasing at the rotational-vibrational transitions of the 0201-0111 (λ = 16.4 µm) and 1001-0111 (λ = 14.1 µm) bands of the CO2 molecule are examined. To obtain population inversion in the indicated channels one should initially populate the 0002 vibrational level, considerable population of which can be accomplished comparatively simply, for example, in an electric discharge. Then a powerful two-frequency radiation resonant with the 0002-0201 (1001) and 0111-1110(0310) transitions acts on the medium excited in such a way. We will discuss by what means such a scheme of lasing in one active medium

The lidar complex of equipment based on CO2 laser specially designed for atmospheric sensing, with tuning on generation lines in the spectral ranges 9-11.3 and 4.5-5.6 µm will be described. Considerable extension of the spectral range to the short-wave region is attained due to effective CO2 laser second harmonic generation in nonlinear crystals. Taking into the real potentialities of the lidar complex in hand, using a package of spectroscopic data HITRAN, computer simulation of atmospheric transmission has been made. On this basis, by the method of differential absorption a method has been elaborated for measuring of

The CO2 laser oscillation spectrum expansion to the long-wave region is of interest for various scientific and practical applications, for example, for spectroscopy, atmosphere monitoring, etc. From this point of view, the use of the P-branch of the hot 0111- 1110 band (10.9—11.4 µm) ( see Fig. 1) has considerable promise. Weak hot band lasing was registered in the middle of the 60s in specific long tube (2—4 m) laser systems. The problem of obtaining the hot band oscillation in commercially available cw CO2 lasers is associated with the low gain realized under conventional conditions. Therefore, the effective hot band cw CO2 laser oscillation demands, first of all, as in the pulsed TEA CO2 system, comprehensive

In this work we present experimental results of searching for optimal conditions of the hot band line lasing in a cw CO2 laser with a commercial 1.2 m sealed-off tube. The hot band gain and output optimization was carried out depending on the active medium composition

The gain in the active medium was measured by small signal probing using the compensation method. We used as a probing laser a specially developed cw stabilized CO2 laser tunable over many of the hot band, sequence 0002-1001(0201) band and regular 0001-

Analysis of the results obtained was carried out on the basis of the universally accepted CO2-molecule vibrational temperature model (Petukhov et. al.., 1985). The vibrational temperatures of the asymmetric (ν3) and bound symmetric-bend (2ν2≈ν1) mode, *T3* and *T2,*  respectively, have been determined from the following expressions (Petukhov et. al.., 1985):

<sup>3380</sup> <sup>960</sup> , , <sup>36</sup> <sup>18</sup> ln ln

*s h t t*

− − <sup>⋅</sup>

*KT KT*

(1)

**2. Effective oscillation of a cw CO2 laser in the range of 11** μ**m** 

study of excitation and active medium composition effects on the hot band gain.

3 2

*T T K K*

= − = −

2.1

can be accomplished.

**(01<sup>1</sup>**

**1-11<sup>1</sup>**

**0 band)** 

as well as on the discharge current.

1000(0200) band lines.

small concentrations of a number of gases.

where Kr *,* Ks*,* Kh are measured small signal gains of the corresponding regular, sequence and hot band lines; T is the translational temperature determined from the gain distribution over the regular band lines (Petukhov et. al.., 1985). The lock-in amplifier and box-car integrator used in the recording system allowed us to achieve a better than 2% measurement gain accuracy for all bands.

Fig. 1. Simplified diagram of lower vibrational levels of the CO2 molecule.

The first step was optimization of active medium composition and pressure *P* and of discharge current. The measurement of the small signal gain Kh has shown that the optimum mixture for the hot band is CO2:N2:He = 1:1.4:3.5 at a total pressure *P* = 11 Torr *(I* = 15 mA) in which on the strong lines *Kh* = 0.08m-1. It is important that this mixture contains less He and has a large partial content of CO2 as compared with the mixture 1:1.6:6.5 (*P* = 15 Torr, *I =* 10 mA) optimum for the regular band 0001-1000(0200). The theoretical and experimental investigations of vibrational temperatures of a CO2 molecule has shown that to obtain considerable hot band gain *Kh* of a CO2 molecule it is necessary to heat up the *v2(v1)*  mode characterized by vibrational temperature *T2* along with the excitation of the *v3* mode (temperature *T3).* For the conventional values of *T3* ≈1600 – 2200 K realized in an electric discharge the Kh gain is shown to achieve its maximum if T2~l/3*T3* (Bertel et. al.., 1983). Such a relationship between *T2* and *T3* can be reached in gas mixtures with greater CO2 and lesser He contents, as compared to those optimal for the regular band oscillation. In addition, an increased specific energy input is also required.

CO2 Lasing on Non-Traditional Bands 107

where gain is fairly high *(Kr*≈0.6 m-1) has shown that in this case an output power increase is

After optimization of the gas content, pressure and discharge current we optimized the laser resonator. In the optimal case, the laser resonator was formed by a flat 100 lines/mm-1 grating and a totally reflecting concave mirror *(R =* 3m). The resonator length was 1.5 m.

Fig. 3. Vibrational T3, T2 and transitional T temperatures (a) and CO2 molecules dissociation degree D (b) vs the discharge current I for the CO2:N2:He – 1:1.4:3.5 (*P* – 11 Torr) mixture

without Xe (•) and with optimal Xe content (0.3 Torr) (×).

About 6% of the radiation was extracted through the grating zeroth order.

not large (~15%).

Fig. 2. A typical pattern of the hot band gain *Kh* (a) and output power *Wh* (b) as functions of the disharge current *I* for the CO2:N2:He – 1:1.4:3.5 (*P* – 11 Torr) mixture without Xe (•) and with optimal Xe content (0.3 Torr) (×).

It is known for the CO2 laser regular band that addition of Xe to the active medium sometimes results in an output power increase (Gorobets et al., 1990). We have also investigated the influence of Xe on the characteristics of the active medium and the lasing parameters (Fig. 2). It has been found that small additions of Xe to the mixture (~ 30% of the CO2 content) increase *Kh* by 25% and the lasing power in the hot band by a factor of 1.5. The analysis of vibrational temperatures shows that this is due to the increase in excitation efficiency of vibrations of N2 and the *v3* asymmetric mode of CO2 in electric discharge [Fig. 3(a)]. Besides, using the reconstruction method of *Kh , Ks* and *Kr* gains we have found from the experimental values of *T3, T2* and *T* that addition of Xe reduces the CO2 molecule dissociation in the discharge [Fig. 3(b)]. This also results in an output increase. It is noteworthy that addition of Xe considerably improves the output parameters only for the low gain transitions. The study of the Xe effect on the laser output for the regular band

Fig. 2. A typical pattern of the hot band gain *Kh* (a) and output power *Wh* (b) as functions of the disharge current *I* for the CO2:N2:He – 1:1.4:3.5 (*P* – 11 Torr) mixture without Xe (•) and

It is known for the CO2 laser regular band that addition of Xe to the active medium sometimes results in an output power increase (Gorobets et al., 1990). We have also investigated the influence of Xe on the characteristics of the active medium and the lasing parameters (Fig. 2). It has been found that small additions of Xe to the mixture (~ 30% of the CO2 content) increase *Kh* by 25% and the lasing power in the hot band by a factor of 1.5. The analysis of vibrational temperatures shows that this is due to the increase in excitation efficiency of vibrations of N2 and the *v3* asymmetric mode of CO2 in electric discharge [Fig. 3(a)]. Besides, using the reconstruction method of *Kh , Ks* and *Kr* gains we have found from the experimental values of *T3, T2* and *T* that addition of Xe reduces the CO2 molecule dissociation in the discharge [Fig. 3(b)]. This also results in an output increase. It is noteworthy that addition of Xe considerably improves the output parameters only for the low gain transitions. The study of the Xe effect on the laser output for the regular band

with optimal Xe content (0.3 Torr) (×).

where gain is fairly high *(Kr*≈0.6 m-1) has shown that in this case an output power increase is not large (~15%).

After optimization of the gas content, pressure and discharge current we optimized the laser resonator. In the optimal case, the laser resonator was formed by a flat 100 lines/mm-1 grating and a totally reflecting concave mirror *(R =* 3m). The resonator length was 1.5 m. About 6% of the radiation was extracted through the grating zeroth order.

Fig. 3. Vibrational T3, T2 and transitional T temperatures (a) and CO2 molecules dissociation degree D (b) vs the discharge current I for the CO2:N2:He – 1:1.4:3.5 (*P* – 11 Torr) mixture without Xe (•) and with optimal Xe content (0.3 Torr) (×).

CO2 Lasing on Non-Traditional Bands 109

1983, Gorobets et al., 1990). According to the measurements, mixtures of the composition CO2:N2:Ne = 1:1:1, in which with an increased specific energy contribution the gain coefficients for a weak signal are — 0.2 m-1 for doubly hot transitions and —0.3 m—1 for sequence hot ones, are optimum for TEA CO2 lasers. The vibrational temperatures *T3* and *T2* must have values of —2000 K and —650 K, respectively. For low-pressure lasers with longitudinal discharge mixtures of the compositions CO2:N2:He:Xe = 1:1.2:2.5:0.4 (doubly hot bands) and 1:1.5:2.5:0.4 (sequence hot) are optimum. The gain coefficient in such mixtures for the aforementioned transitions can reach —0.04 m-1 (*T3*—1800 K, *T2*—600 K). It should be noted that at these transitions the gain is considerably lower than that at the ordinary (~20 times) and hot (~4 times) bands, and consequently a high-Q cavity, lack of harmful losses, and careful selection of the active medium and the conditions of its

The lasing mode on the new transitions was studied first on a TEA CO2 laser with UV preionization. The distance between electrodes that were 4 cm wide was 2 cm. The length of the discharge gap was 70 cm. The main charge and the UV preionization were energized from a battery of low-inductance capacitors with a total capacitance of 0.25 µF, charged to a voltage of 30 kV. The design and of the laser and its performance are described in detail in (Gorobets et al., 1995). A two-transmission three-mirror resonator was used to increase the length of the active medium to 140 cm. A planar grating with 150 lines/mm working in the first order according to an autocollimation scheme with a reflection coefficient not less than —90%, was one of the end mirrors of the resonator. Radiation from the resonator (~5%) was extracted through the zero order of the grating. The other two mirrors were spherical (R = 10 m) with a highly reflective coating. The active medium of the laser was a mixture of gases of the composition CO2:N2:He = 0.8:1.0:1.2 with a total pressure of 200 Torr, which is close to the optimum found from experimental investigations of vibrational temperatures. For this mixture lasing was achieved at more than 10 lines in new bands of the 11.3-11.6 µm range. At the strongest lines the energy in the pulse exceeded 150 mJ. The peak power with a pulse length at half-height of ~0.5 µs attained ~0.3 MW. More thorough investigations of the lasing spectrum of the new transitions were done in the present work for a low-pressure CO2 laser. Experiments were performed with a GL-501 production-type gas-discharge tube of an LG-22 commercial laser (FSUE RPC "Istok", Fryasino, Russia). The inner diameter of the tube— 15 mm, length of the discharge gap —1.2 m. The tube, which worked in the sealed-off mode, was filled with a gas mixture of the composition CO2:N2:He:Xe = 1:1.2:2.5:0.4 under the total pressure of 13.5 Torr. The total reflection spherical mirror (*R* = 3 m) of the commercial laser was not replaced, and a diffraction grating, which worked according to an autocollimation scheme in the first order, was used instead of the output mirror. The emission was extracted through the zero order. The cavity base was 1.5 m. Most of the new lines were obtained with a grating with 100 lines/mm (reflection coefficient – 95%, extraction of emission – 3%). A number of lines in the range of 11.0-11.4 µm, where comparatively strong hot transition are located, were successfully obtained with a more selective grating with 150 lines/mm (93 and 3%, respectively). In addition, to increase the Q-factor of the cavity the germanium etalon was placed before the grating (perpendicular to the output radiation), which not only increased the Q-factor of the grating, returning 75% of the radiation back to the cavity, but also increased its selectivity substantially. As a whole, this device, consisting of a grating and an etalon, was a highly selective output mirror with a reflection coefficient of 97.5% for a grating with 100 lines/mm and 95.5% for a grating with 150 lines/mm. It should be noted,

excitation are necessary to obtain lasing on transitions with such a low gain.

Thus, after the above improvements the commercially available sealed-off laser (LG-22) (FSUE RPC "Istok", Fryasino, Russia) oscillates on more than 30 lines of the P-branch of the 0111- 1110 band in the 10.9—11.3 µm range with output power no less than 0.5 W. On strong lines (P(16)—P(26)) output power was ~ 6W at efficiency ~3% which makes up ~40% of analogous laser parameters in the case of oscillation on the lines of regular bands 0001-1000 (0200) under optimum conditions.

#### **3. New laser transitions of the CO2 molecule in the wavelength range of 11.0-11.6** μ**m**

Construction of powerful and efficient laser sources, generating in various IR ranges, is of importance for further development of a number of trends, e.g., spectroscopy, laser chemistry, isotope separation, sounding of the atmosphere, and metrology. The easiest and most natural way to solve this problem is to use unconventional transitions to produce lasing in commonly used CO2 lasers (Churakov et al., 1987). The spectral range of CO2 lasers is greatly increased in lasing on transitions of the so-called "hot" band 0111-1110, whose Pbranch is in the range of 10.9-11.3 µm. Thorough investigations of gain, vibrational temperatures, and output parameters on lines of the hot band made it possible to achieve efficient lasing both for pulse TEA and for cw longitudinal-discharge CO2 lasers.

In studying the lasing spectrum of hot transitions in TEA CO2 lasers (Bertel at al., 1983). some lines not belonging to the 0111-1110 band occurred in the spectral range of 875-882 cm1 that were not identified due to the poor resolution of the monochromator used and the lack of reliable spectroscopic data in the literature at that time. It was suggested, that these lasing lines belong to higher level transitions, e.g., 10°l-20°0(0400), which were called 'doubly hot," i.e., transitions in which compared to hot transitions two deformation quanta or one symmetric quantum rather than one deformation quantum is added both to the upper and to the lower energy level.

In the present work lasing in both a TEA laser and a low-pressure laser with longitudinal discharge on some transitions of the CO2 molecule in the range of 11.0-11.6 µm is reported for the first time. The rather high resolution of the spectral equipment used and calculation of transition frequencies on the basis of recent spectroscopic constants made it possible to identify definitively the lasing lines obtained as belonging to the doubly hot bands 022l-1220 and 10°1-2000 and the sequence hot band 0112-1111 (Fig. 1).

Within the scope of a commonly used model of vibrational temperatures (Gordiets at al. 1980, Smith and Thompson, 1981) let us analyze what gain coefficients for a weak signal can be realized for the aforementioned bands in electrical-discharge lasers. Estimates showed that to achieve a suitable gain at the new transitions it is necessary, together with the heating up of the asymmetric type of oscillations, characterized by the vibrational temperature *T3,* to strongly excite the connected deformation and symmetric modes *(T2).* Moreover for the sequence hot band 0112-1111 there is one additional condition – the excitation of the asymmetric mode must be at the same high level as for the sequence bands 0002-1001 (02°1) (Petukhov et. al.., 1985).

To find optimum conditions for lasing on the aforementioned bands experimental studies of vibrational temperatures in active media of a TEA CO2 laser and a low-pressure laser with longitudinal discharge were carried out using to the techniques described in (Bertel at al.,

Thus, after the above improvements the commercially available sealed-off laser (LG-22) (FSUE RPC "Istok", Fryasino, Russia) oscillates on more than 30 lines of the P-branch of the 0111- 1110 band in the 10.9—11.3 µm range with output power no less than 0.5 W. On strong lines (P(16)—P(26)) output power was ~ 6W at efficiency ~3% which makes up ~40% of analogous laser parameters in the case of oscillation on the lines of regular bands 0001-1000

**3. New laser transitions of the CO2 molecule in the wavelength range of** 

efficient lasing both for pulse TEA and for cw longitudinal-discharge CO2 lasers.

and 10°1-2000 and the sequence hot band 0112-1111 (Fig. 1).

Construction of powerful and efficient laser sources, generating in various IR ranges, is of importance for further development of a number of trends, e.g., spectroscopy, laser chemistry, isotope separation, sounding of the atmosphere, and metrology. The easiest and most natural way to solve this problem is to use unconventional transitions to produce lasing in commonly used CO2 lasers (Churakov et al., 1987). The spectral range of CO2 lasers is greatly increased in lasing on transitions of the so-called "hot" band 0111-1110, whose Pbranch is in the range of 10.9-11.3 µm. Thorough investigations of gain, vibrational temperatures, and output parameters on lines of the hot band made it possible to achieve

In studying the lasing spectrum of hot transitions in TEA CO2 lasers (Bertel at al., 1983). some lines not belonging to the 0111-1110 band occurred in the spectral range of 875-882 cm1 that were not identified due to the poor resolution of the monochromator used and the lack of reliable spectroscopic data in the literature at that time. It was suggested, that these lasing lines belong to higher level transitions, e.g., 10°l-20°0(0400), which were called 'doubly hot," i.e., transitions in which compared to hot transitions two deformation quanta or one symmetric quantum rather than one deformation quantum is added both to the upper and

In the present work lasing in both a TEA laser and a low-pressure laser with longitudinal discharge on some transitions of the CO2 molecule in the range of 11.0-11.6 µm is reported for the first time. The rather high resolution of the spectral equipment used and calculation of transition frequencies on the basis of recent spectroscopic constants made it possible to identify definitively the lasing lines obtained as belonging to the doubly hot bands 022l-1220

Within the scope of a commonly used model of vibrational temperatures (Gordiets at al. 1980, Smith and Thompson, 1981) let us analyze what gain coefficients for a weak signal can be realized for the aforementioned bands in electrical-discharge lasers. Estimates showed that to achieve a suitable gain at the new transitions it is necessary, together with the heating up of the asymmetric type of oscillations, characterized by the vibrational temperature *T3,* to strongly excite the connected deformation and symmetric modes *(T2).* Moreover for the sequence hot band 0112-1111 there is one additional condition – the excitation of the asymmetric mode must be at the same high level as for the sequence bands 0002-1001 (02°1)

To find optimum conditions for lasing on the aforementioned bands experimental studies of vibrational temperatures in active media of a TEA CO2 laser and a low-pressure laser with longitudinal discharge were carried out using to the techniques described in (Bertel at al.,

(0200) under optimum conditions.

**11.0-11.6** μ**m** 

to the lower energy level.

(Petukhov et. al.., 1985).

1983, Gorobets et al., 1990). According to the measurements, mixtures of the composition CO2:N2:Ne = 1:1:1, in which with an increased specific energy contribution the gain coefficients for a weak signal are — 0.2 m-1 for doubly hot transitions and —0.3 m—1 for sequence hot ones, are optimum for TEA CO2 lasers. The vibrational temperatures *T3* and *T2* must have values of —2000 K and —650 K, respectively. For low-pressure lasers with longitudinal discharge mixtures of the compositions CO2:N2:He:Xe = 1:1.2:2.5:0.4 (doubly hot bands) and 1:1.5:2.5:0.4 (sequence hot) are optimum. The gain coefficient in such mixtures for the aforementioned transitions can reach —0.04 m-1 (*T3*—1800 K, *T2*—600 K). It should be noted that at these transitions the gain is considerably lower than that at the ordinary (~20 times) and hot (~4 times) bands, and consequently a high-Q cavity, lack of harmful losses, and careful selection of the active medium and the conditions of its excitation are necessary to obtain lasing on transitions with such a low gain.

The lasing mode on the new transitions was studied first on a TEA CO2 laser with UV preionization. The distance between electrodes that were 4 cm wide was 2 cm. The length of the discharge gap was 70 cm. The main charge and the UV preionization were energized from a battery of low-inductance capacitors with a total capacitance of 0.25 µF, charged to a voltage of 30 kV. The design and of the laser and its performance are described in detail in (Gorobets et al., 1995). A two-transmission three-mirror resonator was used to increase the length of the active medium to 140 cm. A planar grating with 150 lines/mm working in the first order according to an autocollimation scheme with a reflection coefficient not less than —90%, was one of the end mirrors of the resonator. Radiation from the resonator (~5%) was extracted through the zero order of the grating. The other two mirrors were spherical (R = 10 m) with a highly reflective coating. The active medium of the laser was a mixture of gases of the composition CO2:N2:He = 0.8:1.0:1.2 with a total pressure of 200 Torr, which is close to the optimum found from experimental investigations of vibrational temperatures. For this mixture lasing was achieved at more than 10 lines in new bands of the 11.3-11.6 µm range. At the strongest lines the energy in the pulse exceeded 150 mJ. The peak power with a pulse length at half-height of ~0.5 µs attained ~0.3 MW. More thorough investigations of the lasing spectrum of the new transitions were done in the present work for a low-pressure CO2 laser.

Experiments were performed with a GL-501 production-type gas-discharge tube of an LG-22 commercial laser (FSUE RPC "Istok", Fryasino, Russia). The inner diameter of the tube— 15 mm, length of the discharge gap —1.2 m. The tube, which worked in the sealed-off mode, was filled with a gas mixture of the composition CO2:N2:He:Xe = 1:1.2:2.5:0.4 under the total pressure of 13.5 Torr. The total reflection spherical mirror (*R* = 3 m) of the commercial laser was not replaced, and a diffraction grating, which worked according to an autocollimation scheme in the first order, was used instead of the output mirror. The emission was extracted through the zero order. The cavity base was 1.5 m. Most of the new lines were obtained with a grating with 100 lines/mm (reflection coefficient – 95%, extraction of emission – 3%). A number of lines in the range of 11.0-11.4 µm, where comparatively strong hot transition are located, were successfully obtained with a more selective grating with 150 lines/mm (93 and 3%, respectively). In addition, to increase the Q-factor of the cavity the germanium etalon was placed before the grating (perpendicular to the output radiation), which not only increased the Q-factor of the grating, returning 75% of the radiation back to the cavity, but also increased its selectivity substantially. As a whole, this device, consisting of a grating and an etalon, was a highly selective output mirror with a reflection coefficient of 97.5% for a grating with 100 lines/mm and 95.5% for a grating with 150 lines/mm. It should be noted,

CO2 Lasing on Non-Traditional Bands 111

375 Hz, a length of the excitation pulse of ∼5O μs, an average current of 8.5 mA. Under these conditions with careful adjustment of the diffraction grating and the etalon we managed to obtain more than *50* new lasing lines (see Table 1). Lasing wavelengths were measured with an SPM-2 monochromator (Carl Zeiss Jena, Germany) with a highly selective diffraction grating, whose resolution was not worse than 0.0005 μm. Absolute calibration of the monochromator was done using the technique described in (Gorobets et al., 1992), which is based on a search for a line with an anomalously high gain, e.g., the line *P(23)* of the hot band. In addition, correction calibration against known wavelengths of hot transitions was done on virtually the entire investigated spectrum. New lines were identified by comparing measured and calculated values of transition wavelengths. Calculations were done using standard methods. Values of the constants G, B, D, H were well known (Witteman, 1987). The peak power (intensity) on the strongest lines of the new bands with a lasing pulse length at half-height of *—50* ns was — 30 W. The average output power reached —0.2 W. Lasing was achieved at a number of new transitions and in the continuous mode with the discharge tube being energized from a dc power supply. More than 25 new lasing lines with λ = 11.1-11.4 μm, belonging to all the aforementioned bands, were observed in this mode in

the spectral range studied. The output power on strong lines attained 0.25 W.

broadens the potentialities of simple laser systems on CO2 for various applications.

search new and perfecting of known methods of optimization CO2 lasers.

on the information about the temperatures of the medium.

**4. Optimisation of a cw CO2 laser output** 

**4.1 Optimisation technique** 

The characteristics of the output radiation given in the present work are not the best attainable. Optimization of the active medium composition, the conditions of its excitation, and the cavity parameters will make it possible to increase the efficiency of lasing at the new transitions. However at present the large number of new lasing lines obtained substantially

To the present time the number of optimization methods of CO2 laser power parameters is developed. However, the known methods are either complex, since they are based on the calculations calling for a knowledge of a great number of parameters or by virtue of sufficiently rough approximations, not always provide the necessary accuracy, as in the development of laser systems generating on the nonregular transitions – 0002-1001, 0201 (sequence bands); 0111- 1110 (hot band); 0221-1220, 0201-1200 (double hot bands). The gain on these transitions is much weaker than on the regular transitions 0001-1000, 0200 and hence a careful optimization of the active medium composition and of the resonator and pumping parameters is required to provide the lasing on them. Therefore until now remains to actual

We have developed and experimentally tested the method of optimizations of the cw CO2 lasers energy parameters. To realize it, it is necessary to known the vibrational temperatures of the symmetrical (*T1*), bending (*T2*) and asymmetrical (*T3*) modes of the CO2 molecule vibrations. At the present time, the generally recognized fact is that the knowledge of these temperatures as well of the gas temperature (*T*) of the gas mixture makes it possible to determine all the most important characteristics of the active medium (population of the energy levels, the energy accumulated in different modes of CO2, the efficiency of excitation, and so on). Next, the main energy characteristics of the laser system can be calculated based


that this original technique made it possible to separate weak lines of the new transitions from closely positioned ones in some regions of the spectrum of stronger hot lines.

\*The lines are not identified ambiguously (they may belong to the both lines).

Table 1. Measured and calculated values of wavelengths and experimental values of intensities for new transitions

The lasing spectrum in the range of 11.0-11.6 μm was studied in detail with the gasdischarge tube being energized from a pulsed source. It was found experimentally that the following pumping parameters are optimum for lasing at the new transitions: a pulse rate of

that this original technique made it possible to separate weak lines of the new transitions

0221-1220 1001-2000

Line λmeas, µm λcal, µm Intensity,

*P(46)\** 11.3173 11.317088 35

W

from closely positioned ones in some regions of the spectrum of stronger hot lines.

W

*P(25)* 11.3991 11.399538 25 0112-1111 *P(26)* 11.4117 11.411523 18

\*The lines are not identified ambiguously (they may belong to the both lines).

Table 1. Measured and calculated values of wavelengths and experimental values of

The lasing spectrum in the range of 11.0-11.6 μm was studied in detail with the gasdischarge tube being energized from a pulsed source. It was found experimentally that the following pumping parameters are optimum for lasing at the new transitions: a pulse rate of

*P(27)* 11.4241 11.423790 16 *P(23)* 11.0408 11.041722 25 *P(28)* 11.4357 11.435948 15 *P(24)* 11.0512 11.050460 18 *P(29)* 11.4494 11.448451 15 *P(25)* 11.0650 11.064261 25 *P(30)* 11.4596 11.460775 15 *P(26)* 11.0733 11.072789 15 *P(31)* 11.4730 11.473525 9 *P(28)* 11.0953 11.095487 30 *P(32)* 11.4855 11.486009 10 *P(29)* 11.1096 11.110543 30 *P(33)* 11.4981 11.499017 8 *P(30)* 11.1176 11.118556 25 *P(34)* 11.5112 11.511655 12 *P(32)* 11.1425 11.142003 28 *P(35) 11.5245* 11.524934 4 *P(33)* 11.1591 11.158465 20 *P(36)* 11.5375 11.537715 4 *P(34)* 11.1667 11.165831 30 *P(36)* 11.1908 11.190045 30

*P(12)* 11.2513 11.251536 10 *P(14)* 11.0358 11.036728 10 *P(14)\** 11.2729 11.273239 25 *P(16)* 11.0590 11.058304 10 *P(15)* 11.2834 11.284243 15 *P(18)* 11.0794 11.080312 15 *P(16)* 11.2944 11.295321 16 *P(20)* 11.1027 11.102758 20 *P(17)* 11.3064 11.306522 24 *P(22)* 11.1260 11.125648 20 *P(18)\** 11.3173 11.317785 35 *P(24)* 11.1488 11.148987 16 *P(19)* 11.3300 11.329186 30 *P(28)* 11.1961 11.197036 20 *P(20)* 11.3410 11.340633 28 *P(30)* 11.2223 11.221757 17 *P(21)* 11.3517 11.352241 25 *P(32)* 11.2467 11.246953 20 *P(22)* 11.3634 11.363870 20 *P(34)* 11.2729 11.272628 25 *P(23)* 11.3754 11.375690 20 *P(36)* 11.2978 11.298791 20 *P(24)* 11.3872 11.387499 30 *P(38)* 11.3251 11.325449 10

Line λmeas, µm λcal, µm Intensity,

0111-1110

*P(47)* 11.3075 11.307393 40 *P(49)* 11.3352 11.334278 35 *P(50)* 11.3601 11.359850 40 *P(51)* 11.3610 11.361589 18 *P(53)* 11.3907 11.389331 20

intensities for new transitions

375 Hz, a length of the excitation pulse of ∼5O μs, an average current of 8.5 mA. Under these conditions with careful adjustment of the diffraction grating and the etalon we managed to obtain more than *50* new lasing lines (see Table 1). Lasing wavelengths were measured with an SPM-2 monochromator (Carl Zeiss Jena, Germany) with a highly selective diffraction grating, whose resolution was not worse than 0.0005 μm. Absolute calibration of the monochromator was done using the technique described in (Gorobets et al., 1992), which is based on a search for a line with an anomalously high gain, e.g., the line *P(23)* of the hot band. In addition, correction calibration against known wavelengths of hot transitions was done on virtually the entire investigated spectrum. New lines were identified by comparing measured and calculated values of transition wavelengths. Calculations were done using standard methods. Values of the constants G, B, D, H were well known (Witteman, 1987).

The peak power (intensity) on the strongest lines of the new bands with a lasing pulse length at half-height of *—50* ns was — 30 W. The average output power reached —0.2 W. Lasing was achieved at a number of new transitions and in the continuous mode with the discharge tube being energized from a dc power supply. More than 25 new lasing lines with λ = 11.1-11.4 μm, belonging to all the aforementioned bands, were observed in this mode in the spectral range studied. The output power on strong lines attained 0.25 W.

The characteristics of the output radiation given in the present work are not the best attainable. Optimization of the active medium composition, the conditions of its excitation, and the cavity parameters will make it possible to increase the efficiency of lasing at the new transitions. However at present the large number of new lasing lines obtained substantially broadens the potentialities of simple laser systems on CO2 for various applications.

#### **4. Optimisation of a cw CO2 laser output**

#### **4.1 Optimisation technique**

To the present time the number of optimization methods of CO2 laser power parameters is developed. However, the known methods are either complex, since they are based on the calculations calling for a knowledge of a great number of parameters or by virtue of sufficiently rough approximations, not always provide the necessary accuracy, as in the development of laser systems generating on the nonregular transitions – 0002-1001, 0201 (sequence bands); 0111- 1110 (hot band); 0221-1220, 0201-1200 (double hot bands). The gain on these transitions is much weaker than on the regular transitions 0001-1000, 0200 and hence a careful optimization of the active medium composition and of the resonator and pumping parameters is required to provide the lasing on them. Therefore until now remains to actual search new and perfecting of known methods of optimization CO2 lasers.

We have developed and experimentally tested the method of optimizations of the cw CO2 lasers energy parameters. To realize it, it is necessary to known the vibrational temperatures of the symmetrical (*T1*), bending (*T2*) and asymmetrical (*T3*) modes of the CO2 molecule vibrations. At the present time, the generally recognized fact is that the knowledge of these temperatures as well of the gas temperature (*T*) of the gas mixture makes it possible to determine all the most important characteristics of the active medium (population of the energy levels, the energy accumulated in different modes of CO2, the efficiency of excitation, and so on). Next, the main energy characteristics of the laser system can be calculated based on the information about the temperatures of the medium.

CO2 Lasing on Non-Traditional Bands 113

obtain expressions for determining *T3* for the above-indicated bands. For example, for the

3 3 3 \* \* \* 3 3 1 3

(5)

<sup>1</sup> 1 exp exp exp exp ,

6 2 3

6 2 3

1

15

3 3 3 \* \* \* 3 3 1 3

*K K hv hv hv hv K kT kT k kT T*

<sup>−</sup> = ⋅− − ⋅ − − − −

Similar expressions are also true for other bands. Thus, if the all temperatures in the regime of amplification and the loss factors are known, it is an easy matter to calculate the output power for different bands. The temperatures *T3, T2, T1* and *T* can be determined from the measurement of the gain factor of a weak signal on the lines of different bands by the

Figure 4 shows a block diagram of the experimental setup for CO2 laser optimization. A sealed off a cw CO2 laser was the source of probe radiation. It could be tuned over the vibrational-rotational lines of the regular (0001-1000*,* 0200) bands, the sequence (0002-1001,

0201) bands, the hot (0111- 1110) band or the new (0221-1220, 0201-1200….) bands.

1 – probing laser; 2 – discharge tube; 3 – 100% reflection mirror; 4 – grating; 5 – additional mirror; 6 – iris diaphragm; 7 – chopper; 8 – ZnSe plane-parallel plate; 9 – mirror; 10 – interference filter; 11 – photo detector; 12 – polarizer; 13 – spectrum analyzer; 14 – ADC; 15 – computer; 16 gas valve.

14

14

Fig. 4. Experimental setup for CO2 laser optimization

*hv hv hv hv kT kT kT kT*

−− ⋅ −−− − =

<sup>1</sup> 1 exp exp exp exp

0002-1001 band it has the form

**4.2 Experimental setup** 

5

7

12 10

12

13

11

11

1

4

*h us loss loss s g*

method described in (Petukhov et. al.., 1985).

In our works we used the method of determination of vibrational temperatures, which is based on the measurements of the gain on separate vibrational lines of regular and nonregular CO2 bands (Petukhov et. al.., 1985). The advantages of this method are the possibility of determination of all vibrational and translational temperatures at once, a relative simplicity and sufficiently high accuracy as compared with other known methods. Besides, a knowledge of the absolute values of the gain factors and of the active medium composition is not needed here, which is sometimes very important.

It would appear reasonable that within the limits of the model of vibrational temperatures the output power (*P*) for every above-indicated bands is dependent only on temperatures. The experimental investigations performed by us show that for a typical low-pressure CO2 laser with a longitudinal continuous discharge the active medium in the lasing regime differs significantly from that in the absence of lasing in only the value of the asymmetric vibration temperatures *T3*, while for the other temperatures *T2, T1* and *T* the difference is insignificant (less than 10 %). Such a temperature approximation is predominantly due to fact that the energy capacitance for vibrations of symmetric and bending modes of CO2 is much greater than that for vibrations of the asymmetric mode as well as due to the constant effective heat abstraction from the low laser levels. This approximation may be thought of as by true for laser system with on efficiency of transformation of the energy contributed to the discharge to the lasing energy of —10 % or less percent, which is characteristic of all real continuous CO2 lasers. In this case, using the ratio between the temperature of the asymmetric mode and average number of vibrational quanta accumulated in this mode we can write the following simple expression for the output power in every above-indicated band:

$$\mathbf{e}\_3 = \exp\left(-\frac{hv\_3}{kT\_3}\right) \Big/ \left[1 - \exp\left(\frac{hv\_3}{kT\_3}\right)\right] \tag{2}$$

$$P = A \cdot \frac{K\_{\rm loss}^{\rm ns}}{K\_{\rm loss}^{h} - K\_{\rm loss}^{\rm ns}} \cdot \left( \frac{\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)}{\left[1 - \exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)\right]} - \frac{\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)}{\left[1 - \exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)\right]} \right) \tag{3}$$

where *A* is the proportionality factor dependent on the CO2 content and independent on the lasing band; *Klossus* is the useful loss factor; *Klossh* is the harmful loss factor; *T3* and *T3\** are the vibrational temperatures of the asymmetric mode of the CO2 molecule in the regime of amplification and lasing, respectively.

The temperature *T3* as well as *T2, T1* and *T* can be found if the gain factors of the weak signal in different bands are known (Petukhov et. al.., 1985). To determine the temperature *T3\** we will draw on the fact that in the regime of lasing (continuous) the gain factor is equal to the total loss factor:

$$K\_{\mathcal{g}}^{\*}\left(T\_3^{\*}, T\_2, T\_1, T\right) = K\_{\text{loss}}^{h} - K\_{\text{loss}}^{us} \tag{4}$$

Then, using the dependence of the gain factor on the difference in the population of the upper and low laser levels, expressed through vibrational temperatures. We can easily

In our works we used the method of determination of vibrational temperatures, which is based on the measurements of the gain on separate vibrational lines of regular and nonregular CO2 bands (Petukhov et. al.., 1985). The advantages of this method are the possibility of determination of all vibrational and translational temperatures at once, a relative simplicity and sufficiently high accuracy as compared with other known methods. Besides, a knowledge of the absolute values of the gain factors and of the active medium

It would appear reasonable that within the limits of the model of vibrational temperatures the output power (*P*) for every above-indicated bands is dependent only on temperatures. The experimental investigations performed by us show that for a typical low-pressure CO2 laser with a longitudinal continuous discharge the active medium in the lasing regime differs significantly from that in the absence of lasing in only the value of the asymmetric vibration temperatures *T3*, while for the other temperatures *T2, T1* and *T* the difference is insignificant (less than 10 %). Such a temperature approximation is predominantly due to fact that the energy capacitance for vibrations of symmetric and bending modes of CO2 is much greater than that for vibrations of the asymmetric mode as well as due to the constant effective heat abstraction from the low laser levels. This approximation may be thought of as by true for laser system with on efficiency of transformation of the energy contributed to the discharge to the lasing energy of —10 % or less percent, which is characteristic of all real continuous CO2 lasers. In this case, using the ratio between the temperature of the asymmetric mode and average number of vibrational quanta accumulated in this mode we can write the

composition is not needed here, which is sometimes very important.

following simple expression for the output power in every above-indicated band:

3

*us loss h us loss loss*

*P A*

amplification and lasing, respectively.

total loss factor:

3 3

(2)

(3)

3 3 exp 1 exp , *hv hv kT kT* 

exp exp

*K kT kT*

*K K hv hv*

=⋅ ⋅ <sup>−</sup> <sup>−</sup> − − − −

where *A* is the proportionality factor dependent on the CO2 content and independent on the lasing band; *Klossus* is the useful loss factor; *Klossh* is the harmful loss factor; *T3* and *T3\** are the vibrational temperatures of the asymmetric mode of the CO2 molecule in the regime of

The temperature *T3* as well as *T2, T1* and *T* can be found if the gain factors of the weak signal in different bands are known (Petukhov et. al.., 1985). To determine the temperature *T3\** we will draw on the fact that in the regime of lasing (continuous) the gain factor is equal to the

Then, using the dependence of the gain factor on the difference in the population of the upper and low laser levels, expressed through vibrational temperatures. We can easily

( ) \* \*

1 exp 1 exp

3 3

*hv hv*

<sup>−</sup> <sup>−</sup>

3 3 3 3

*kT kT*

3 3

3 21 ,,, , *h us K T TTT K K <sup>g</sup>* = − *loss loss* (4)

\*

\*

,

ε= − −

obtain expressions for determining *T3* for the above-indicated bands. For example, for the 0002-1001 band it has the form

$$\begin{aligned} &\left[1-\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)\right]\cdot\left\{\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)-\exp\left(-\frac{h\upsilon\mathbf{1}}{kT\_{1}}\right)\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)\right\}=\\ &=\frac{K\_{\text{loss}}^{h}-K\_{\text{loss}}^{us}}{K\_{\text{s}}^{s}}\cdot\left[1-\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)\right]\cdot\left\{\exp\left(-\frac{h\upsilon\_{3}}{kT\_{3}}\right)-\exp\left(-\frac{h\upsilon\mathbf{1}}{kT\_{1}}\right)\exp\left(-\frac{h\upsilon\mathbf{1}}{kT\_{3}}\right)\right\}\,,\end{aligned} \tag{5}$$

Similar expressions are also true for other bands. Thus, if the all temperatures in the regime of amplification and the loss factors are known, it is an easy matter to calculate the output power for different bands. The temperatures *T3, T2, T1* and *T* can be determined from the measurement of the gain factor of a weak signal on the lines of different bands by the method described in (Petukhov et. al.., 1985).

#### **4.2 Experimental setup**

Figure 4 shows a block diagram of the experimental setup for CO2 laser optimization. A sealed off a cw CO2 laser was the source of probe radiation. It could be tuned over the vibrational-rotational lines of the regular (0001-1000*,* 0200) bands, the sequence (0002-1001, 0201) bands, the hot (0111- 1110) band or the new (0221-1220, 0201-1200….) bands.

1 – probing laser; 2 – discharge tube; 3 – 100% reflection mirror; 4 – grating; 5 – additional mirror; 6 – iris diaphragm; 7 – chopper; 8 – ZnSe plane-parallel plate; 9 – mirror; 10 – interference filter; 11 – photo detector; 12 – polarizer; 13 – spectrum analyzer; 14 – ADC; 15 – computer; 16 gas valve.

Fig. 4. Experimental setup for CO2 laser optimization

CO2 Lasing on Non-Traditional Bands 115

Fig. 5. Dependencies of temperatures *T3* (∇), *T2* (O), and *T* (×) (a) and output power *P* (b) from a discharge current (× - for P(18) 0001-1000, O - for P(19) 0002-1001, ∇ - for P(19) 0111-

Figure 5b shows the calculated curves and experimental values of the output power for the considered bands. At first we calculated the value of *P/A* for every band in accordance with discharge current. Then, we determined the proportionality coefficient A from the experimental data for the 0001-1001 band at *I*=25 mA. As this takes place, the coefficient A has a common value for all lasing bands. Next, the dependence P on I was constructed.

The method of output optimization of cw CO2 lasers has been developed. The method is based on vibrational and translational temperatures determination by gain measurements on the ro-vibrational lines of regular (0001-1000, 0200) and nonregular (0002-1001,0201; 0111- 1110; (0221-1220, 0201-1200…) bands of CO2 molecule. To test the validity of the method, the experiment realization has been done for a low pressure CO2 laser with the cw longitudinal discharge, that can oscillate on the lines of regular and nonregular lines. The good agreement between calculation and experiment data has been observed. Thus, a good agreement between the calculated and experimental data, which is observed, as a whole, for all the investigated bands, is demonstration that this method can be applied to the optimization of the output power of cw CO2 lasers. This method can be also successfully used for the optimization of the output parameters depending on the pumping and Q-factor of the resonator of the lasers generating only on the regular transitions 0001-1000 and 0001-0200.

Earlier the lasing on the 0200(1000)-0110 band of the CO2 molecule (see Fig. 1) has been obtained in the specific systems at cryogenic temperatures under the lowest efficiency (Wexler, 1987). The optimization of the active medium and its electrical discharge pumping conditions based on the original technique of the temperature model (gain measurements on the several bands: 0001-1000, 0002-1001, 0111- 1110 of CO2 molecule) allowed to obtain in the simple TE CO2 laser with UV preionization (the active media length is 65 cm the width of electrodes is 2.5 cm, the interval between electrodes is 1.8 cm, (the voltage on the 0.2 micro Farad capacitor is 6.5 kV) the powerful lasing on the 0200(1000)-0110 bands at the room temperature. The output pulse energy of 57 mJ and the peak power of some tens kWatt have

**0(10<sup>0</sup>**

**0)-01<sup>1</sup>**

**0 and 02<sup>0</sup>**

**1(10<sup>0</sup> 1)-**

**5. 16(14) microns TE CO2 laser working on the 02<sup>0</sup>**

1110, - for P(19) 0221-1220)

**01<sup>1</sup>**

**1 bands** 

A production-type water-cooled sealed-off gas-discharge tube of GL-501 type (FSUE RPC "Istok", Fryasino, Russia) was used as an active element of the probe laser. It has dischargegap length of ~1 .2 m, and the inside diameter is of 15 mm. The tube was filled with a CO : N2 : He :Xe mixture in a proportion of 1.0:1.6:4.0:0.6 at a total pressure of *13.5* Torr. The laser cavity was formed by ~100% reflecting mirror with a curvature radius of 3 m built in the tube, a plane diffraction grating and an additional mirror with a large curvature radius.

We used a nonconventional scheme of the laser cavity. The diffraction grating operated in the first diffraction order in the nonLittrow scheme. Laser radiation was extracted from the cavity through the zero order. Our studies have shown that the diffraction grating with 150 lines/mm and a reflectance of >95%, combined with the additional mirror with a curvature radius of 10 m, are optimal for obtaining the necessary high spectral resolution with a sufficiently high output power. A more detailed description of the construction of the probe laser is given in the next part.

A signal from the probe laser passed a two times through the active medium under study in the discharge tube and was recorded by a liquid nitrogen cooled photo detector. This discharge tube was similar to one used as the active element of the probe laser. In addition to the measuring signal, we used a reference signal that does not pass along the investigated active medium and appears as a result of reflection of a portion of radiation from the ZnSe plane-parallel plate (see Fig. 4). This portion of radiation was directed to the another liquid nitrogen cooled Ge:Au photodetector of the reference channel, which makes automatically possible to account for the possible instability of the output laser radiation by way of normalization of the measuring signal to reference one.

The electric signals from two photodetectors were fed into an two-channel digital registration system on the base of PC. Lasing wavelengths were measured with SPM-2 spectrum analyzer (Carl Zeiss Jena, Germany) with a highly selective diffraction grating, whose resolution was not worse than 0.0005 µm.

#### **4.3 Results and discussions**

To test the method proposed we have performed experimental investigations and calculations of the output power (*P*) dependence on the discharge current (*I*) for a cw CO2 laser, operated on four different bands (0001-1000, 0002-1001, 111- 1110 and 0221-1220). The cw CO2 laser was similar to one used as the probe laser. The only distinction is the using of the appropriate diffraction grating with optimum Q-factor for each band.

The temperatures T3, T2 and T (see Fig. 5a), used in the calculations, were determined from the measurement of the gain factor of a weak signal by the method described in (Petukhov et. al.., 1985). For our experiments *T1* is approximately equal *T2*. According to our calculations the loss factors for different bands have the following values:

$$\begin{aligned} \text{for } P \text{ (18) } \ 00^0 \mathbf{1} - 10^0 \mathbf{0} - K\_{\text{loss}}^h &= \mathbf{4}.8 \times 10^{-4} \, cm^{-1} \, \text{;} \, K\_{\text{loss}}^{us} = \mathbf{5}.3 \times 10^{-4} \, cm^{-1}, \\\\ \text{for } P \text{ (19) } \ 00^0 \mathbf{2} - 10^0 \mathbf{1} - K\_{\text{loss}}^h &= \mathbf{4}.8 \times 10^{-4} \, cm^{-1} \, \text{;} \, K\_{\text{loss}}^{us} = \mathbf{5}.3 \times 10^{-4} \, cm^{-1}, \\\\ \text{for } P \text{ (19) } \ 01^1 \mathbf{1} - 11^1 \mathbf{0} - K\_{\text{loss}}^h &= \mathbf{2}.3 \times 10^{-4} \, cm^{-1} \, \text{;} \, K\_{\text{loss}}^{us} = \mathbf{1}.9 \times 10^{-4} \, cm^{-1}, \\\\ \text{for } P \text{ (19) } \ 02^2 \mathbf{1} - \mathbf{1}2^2 \mathbf{0} - K\_{\text{loss}}^h &= \mathbf{2}.1 \times 10^{-4} \, cm^{-1} \, \text{;} \, K\_{\text{loss}}^{us} = \mathbf{1}.1 \times 10^{-4} \, cm^{-1}. \end{aligned}$$

A production-type water-cooled sealed-off gas-discharge tube of GL-501 type (FSUE RPC "Istok", Fryasino, Russia) was used as an active element of the probe laser. It has dischargegap length of ~1 .2 m, and the inside diameter is of 15 mm. The tube was filled with a CO : N2 : He :Xe mixture in a proportion of 1.0:1.6:4.0:0.6 at a total pressure of *13.5* Torr. The laser cavity was formed by ~100% reflecting mirror with a curvature radius of 3 m built in the tube, a plane diffraction grating and an additional mirror with a large curvature radius.

We used a nonconventional scheme of the laser cavity. The diffraction grating operated in the first diffraction order in the nonLittrow scheme. Laser radiation was extracted from the cavity through the zero order. Our studies have shown that the diffraction grating with 150 lines/mm and a reflectance of >95%, combined with the additional mirror with a curvature radius of 10 m, are optimal for obtaining the necessary high spectral resolution with a sufficiently high output power. A more detailed description of the construction of the probe

A signal from the probe laser passed a two times through the active medium under study in the discharge tube and was recorded by a liquid nitrogen cooled photo detector. This discharge tube was similar to one used as the active element of the probe laser. In addition to the measuring signal, we used a reference signal that does not pass along the investigated active medium and appears as a result of reflection of a portion of radiation from the ZnSe plane-parallel plate (see Fig. 4). This portion of radiation was directed to the another liquid nitrogen cooled Ge:Au photodetector of the reference channel, which makes automatically possible to account for the possible instability of the output laser radiation by way of

The electric signals from two photodetectors were fed into an two-channel digital registration system on the base of PC. Lasing wavelengths were measured with SPM-2 spectrum analyzer (Carl Zeiss Jena, Germany) with a highly selective diffraction grating,

To test the method proposed we have performed experimental investigations and calculations of the output power (*P*) dependence on the discharge current (*I*) for a cw CO2 laser, operated on four different bands (0001-1000, 0002-1001, 111- 1110 and 0221-1220). The cw CO2 laser was similar to one used as the probe laser. The only distinction is the using of the

The temperatures T3, T2 and T (see Fig. 5a), used in the calculations, were determined from the measurement of the gain factor of a weak signal by the method described in (Petukhov et. al.., 1985). For our experiments *T1* is approximately equal *T2*. According to our

> ( ) 0 0 4 1 4 1 18 00 1 10 0 4.8 10 ; 5.3 10 , *h us loss loss for P K cm K cm* − − − − − − =× =×

> ( ) 0 0 4 1 4 1 19 00 2 10 1 4.8 10 ; 5.3 10 , *h us loss loss for P K cm K cm* − − − − − − =× =×

( ) 1 1 4 1 4 1 19 01 1 11 0 2.3 10 ; 1.9 10 , *h us loss loss for P K cm K cm* − − − − − − =× =×

( ) 2 2 4 1 4 1 19 02 1 12 0 2.1 10 ; 1.1 10 , *h us loss loss for P K cm K cm* − − − − − − =× =×

appropriate diffraction grating with optimum Q-factor for each band.

calculations the loss factors for different bands have the following values:

laser is given in the next part.

**4.3 Results and discussions** 

normalization of the measuring signal to reference one.

whose resolution was not worse than 0.0005 µm.

Fig. 5. Dependencies of temperatures *T3* (∇), *T2* (O), and *T* (×) (a) and output power *P* (b) from a discharge current (× - for P(18) 0001-1000, O - for P(19) 0002-1001, ∇ - for P(19) 0111- 1110, - for P(19) 0221-1220)

Figure 5b shows the calculated curves and experimental values of the output power for the considered bands. At first we calculated the value of *P/A* for every band in accordance with discharge current. Then, we determined the proportionality coefficient A from the experimental data for the 0001-1001 band at *I*=25 mA. As this takes place, the coefficient A has a common value for all lasing bands. Next, the dependence P on I was constructed.

The method of output optimization of cw CO2 lasers has been developed. The method is based on vibrational and translational temperatures determination by gain measurements on the ro-vibrational lines of regular (0001-1000, 0200) and nonregular (0002-1001,0201; 0111- 1110; (0221-1220, 0201-1200…) bands of CO2 molecule. To test the validity of the method, the experiment realization has been done for a low pressure CO2 laser with the cw longitudinal discharge, that can oscillate on the lines of regular and nonregular lines. The good agreement between calculation and experiment data has been observed. Thus, a good agreement between the calculated and experimental data, which is observed, as a whole, for all the investigated bands, is demonstration that this method can be applied to the optimization of the output power of cw CO2 lasers. This method can be also successfully used for the optimization of the output parameters depending on the pumping and Q-factor of the resonator of the lasers generating only on the regular transitions 0001-1000 and 0001-0200.

#### **5. 16(14) microns TE CO2 laser working on the 02<sup>0</sup> 0(10<sup>0</sup> 0)-01<sup>1</sup> 0 and 02<sup>0</sup> 1(10<sup>0</sup> 1)- 01<sup>1</sup> 1 bands**

Earlier the lasing on the 0200(1000)-0110 band of the CO2 molecule (see Fig. 1) has been obtained in the specific systems at cryogenic temperatures under the lowest efficiency (Wexler, 1987). The optimization of the active medium and its electrical discharge pumping conditions based on the original technique of the temperature model (gain measurements on the several bands: 0001-1000, 0002-1001, 0111- 1110 of CO2 molecule) allowed to obtain in the simple TE CO2 laser with UV preionization (the active media length is 65 cm the width of electrodes is 2.5 cm, the interval between electrodes is 1.8 cm, (the voltage on the 0.2 micro Farad capacitor is 6.5 kV) the powerful lasing on the 0200(1000)-0110 bands at the room temperature. The output pulse energy of 57 mJ and the peak power of some tens kWatt have

CO2 Lasing on Non-Traditional Bands 117

present time is widely used to describe processes occurring in the active media of CO2 lasers and amplifiers. According to this model, population of the vibrational levels is unambiguously connected with the vibrational temperature of the symmetric (*T1*), bending (*T2*). and asymmetric (*T3*) modes of the CO2 molecule. We performed experimental investigations of the vibrational temperatures in the active medium of the TEA CO2 laser, directed toward a search for the optimum conditions for lasing in the 16(14) µm channel. The vibrational temperatures *T3* and *T2* (*T1=T2* for conditions examined) were determined from the ratios of the measured amplification coefficients of a weak signal at the individual rotational-vibrational

Let us examine what kind of the small gain and the output energy can be attained in the TEA CO2 laser on the 0201(1001)-0111 transitions. On the basis of the experimentally determined vibrational temperatures *T3* and *T2* (see Fig. 6) using the well-known expression (Gordiets et al., 1980) we calculated the small gain. The calculations shown that the small gain in the 0201(1001)- 0111 band can attain a significant value (>1m-1). The necessary conditions for the effective lasing have been determined. It is shown that in optimum conditions the output energy can reach *1.3* J/l at the peak power 5 MW and at the full

**6. A stabilized cw CO2 laser automatically switched between generations** 

This part describes a cw CO2 (CO) laser with stabilized output parameters that can be automatically switched from line to line. The laser generates 115 vibration-rotation CO2 lines between 9.15 and 11.3 μm and 100 CO lines between 5.3 and 6.4 μm. The laser is switched from CO2 operation to CO operation by replacing a sealed laser tube. Then computerized

Although there are many publications on tunable lasers (Gorobets et al., 1992) it is premature to think that all design and operation problems of tunable CO2, and especially of CO lasers, have been resolved. Computer control over the tuning of the generation wavelength is required (Gorobets et al., 1992). Fully computerized CO2, and CO lasers could be extensively used to monitor active media to improve lidar systems, in the spectroscopy

We have described the design of a laser head with a sealed tube and separate units (a highvoltage power supply, unit for tuning the lasing wavelength, an AFT unit, and a modulator) of an actively stabilized a cw CO2 (CO laser) that can he automatically switched between generation lines. The laser is switched from CO2 to CO operation by replacing the discharge

Further improvements include an electro-mechanical drive for the diffraction grating, an electronic control unit compatible with various computers, interfaces, and a control

The laser structure is shown in Fig. 7. The GL 501 (CO2) or GL-509 (CO) (FSUE RPC "Istok", Fryasino, Russia) commercial discharge tubes 1 are used because they have similar

lines of the 0001-1000, 0002-1001 and 111-1110 bands by the procedure described early.

efficiency of 2 *%.* 

and analysis of gases.

**6.1 Laser structure** 

control of the laser spectrum is described.

algorithm to link the laser to the computer.

**lines** 

tube.

been reached. The dependencies of the output and spectral performances of the 16 (14) micrometers lasing vs. a content of the active medium, pumping parameters and cavity characteristics have been carried out.

To increase the power performances of the 16 (14) microns CO2 laser the possibility of lasing on the 0201(1001)-0111 band have been experimentally and theoretically investigated under the combined (electrical + optical) excitation of the active medium. The conditions for obtaining effective lasing at the rotational-vibrational transitions of the 0201-0111 (λ = 16.4 µm) and 1001-0111 (λ= 14.1 µm) bands of the CO2 molecule are examined. To obtain population inversion in the indicated channels one should initially populate the 0002 vibrational level, considerable population of which can he accomplished comparatively simply, for example. in an electric discharge (Petukhov et. al.., 1985)*.* Then a powerful twofrequency radiation resonant with the 0002-0201(1001) and 0111-1110 (0310) transitions, saturating an individual rotational-vibrational transition, acts on the medium excited in such a way. As a result of this the first electromagnetic field, resonant with the 0002- 0201(1001) transition, populates the upper laser level 0201(1001), while simultaneously the second field, resonant with the 0111-1110 (0310) transitions, depopulates the lower level 0111 which also leads to inversion of the populations in the 0201 (1001)-0111 16(14) µm channel. In (Churakov et al., 1987). we have discussed by what means such a scheme of lasing in one active medium can be accomplished.

Fig. 6. Vibrational temperatures *T2* and *T3* vs N2 content at fixed values of *PCO2* 5(1), 10 (2), 20 (3), and 30% (4) in the mixture CO2:N2:He (*P* = 200 Torr, *U*= 30 kV, *C* = 0.25 μF)

Let us examine formation of inversion on the 0201(1001)-0111 transition using the example of an ordinary pulsed TEA CO2 laser. For this we employ a temperature model which at the

been reached. The dependencies of the output and spectral performances of the 16 (14) micrometers lasing vs. a content of the active medium, pumping parameters and cavity

To increase the power performances of the 16 (14) microns CO2 laser the possibility of lasing on the 0201(1001)-0111 band have been experimentally and theoretically investigated under the combined (electrical + optical) excitation of the active medium. The conditions for obtaining effective lasing at the rotational-vibrational transitions of the 0201-0111 (λ = 16.4 µm) and 1001-0111 (λ= 14.1 µm) bands of the CO2 molecule are examined. To obtain population inversion in the indicated channels one should initially populate the 0002 vibrational level, considerable population of which can he accomplished comparatively simply, for example. in an electric discharge (Petukhov et. al.., 1985)*.* Then a powerful twofrequency radiation resonant with the 0002-0201(1001) and 0111-1110 (0310) transitions, saturating an individual rotational-vibrational transition, acts on the medium excited in such a way. As a result of this the first electromagnetic field, resonant with the 0002- 0201(1001) transition, populates the upper laser level 0201(1001), while simultaneously the second field, resonant with the 0111-1110 (0310) transitions, depopulates the lower level 0111 which also leads to inversion of the populations in the 0201 (1001)-0111 16(14) µm channel. In (Churakov et al., 1987). we have discussed by what means such a scheme of lasing in one

Fig. 6. Vibrational temperatures *T2* and *T3* vs N2 content at fixed values of *PCO2* 5(1), 10 (2), 20

Let us examine formation of inversion on the 0201(1001)-0111 transition using the example of an ordinary pulsed TEA CO2 laser. For this we employ a temperature model which at the

(3), and 30% (4) in the mixture CO2:N2:He (*P* = 200 Torr, *U*= 30 kV, *C* = 0.25 μF)

characteristics have been carried out.

active medium can be accomplished.

present time is widely used to describe processes occurring in the active media of CO2 lasers and amplifiers. According to this model, population of the vibrational levels is unambiguously connected with the vibrational temperature of the symmetric (*T1*), bending (*T2*). and asymmetric (*T3*) modes of the CO2 molecule. We performed experimental investigations of the vibrational temperatures in the active medium of the TEA CO2 laser, directed toward a search for the optimum conditions for lasing in the 16(14) µm channel. The vibrational temperatures *T3* and *T2* (*T1=T2* for conditions examined) were determined from the ratios of the measured amplification coefficients of a weak signal at the individual rotational-vibrational lines of the 0001-1000, 0002-1001 and 111-1110 bands by the procedure described early.

Let us examine what kind of the small gain and the output energy can be attained in the TEA CO2 laser on the 0201(1001)-0111 transitions. On the basis of the experimentally determined vibrational temperatures *T3* and *T2* (see Fig. 6) using the well-known expression (Gordiets et al., 1980) we calculated the small gain. The calculations shown that the small gain in the 0201(1001)- 0111 band can attain a significant value (>1m-1). The necessary conditions for the effective lasing have been determined. It is shown that in optimum conditions the output energy can reach *1.3* J/l at the peak power 5 MW and at the full efficiency of 2 *%.* 

#### **6. A stabilized cw CO2 laser automatically switched between generations lines**

This part describes a cw CO2 (CO) laser with stabilized output parameters that can be automatically switched from line to line. The laser generates 115 vibration-rotation CO2 lines between 9.15 and 11.3 μm and 100 CO lines between 5.3 and 6.4 μm. The laser is switched from CO2 operation to CO operation by replacing a sealed laser tube. Then computerized control of the laser spectrum is described.

Although there are many publications on tunable lasers (Gorobets et al., 1992) it is premature to think that all design and operation problems of tunable CO2, and especially of CO lasers, have been resolved. Computer control over the tuning of the generation wavelength is required (Gorobets et al., 1992). Fully computerized CO2, and CO lasers could be extensively used to monitor active media to improve lidar systems, in the spectroscopy and analysis of gases.

We have described the design of a laser head with a sealed tube and separate units (a highvoltage power supply, unit for tuning the lasing wavelength, an AFT unit, and a modulator) of an actively stabilized a cw CO2 (CO laser) that can he automatically switched between generation lines. The laser is switched from CO2 to CO operation by replacing the discharge tube.

Further improvements include an electro-mechanical drive for the diffraction grating, an electronic control unit compatible with various computers, interfaces, and a control algorithm to link the laser to the computer.

#### **6.1 Laser structure**

The laser structure is shown in Fig. 7. The GL 501 (CO2) or GL-509 (CO) (FSUE RPC "Istok", Fryasino, Russia) commercial discharge tubes 1 are used because they have similar

CO2 Lasing on Non-Traditional Bands 119

The rotating arm *4* comprises the grating holder *12* which aligns the grating in vertical and horizontal planes, a two-stage reduction gear-box *13* with a worm-wheel (the transfer ratio is 1/1620), and a small stepper motor *14*. The precise reduction box, which has split gears, can rotate the grating and the corner mirror 6 through 40° and can set the grating angle to within 10". The laser spectrum can be also tuned manually with a calibrated wheel 15. When active, the control unit feeds pulses to the stepper motor, and the counter displays the number of motor steps on a front panel. The turning rate can be set to between 50—500 step/sec (up to 5 lines/sec). It can be also made to go in single steps. The motion of the arm

An initial-state indicator with a low-voltage spark discharger acts as one limit switch and was designed to set the rotation arm in the starting position. At a constant voltage of several volts, the spark discharge in air occurs at a very small gap width (~1.5 µm*)* and, hence, the discharger generates a signal. The uncertainty the gap width at which the discharger generates a signal is less than 1 µm, with corresponds to a grating turn of ±4". Thus the reproducibi1ity and accuracy of the initial position is good and corresponds to one step of the system. Note that an error of one step is not significant when switching the laser to a particular line since the distance between neighboring lines in CO2 and CO lasers in terms of

The laser tuning system can be linked to computers through appropriate interfaces and software. The turning angles of the diffraction grating with respect to the cavity axis corresponding to each laser line are leaded into the computer. The turning angles in terms of motor steps are derived from the grating pitch. When the laser is operating, the calculated angles may differ from the real values by some constant. This difference may be due to composition variations of the gas in the tube as a result of the electric discharge. Even so the intervals between neighboring spectral lines, and hence the distance between the grating positions in terms of the turning angle remain unchanged. The correction to the calculated positions should been found experimentally for all lines in terms of motor steps. This experimental correction also takes into account the uncertainty of the position of the zero-

The correction can be determined in two ways using the laser tuning software. The first method is semiautomatic and requires an external spectral device (a monochromator or a gas cell with a known absorption spectrum, e.g., NH3). The position of the grating for the selected reference line is determined, and the difference between this value and the calculated posit ion is fed into computer as the correction. In the second method, the correction is determined automatically by finding a reference line without an external spectral reference (Gorobets et al., 1992). The correction is determined using bright lines which can be easily identified in the output spectrum. In the case of the CO2 laser a good line is P(56) in the 0001-1000 band, which coincides with the P(23) line of the 0111-1110 band. The algorithm for finding this line was described in (Gorobets et al., 1992) and it reliably

Once the experimental correction is found, the laser is tuned to the selected line. The correction is added to the angle corresponding to the selected line, and the computer moves the grating to the correct angle with respect to the previous position, then it activates the AFC system.

The temperature of the liquid cooling the laser tube should be kept constant. This is particularly important for the CO laser since the number of lasing lines, especially in the

determines the correction. A similar method is possible for the CO laser.

the grating turning angle is ~ 240", which is equivalent to 60 steps of the motor.

is limited in both directions by limit switches.

angle discharger.

structures and the same discharge distance – 1.2 m. The laser cavity is formed by a 100% end mirror *2* with a curvature radius of ~3 m that is integrated in the tube and a flat diffraction grating *3* with 100 lines/mm set on a rotating arm 4 and a PZT drive *5*. The grating reflects in the first diffraction order when operating with CO2 and in the second order with CO (the reflectivity is about 90% in both cases). There is an additional mirror 6 on the rotating arm which forms a corner reflector (Gorobets et al., 1992) to keep the direction of the output beam unchanged when the laser is switched from line to line. This optic layout is particularly suited to the laser tubes we were employing. Besides, when the output beam has zero-order reflection at the grating, the optic losses are much lower, and more laser lines can he generated, which is essential for CO tubes whose gains are relatively small.

The diffraction-grating rotating arm and the tube braces 7 are fixed on three invar rods *8*. The end plate *9* is rigidly fixed to the laser frame, and unit *4* is attached to the lower rod via two bearings. As a result, thermal expansion in the rods does not lead to any misalignment of the grating. The use of invar rods and the high rigidity of the structure leads to a good passive stability of the cavity length.

1 – laser tube; 2 – end mirror; 3 - diffraction grating; 4 – rotating arm stage; 5 – piezo-electric drive; 6 – turning mirror; 7 – laser tube braces; 8 – invar rods; 9 – end plate; 10 – pyro-electric detector; 11 – iris diaphragm; 12 – holder of the diffraction grating; 13 – gear-box with a worm wheel; 14 – stepper motor; 15 – graduated wheel; 16 – turning mirror

Fig. 7. Diagram of the laser structure

The radiation frequency is stabilized by coupling the output power to the wavelength and an appropriate curve is used in the stabilization system. The laser is in fact stabilized by automatically tuning the cavity length with the PZT drive *5* to which the diffraction grating *3* is fixed. The AFC circuit is similar to that of the Edinburgh instruments lasers. The signal for feedback loop is taken from a pyro-electric detector 10 which is exposed to the radiation reflected from the GaAs Brewster window of the discharge tube (see Fig. 7). The laser only generates the fundamental transverse mode because of the iris diaphragm 11 and the AFC system.

The key element in the laser is the system for tuning the lasing wavelength. Structurally, it is the rotating arm *4* of the diffraction grating and driven by the electronics driving the AFC system. The laser is switched between the lines by turning the grating with respect to the cavity axis.

structures and the same discharge distance – 1.2 m. The laser cavity is formed by a 100% end mirror *2* with a curvature radius of ~3 m that is integrated in the tube and a flat diffraction grating *3* with 100 lines/mm set on a rotating arm 4 and a PZT drive *5*. The grating reflects in the first diffraction order when operating with CO2 and in the second order with CO (the reflectivity is about 90% in both cases). There is an additional mirror 6 on the rotating arm which forms a corner reflector (Gorobets et al., 1992) to keep the direction of the output beam unchanged when the laser is switched from line to line. This optic layout is particularly suited to the laser tubes we were employing. Besides, when the output beam has zero-order reflection at the grating, the optic losses are much lower, and more laser lines

can he generated, which is essential for CO tubes whose gains are relatively small.

passive stability of the cavity length.

15 – graduated wheel; 16 – turning mirror Fig. 7. Diagram of the laser structure

system.

The diffraction-grating rotating arm and the tube braces 7 are fixed on three invar rods *8*. The end plate *9* is rigidly fixed to the laser frame, and unit *4* is attached to the lower rod via two bearings. As a result, thermal expansion in the rods does not lead to any misalignment of the grating. The use of invar rods and the high rigidity of the structure leads to a good

1 – laser tube; 2 – end mirror; 3 - diffraction grating; 4 – rotating arm stage; 5 – piezo-electric drive; 6 – turning mirror; 7 – laser tube braces; 8 – invar rods; 9 – end plate; 10 – pyro-electric detector; 11 – iris diaphragm; 12 – holder of the diffraction grating; 13 – gear-box with a worm wheel; 14 – stepper motor;

The radiation frequency is stabilized by coupling the output power to the wavelength and an appropriate curve is used in the stabilization system. The laser is in fact stabilized by automatically tuning the cavity length with the PZT drive *5* to which the diffraction grating *3* is fixed. The AFC circuit is similar to that of the Edinburgh instruments lasers. The signal for feedback loop is taken from a pyro-electric detector 10 which is exposed to the radiation reflected from the GaAs Brewster window of the discharge tube (see Fig. 7). The laser only generates the fundamental transverse mode because of the iris diaphragm 11 and the AFC

The key element in the laser is the system for tuning the lasing wavelength. Structurally, it is the rotating arm *4* of the diffraction grating and driven by the electronics driving the AFC system. The laser is switched between the lines by turning the grating with respect to the cavity axis.

The rotating arm *4* comprises the grating holder *12* which aligns the grating in vertical and horizontal planes, a two-stage reduction gear-box *13* with a worm-wheel (the transfer ratio is 1/1620), and a small stepper motor *14*. The precise reduction box, which has split gears, can rotate the grating and the corner mirror 6 through 40° and can set the grating angle to within 10". The laser spectrum can be also tuned manually with a calibrated wheel 15. When active, the control unit feeds pulses to the stepper motor, and the counter displays the number of motor steps on a front panel. The turning rate can be set to between 50—500 step/sec (up to 5 lines/sec). It can be also made to go in single steps. The motion of the arm is limited in both directions by limit switches.

An initial-state indicator with a low-voltage spark discharger acts as one limit switch and was designed to set the rotation arm in the starting position. At a constant voltage of several volts, the spark discharge in air occurs at a very small gap width (~1.5 µm*)* and, hence, the discharger generates a signal. The uncertainty the gap width at which the discharger generates a signal is less than 1 µm, with corresponds to a grating turn of ±4". Thus the reproducibi1ity and accuracy of the initial position is good and corresponds to one step of the system. Note that an error of one step is not significant when switching the laser to a particular line since the distance between neighboring lines in CO2 and CO lasers in terms of the grating turning angle is ~ 240", which is equivalent to 60 steps of the motor.

The laser tuning system can be linked to computers through appropriate interfaces and software. The turning angles of the diffraction grating with respect to the cavity axis corresponding to each laser line are leaded into the computer. The turning angles in terms of motor steps are derived from the grating pitch. When the laser is operating, the calculated angles may differ from the real values by some constant. This difference may be due to composition variations of the gas in the tube as a result of the electric discharge. Even so the intervals between neighboring spectral lines, and hence the distance between the grating positions in terms of the turning angle remain unchanged. The correction to the calculated positions should been found experimentally for all lines in terms of motor steps. This experimental correction also takes into account the uncertainty of the position of the zeroangle discharger.

The correction can be determined in two ways using the laser tuning software. The first method is semiautomatic and requires an external spectral device (a monochromator or a gas cell with a known absorption spectrum, e.g., NH3). The position of the grating for the selected reference line is determined, and the difference between this value and the calculated posit ion is fed into computer as the correction. In the second method, the correction is determined automatically by finding a reference line without an external spectral reference (Gorobets et al., 1992). The correction is determined using bright lines which can be easily identified in the output spectrum. In the case of the CO2 laser a good line is P(56) in the 0001-1000 band, which coincides with the P(23) line of the 0111-1110 band. The algorithm for finding this line was described in (Gorobets et al., 1992) and it reliably determines the correction. A similar method is possible for the CO laser.

Once the experimental correction is found, the laser is tuned to the selected line. The correction is added to the angle corresponding to the selected line, and the computer moves the grating to the correct angle with respect to the previous position, then it activates the AFC system.

The temperature of the liquid cooling the laser tube should be kept constant. This is particularly important for the CO laser since the number of lasing lines, especially in the

CO2 Lasing on Non-Traditional Bands 121

be monitored. The instability over the measurement time needs to be known in many applications. For example, when determining contaminants by the differential method (at the absorption line and off the line), the measurement may last from several seconds to a

The laser beam was modulated by the chapter and fed to a light detector cooled by liquid nitrogen (Gorobets et al., 1995). The detector's electric signal was processed by a lock-in amplifier, digitized and sent to a computer. One measurement, including the signal processing in the ADC took about 0.7 s. Measurements lasting over 70 s demonstrated that the output power of the laser generating at the P(24) line of the 00°1-1000 band of the CO2 molecule varied by ±1.6% around the mean with the AFC system on and by 12.5% with the AFC system off. The larger instability measured by the second method may be due to longer time constant of the calorimeter. The short-term power instability was also measured using an digital oscilloscope (band-width of about 1MHz) connected to the Ge:Au detector. The instability over times of the order of microseconds was estimated to be several times smaller than the long-term instability quoted above. Several lasers have been used to monitor the atmosphere and to obtain spectroscopic measurements over a long time. They have proven

Fig. 8. Trace of the output power over 1 h at the P(16) line of the CO2 molecule's 0001-0200

**7. Detection of small N2O concentrations using a frequency doubling 12C18O2**

The destruction of the protective ozone layer of the Earth (so called "ozone holes") can result in a global environmental and climatic catastrophe showing for many years a continuous unflagging. It is well known that the products of human activity such as freons and nitrous oxide (N2O) are responsible for "ozone holes". Freons appear as a result of manufacturing some kinds of plastics and using refrigerators. Nitrous oxides penetrate into the atmosphere primarily due to microbiological changes in soil caused by agricultural human activity. Moreover, (Crutzen, 1996) determined that there is a direct coupling

between the life of microorganisms in soil and the ozone layer thickness.

minute. The output power instability in this time interval was measured as follows.

to the reliable devices with a long service life.

band

**laser** 

short-wave band, depends on the gas temperature in the tube (Aleinikov and Masychev, 1990). We used a standard water cooler with a closed cycle to remove the heat from the laser tube. It cools the tube with distilled water at a temperature between 2 and 10 °C and keeps it constant to within 1 °C.

The stabilized power unit is standard for CO2 lasers and an additional current stabilizer built around a vacuum tube. The current stabilizer suppresses current oscillations by several orders of magnitude, especially those at the mains frequency of 50 Hz. The current through the tube can be tuned between 10 and 40 mA.

To modulate the laser power, we used a electromechanical chopper. It was built around a electric motor. A thin precisely made disk with sixteen slits made from titanium foil 0.1 mm thick was mounted on the motor axis. The signal for the feedback of the active frequency control was taken from an optic couple. The electronics drive the modulator at 125, 250, 500, and 1000 Hz, and it can be detuned by ±5.9% from these frequencies. With a crystal oscillator and automatic control of the modulation frequency its very stable (the frequency usually differs from the preset value by less than 0.01%).

#### **6.2 Output laser parameters**

The laser characteristics have been measured on an optic bench using traditional techniques (Gorobets et al., 1995). We first consider the spectral and energy parameters.

Since the diffraction grating has a reflectivity of 90% the laser with a CO2 tube, generates about 90 lines between 9.15 and 10. 95 µm (0001-1000, 02°0 bands) The output power in the fundamental mode reaches 10 W for strong lines and is over 1 W side lines. Using the same grating, the laser generates 25 lines in the P-branch of he hot 0111–1110 band of the CO2 molecule. In this case the spectrum is shifted to the red to 10.94 –11.25 µm. The output power at strong lines was 3-4 W and 0.5 W at the band edge. However the conditions needed for the hot baud, where the gain is considerably smaller, are not optimum. When the laser tube is filled with CO2, N2, He and Xe, output was considerably higher and, the number of lines was larger (see 1-3 parts).

When the CL-509 tube is inserted, the laser efficiently generates about 100 vibration-rotation lines of the CO molecule between 5.28 and 6.43 µm. Output powers at the strongest lines were ~1 W in the fundamental mode at the optimum discharge current. The lines were identified using the data in (Aleinikov and Masychev, 1990).

Note that the parameters of the grating are better when generating CO and hot of CO2 lines, where the gain is smaller than in the more conventional 0001-1000,0200 bands. The lines in the conventional bands will clearly be stronger in a cavity with a lower Q factor.

#### **6.3 Instability of the output laser power**

The long-term instability of the output power was checked using a laser calorimeter whose signal was fed to a chart-recorder. Figure 8 shows a typical plot of the laser output power over one hour. The instability in the laser output power on the P(16) line of the 00°1-02°0 band over one hour was ±1.1%. Similar measurements with other lines of CO and CO2 molecules demonstrated that the long-term instability of the laser power is less than ±1.25%. However the time constant of the calorimeter is long and the short-term instability could not

short-wave band, depends on the gas temperature in the tube (Aleinikov and Masychev, 1990). We used a standard water cooler with a closed cycle to remove the heat from the laser tube. It cools the tube with distilled water at a temperature between 2 and 10 °C and keeps it

The stabilized power unit is standard for CO2 lasers and an additional current stabilizer built around a vacuum tube. The current stabilizer suppresses current oscillations by several orders of magnitude, especially those at the mains frequency of 50 Hz. The current through

To modulate the laser power, we used a electromechanical chopper. It was built around a electric motor. A thin precisely made disk with sixteen slits made from titanium foil 0.1 mm thick was mounted on the motor axis. The signal for the feedback of the active frequency control was taken from an optic couple. The electronics drive the modulator at 125, 250, 500, and 1000 Hz, and it can be detuned by ±5.9% from these frequencies. With a crystal oscillator and automatic control of the modulation frequency its very stable (the frequency

The laser characteristics have been measured on an optic bench using traditional techniques

Since the diffraction grating has a reflectivity of 90% the laser with a CO2 tube, generates about 90 lines between 9.15 and 10. 95 µm (0001-1000, 02°0 bands) The output power in the fundamental mode reaches 10 W for strong lines and is over 1 W side lines. Using the same grating, the laser generates 25 lines in the P-branch of he hot 0111–1110 band of the CO2 molecule. In this case the spectrum is shifted to the red to 10.94 –11.25 µm. The output power at strong lines was 3-4 W and 0.5 W at the band edge. However the conditions needed for the hot baud, where the gain is considerably smaller, are not optimum. When the laser tube is filled with CO2, N2, He and Xe, output was considerably higher and, the

When the CL-509 tube is inserted, the laser efficiently generates about 100 vibration-rotation lines of the CO molecule between 5.28 and 6.43 µm. Output powers at the strongest lines were ~1 W in the fundamental mode at the optimum discharge current. The lines were

Note that the parameters of the grating are better when generating CO and hot of CO2 lines, where the gain is smaller than in the more conventional 0001-1000,0200 bands. The lines in

The long-term instability of the output power was checked using a laser calorimeter whose signal was fed to a chart-recorder. Figure 8 shows a typical plot of the laser output power over one hour. The instability in the laser output power on the P(16) line of the 00°1-02°0 band over one hour was ±1.1%. Similar measurements with other lines of CO and CO2 molecules demonstrated that the long-term instability of the laser power is less than ±1.25%. However the time constant of the calorimeter is long and the short-term instability could not

the conventional bands will clearly be stronger in a cavity with a lower Q factor.

(Gorobets et al., 1995). We first consider the spectral and energy parameters.

constant to within 1 °C.

**6.2 Output laser parameters** 

number of lines was larger (see 1-3 parts).

**6.3 Instability of the output laser power** 

identified using the data in (Aleinikov and Masychev, 1990).

the tube can be tuned between 10 and 40 mA.

usually differs from the preset value by less than 0.01%).

be monitored. The instability over the measurement time needs to be known in many applications. For example, when determining contaminants by the differential method (at the absorption line and off the line), the measurement may last from several seconds to a minute. The output power instability in this time interval was measured as follows.

The laser beam was modulated by the chapter and fed to a light detector cooled by liquid nitrogen (Gorobets et al., 1995). The detector's electric signal was processed by a lock-in amplifier, digitized and sent to a computer. One measurement, including the signal processing in the ADC took about 0.7 s. Measurements lasting over 70 s demonstrated that the output power of the laser generating at the P(24) line of the 00°1-1000 band of the CO2 molecule varied by ±1.6% around the mean with the AFC system on and by 12.5% with the AFC system off. The larger instability measured by the second method may be due to longer time constant of the calorimeter. The short-term power instability was also measured using an digital oscilloscope (band-width of about 1MHz) connected to the Ge:Au detector. The instability over times of the order of microseconds was estimated to be several times smaller than the long-term instability quoted above. Several lasers have been used to monitor the atmosphere and to obtain spectroscopic measurements over a long time. They have proven to the reliable devices with a long service life.

Fig. 8. Trace of the output power over 1 h at the P(16) line of the CO2 molecule's 0001-0200 band

#### **7. Detection of small N2O concentrations using a frequency doubling 12C18O2 laser**

The destruction of the protective ozone layer of the Earth (so called "ozone holes") can result in a global environmental and climatic catastrophe showing for many years a continuous unflagging. It is well known that the products of human activity such as freons and nitrous oxide (N2O) are responsible for "ozone holes". Freons appear as a result of manufacturing some kinds of plastics and using refrigerators. Nitrous oxides penetrate into the atmosphere primarily due to microbiological changes in soil caused by agricultural human activity. Moreover, (Crutzen, 1996) determined that there is a direct coupling between the life of microorganisms in soil and the ozone layer thickness.

CO2 Lasing on Non-Traditional Bands 123

lasers the discharge chambers of which are much more difficult to pump out as compared to low-pressure sealed-off lasers. Another problem is the necessity of proper choice of materials which accumulate less ordinary oxygen. Therefore, we have performed detailed investigations aimed at active medium optimization for high-energy parameters with a simultaneous decrease in the price of the active medium based on isotopically substituted molecules 12C18O2 at the expense of its dilution with inexpensive carbon dioxide 12C16O2 .

This section gives the results of our spectral investigations of the gain and the lasing for the TEA CO2 laser operating both on 12C18O2 and, just for comparison, on ordinary 12C16O2 . The analysis of the conditions required for efficient lasing in the range of 9 µm is given too.

Experiments were performed with a UV-preionized TEA module specialty developed for lidar systems (Gorobets et al., 1995). The module had a working volume of 70 × 2.5 × 2 cm. The distance between electrodes was 2 cm. Both main and auxiliary discharges were fed from low-inductance capacitors having a total capacity of 0.2 µF charged up to the 25 kV

The isotopically substituted form of carbon dioxide 12C18O2 with an 18O enrichment factor of 80% obtained as a gas mixture containing 4% 12C16O2 , 32% 12C16O18O , and 64% 12C1802 was used in the experiments. It is much more expensive to prepare a mixture with a higher factor of enrichment for 12C18O2 . The first measurements and calculations concerned the gain. For example, Fig. 9 shows respective gain for some lines of the P-branch of 00°1-10°0 band of the 12C18O2 molecule (λ~9.4 µm) and of the 12C1602 molecule (λ~10.6 µm) for the mixture 12C16O2 : 12C16O18O : 12C18O2 : N2 : He = 10:3:7:20:60 (the manufactured mixture was diluted with 12C16O2) with a total pressure of 500 Torr. Measurements carried out at t = 4 µs after the start of the discharge when the highest gains were realized. Gain measurements were performed by probing the active medium with a cw laser, lasing on the corresponding lines.

Fig. 9. Measured ( Ο ) and calculated ( ⏐ ) values of the gain at the lines of the 10P(12C16O2) (a) and 9P(12C18O2 ) (b). Dashed lines – the gain calculated without lines overlapping.

voltage. The discharge duration was ~500 ns.

The conservation of the ozone envelope depends on many factors. However it is beyond doubt that modern reliable techniques monitoring the atmosphere for the presence of freons and nitrous oxide would assist greatly in a solution of this serious global problem. Laser gas-analysis methods are well suited to this task. They are capable of working with high speed, i.e. practically in real time mode. The ability to determine extremely low gas concentrations (for laser photoacoustics on the level of 0.1 ppb) and to cover extensive areas of the earth from a single point of observation (for lidars – about 10 km) give them unquestionable advantages as compared to other known diagnostic methods. There is reliable and effective laser procedure based on CO2 laser for the detection of prevailing freons, the strong absorption bands of which overlap with emission lines of the laser.

Spectral analysis of N2O has shown that the characteristic feature of this molecule consists of the absorption now low in the ranges where known effective lasers can operate. There are only the complex and (or) inefficient multitasked systems with nonlinear frequency conversation (generation of harmonics with the subsequent frequency summation), parametric oscillators, and tunable diode lasers. Therefore, the development of reliable and efficient laser methods for N2O sensing remains a topical problem. An additional difficulty arising with the development of such methods applies to the necessity to detect low concentrations of nitrous oxide (background content of this gas in the atmosphere is 0.2—0.4 ppm).

The main goal of the present investigation is the development of a reliable and highefficiency laser method for detecting low concentrations of N2O. The other goal of the work is the test of this method as a remote gas analyzer. The procedure is based on the idea of using a nonlinear frequency-doubled CO2 laser operating on the isotopic carbon dioxide modification 12*C*18O2. Such a powerful laser system would emit neighboring lines both coinciding well and adjacent to N2O absorption lines. This fact allows one to apply the highly accurate technique which uses corresponding on/off line pairs for the differential absorption. The high efficiency of the system and strong absorption of N2O molecules (we use the strongest band in the range of λ ~ 4.5 µm) would give a possibility to measure low gas concentrations both in short and long (~10 km) measurement paths.

#### **7.1 Active medium optimization of the 12C18O2 laser**

It is known that the use isotopically substituted carbon dioxide molecules make it possible to increase substantially the number of lines and to extend the spectral range of CO2 lasers. That is important for different applications, in particular for atmospheric gas detection. The use of 12C18O2 as molecules of the active medium of lasers is of special interest, since for this molecule the maximum gain lies at wavelength ~9.4 µm and not ~10.6 µm, as for 12C16O2, and, consequently. there is a possibility for efficient lasing in a shorter wavelength range down to 8.9 µm. The doubled emission frequencies of 12C18O2 laser well coincide with absorption lines of many molecules including nitrous oxide.

However, for a number of reasons, and particularly because of the much higher price, CO2 lasers based on isotopically substituted carbon dioxide molecules are not in wide use. For 12C18O2, molecules there is also the problem of the isotoporeplacement of 18O2 with 16O2 as these molecules are active in discharge plasma. The electrode surface, discharge chamber and tubes walls accumulate with time ordinary oxygen 16O2. Then, under the discharge conditions, 16O2 replaces (isotopically) 18O2 *,* in the active medium. This results in rapid degradation of the 12C18O2 active medium. This fact is especially important for TEA CO2-

The conservation of the ozone envelope depends on many factors. However it is beyond doubt that modern reliable techniques monitoring the atmosphere for the presence of freons and nitrous oxide would assist greatly in a solution of this serious global problem. Laser gas-analysis methods are well suited to this task. They are capable of working with high speed, i.e. practically in real time mode. The ability to determine extremely low gas concentrations (for laser photoacoustics on the level of 0.1 ppb) and to cover extensive areas of the earth from a single point of observation (for lidars – about 10 km) give them unquestionable advantages as compared to other known diagnostic methods. There is reliable and effective laser procedure based on CO2 laser for the detection of prevailing

freons, the strong absorption bands of which overlap with emission lines of the laser.

oxide (background content of this gas in the atmosphere is 0.2—0.4 ppm).

gas concentrations both in short and long (~10 km) measurement paths.

**7.1 Active medium optimization of the 12C18O2 laser** 

absorption lines of many molecules including nitrous oxide.

Spectral analysis of N2O has shown that the characteristic feature of this molecule consists of the absorption now low in the ranges where known effective lasers can operate. There are only the complex and (or) inefficient multitasked systems with nonlinear frequency conversation (generation of harmonics with the subsequent frequency summation), parametric oscillators, and tunable diode lasers. Therefore, the development of reliable and efficient laser methods for N2O sensing remains a topical problem. An additional difficulty arising with the development of such methods applies to the necessity to detect low concentrations of nitrous

The main goal of the present investigation is the development of a reliable and highefficiency laser method for detecting low concentrations of N2O. The other goal of the work is the test of this method as a remote gas analyzer. The procedure is based on the idea of using a nonlinear frequency-doubled CO2 laser operating on the isotopic carbon dioxide modification 12*C*18O2. Such a powerful laser system would emit neighboring lines both coinciding well and adjacent to N2O absorption lines. This fact allows one to apply the highly accurate technique which uses corresponding on/off line pairs for the differential absorption. The high efficiency of the system and strong absorption of N2O molecules (we use the strongest band in the range of λ ~ 4.5 µm) would give a possibility to measure low

It is known that the use isotopically substituted carbon dioxide molecules make it possible to increase substantially the number of lines and to extend the spectral range of CO2 lasers. That is important for different applications, in particular for atmospheric gas detection. The use of 12C18O2 as molecules of the active medium of lasers is of special interest, since for this molecule the maximum gain lies at wavelength ~9.4 µm and not ~10.6 µm, as for 12C16O2, and, consequently. there is a possibility for efficient lasing in a shorter wavelength range down to 8.9 µm. The doubled emission frequencies of 12C18O2 laser well coincide with

However, for a number of reasons, and particularly because of the much higher price, CO2 lasers based on isotopically substituted carbon dioxide molecules are not in wide use. For 12C18O2, molecules there is also the problem of the isotoporeplacement of 18O2 with 16O2 as these molecules are active in discharge plasma. The electrode surface, discharge chamber and tubes walls accumulate with time ordinary oxygen 16O2. Then, under the discharge conditions, 16O2 replaces (isotopically) 18O2 *,* in the active medium. This results in rapid degradation of the 12C18O2 active medium. This fact is especially important for TEA CO2lasers the discharge chambers of which are much more difficult to pump out as compared to low-pressure sealed-off lasers. Another problem is the necessity of proper choice of materials which accumulate less ordinary oxygen. Therefore, we have performed detailed investigations aimed at active medium optimization for high-energy parameters with a simultaneous decrease in the price of the active medium based on isotopically substituted molecules 12C18O2 at the expense of its dilution with inexpensive carbon dioxide 12C16O2 .

This section gives the results of our spectral investigations of the gain and the lasing for the TEA CO2 laser operating both on 12C18O2 and, just for comparison, on ordinary 12C16O2 . The analysis of the conditions required for efficient lasing in the range of 9 µm is given too.

Experiments were performed with a UV-preionized TEA module specialty developed for lidar systems (Gorobets et al., 1995). The module had a working volume of 70 × 2.5 × 2 cm. The distance between electrodes was 2 cm. Both main and auxiliary discharges were fed from low-inductance capacitors having a total capacity of 0.2 µF charged up to the 25 kV voltage. The discharge duration was ~500 ns.

The isotopically substituted form of carbon dioxide 12C18O2 with an 18O enrichment factor of 80% obtained as a gas mixture containing 4% 12C16O2 , 32% 12C16O18O , and 64% 12C1802 was used in the experiments. It is much more expensive to prepare a mixture with a higher factor of enrichment for 12C18O2 . The first measurements and calculations concerned the gain. For example, Fig. 9 shows respective gain for some lines of the P-branch of 00°1-10°0 band of the 12C18O2 molecule (λ~9.4 µm) and of the 12C1602 molecule (λ~10.6 µm) for the mixture 12C16O2 : 12C16O18O : 12C18O2 : N2 : He = 10:3:7:20:60 (the manufactured mixture was diluted with 12C16O2) with a total pressure of 500 Torr. Measurements carried out at t = 4 µs after the start of the discharge when the highest gains were realized. Gain measurements were performed by probing the active medium with a cw laser, lasing on the corresponding lines.

Fig. 9. Measured ( Ο ) and calculated ( ⏐ ) values of the gain at the lines of the 10P(12C16O2) (a) and 9P(12C18O2 ) (b). Dashed lines – the gain calculated without lines overlapping.

CO2 Lasing on Non-Traditional Bands 125

Fig. 10. Lasing energy measured in the ranges of 9.4 μm for 12C18O2 (Ο) and 10.4 μm for

Thus, the results of the investigations demonstrate that efficient lasing of the CO2 laser even with non-selective cavity is possible in the range of 9.4 µm when the 12C18O2, content is 30% of total carbon dioxide amount. When the laser operates with selective cavity such as that based on a diffraction grating, the percentage of 12C18O2, can go down to ~20%. This fact is

An experimental series performed as well by us was oriented toward providing longduration autonomous laser operation without active mixture replacement and noticeable degradation of its composition. To this end, the discharge chamber was well evacuated (no more than 0.2 Torr/day inleakage) and the material it was made of was properly selected. The best results were achieved with a glass-epoxy cylinder when the operation was virtually quasi-sealed-off, i.e. without replacement of the active medium on 12C18O2 during 1—2 months (more than 105 pulses) without noticeable decrease of the laser energy. In addition, after long operation and before working gases replacement. the old mixture was pumped

**7.2 Using a nonlinear crystal etalon for second harmonic generation from CO2 lasers**  The poor efficiency of the frequency conversion attributable on the whole to mid IR lasers can be compensated to a large degree by application of non-traditional optical schemes. Therefore, the problem remaining topical in the mid IR range along with creation of higherquality crystals applies to development of novel nonlinear conversion schemes and search for the laser operation modes which are optimal for frequency conversion. To this end and with the aim of reaching high conversion efficiency, we have performed some investigations on the basis of which it was possible to realize original optical frequency conversion

through liquid nitrogen traps to recover carbon dioxide for repeated use.

12C16O2 (∆) versus 12C18O2 content

key for reduction of the price of the active medium.

schemes including intracavity versions.

After passing the medium in question, the probing emission came to a photodetector producing a signal to a digital oscilloscope, connected to a personal computer where the measurements were stored and averaged. The calculations were performed based on a vibrational temperature model (Petukhov et. al.., 1985) that is in wide use for simulations of the active medium of CO2, lasers. The measurements have shown that under the above conditions: *T=* 350 ± 10 K, *T1* = *T2* = 420±20 K, and *T3=*1475, 1510 and 1550, ±15 for molecules 12C16O2 *,* 12C16O18O, and 12C18O2, accordingly. T designates the gas temperature. T1 and T2 are the temperatures of symmetric and deformation vibrations that are virtually the same for the whole scope of carbon dioxide variations in question. T3 is the temperature of asymmetric vibrations. The technique used and apparatus to measure gains and to determine vibrational temperatures were described early. The gain spectrum was calculated using the scheme described in (Gordiets et al., 1980). Additionally the overlap of individual vibration— rotation lines in bands 0001-1000, 0001—0200, 0002-1001, 0002-0201, 0111-1110, 0111- 0310 for molecules 12C16O2 and 12C18O2 and bands 0001-1000 , 0001—0200 for molecule 12C16O18O and spectroscopic data given in (Witteman,.1987) were allowed for.

As is evident in Fig. 9, the gain maximum in the P-branch of the band 0001-1000 of the 12C16O2 molecule in the mixture of isotopic forms of carbon dioxide 12C16O2, 12C16O18O and 12C18O2, occurred at lines P(18) and P(20). These lines are especially affected by the overlap with lines from other bands. The P(18) line of the 00°1-10°0 band for the 12C18O2, molecule is shifted from lines P(3) 00°1-02°0 12C16O18O, R(8) 00°1-02°0 12C16O2 and P(26) 0111-1110 12C18O2, at 0.046, 0.045 and 0.021 cm-1, and line P(20) 0001-1000 12C18O2-from lines P(5) 00°1- 02°0 12C16O18O,R(6) 00°1-02°0 12C16O2, and P(28) 0111- 1110 12C18O2 at 0.007, 0.072, 0.085 cm-1, respectively. The homogeneous width of the line at half-height under our conditions is ~0.05 cm-1. We note that the calculation and experimental data are in a good agreement. For instance, the gain calculated for line P(18) 0001-1000 12C18O2 is 1.83×10-2 cm-1 while the measured value is (1.81 ± 0.06) x 10-2 cm-1

It's also worth noting that higher gains are realized for the 12C18O2 molecule than for the 12C16O2 molecule. As seen from Fig. 9, the gains on the strongest lines of the P-branches for both isotopes are approximately equal, though this mixture contains 1.8 times less 12C18O2 than 12C16O2. There are three reasons for this. First, the limiting gain for the lines of the Pbranch of the band 0001-1000 of 12C18O2 is approximately 1.5 times higher than that for the Pbranch of the band 0001-1000 of 12C16O2 (Witteman,.1987); second, for the lines of the Pbranch of this band of the 12C18O2 molecule in the 12C16O2+12C16O18O mixture the effect of the overlap with other bands is essential; and, finally, under the conditions of dynamic equilibrium between the v3 modes of both isotopic forms the temperature T3 for 12C18O2, is higher than for 12C16O2 .

We also measured the effect of the dilution of molecules 12C18O2 by the usual form of carbon dioxide 12C16O2, on the output energy. The lasing pulse energies measured in the ranges of 9.4 µm (12C18O2) (1) and 10.4 µm (12C16O2) (2) are given in Fig. 10. These data were acquired for the TEA-module described above using a non-selective cavity composed of a nontransmitting and germanium output (R=~50%) mirrors. The energies emitted in the ranges 10.4 and 9.4 µm are approximately equal to each other at the 30 Torr content of 12C18O2, approaching to the content of 12C18O2 at which the corresponding gains get equal. Also note that the total emission energy (E9.4 + E10.6) is independent in this case of isotoporeplacement of carbon dioxide and reaches the value of 5 J.

After passing the medium in question, the probing emission came to a photodetector producing a signal to a digital oscilloscope, connected to a personal computer where the measurements were stored and averaged. The calculations were performed based on a vibrational temperature model (Petukhov et. al.., 1985) that is in wide use for simulations of the active medium of CO2, lasers. The measurements have shown that under the above conditions: *T=* 350 ± 10 K, *T1* = *T2* = 420±20 K, and *T3=*1475, 1510 and 1550, ±15 for molecules 12C16O2 *,* 12C16O18O, and 12C18O2, accordingly. T designates the gas temperature. T1 and T2 are the temperatures of symmetric and deformation vibrations that are virtually the same for the whole scope of carbon dioxide variations in question. T3 is the temperature of asymmetric vibrations. The technique used and apparatus to measure gains and to determine vibrational temperatures were described early. The gain spectrum was calculated using the scheme described in (Gordiets et al., 1980). Additionally the overlap of individual vibration— rotation lines in bands 0001-1000, 0001—0200, 0002-1001, 0002-0201, 0111-1110, 0111- 0310 for molecules 12C16O2 and 12C18O2 and bands 0001-1000 , 0001—0200 for molecule

12C16O18O and spectroscopic data given in (Witteman,.1987) were allowed for.

measured value is (1.81 ± 0.06) x 10-2 cm-1

of carbon dioxide and reaches the value of 5 J.

higher than for 12C16O2 .

As is evident in Fig. 9, the gain maximum in the P-branch of the band 0001-1000 of the 12C16O2 molecule in the mixture of isotopic forms of carbon dioxide 12C16O2, 12C16O18O and 12C18O2, occurred at lines P(18) and P(20). These lines are especially affected by the overlap with lines from other bands. The P(18) line of the 00°1-10°0 band for the 12C18O2, molecule is shifted from lines P(3) 00°1-02°0 12C16O18O, R(8) 00°1-02°0 12C16O2 and P(26) 0111-1110 12C18O2, at 0.046, 0.045 and 0.021 cm-1, and line P(20) 0001-1000 12C18O2-from lines P(5) 00°1- 02°0 12C16O18O,R(6) 00°1-02°0 12C16O2, and P(28) 0111- 1110 12C18O2 at 0.007, 0.072, 0.085 cm-1, respectively. The homogeneous width of the line at half-height under our conditions is ~0.05 cm-1. We note that the calculation and experimental data are in a good agreement. For instance, the gain calculated for line P(18) 0001-1000 12C18O2 is 1.83×10-2 cm-1 while the

It's also worth noting that higher gains are realized for the 12C18O2 molecule than for the 12C16O2 molecule. As seen from Fig. 9, the gains on the strongest lines of the P-branches for both isotopes are approximately equal, though this mixture contains 1.8 times less 12C18O2 than 12C16O2. There are three reasons for this. First, the limiting gain for the lines of the Pbranch of the band 0001-1000 of 12C18O2 is approximately 1.5 times higher than that for the Pbranch of the band 0001-1000 of 12C16O2 (Witteman,.1987); second, for the lines of the Pbranch of this band of the 12C18O2 molecule in the 12C16O2+12C16O18O mixture the effect of the overlap with other bands is essential; and, finally, under the conditions of dynamic equilibrium between the v3 modes of both isotopic forms the temperature T3 for 12C18O2, is

We also measured the effect of the dilution of molecules 12C18O2 by the usual form of carbon dioxide 12C16O2, on the output energy. The lasing pulse energies measured in the ranges of 9.4 µm (12C18O2) (1) and 10.4 µm (12C16O2) (2) are given in Fig. 10. These data were acquired for the TEA-module described above using a non-selective cavity composed of a nontransmitting and germanium output (R=~50%) mirrors. The energies emitted in the ranges 10.4 and 9.4 µm are approximately equal to each other at the 30 Torr content of 12C18O2, approaching to the content of 12C18O2 at which the corresponding gains get equal. Also note that the total emission energy (E9.4 + E10.6) is independent in this case of isotoporeplacement

Fig. 10. Lasing energy measured in the ranges of 9.4 μm for 12C18O2 (Ο) and 10.4 μm for 12C16O2 (∆) versus 12C18O2 content

Thus, the results of the investigations demonstrate that efficient lasing of the CO2 laser even with non-selective cavity is possible in the range of 9.4 µm when the 12C18O2, content is 30% of total carbon dioxide amount. When the laser operates with selective cavity such as that based on a diffraction grating, the percentage of 12C18O2, can go down to ~20%. This fact is key for reduction of the price of the active medium.

An experimental series performed as well by us was oriented toward providing longduration autonomous laser operation without active mixture replacement and noticeable degradation of its composition. To this end, the discharge chamber was well evacuated (no more than 0.2 Torr/day inleakage) and the material it was made of was properly selected. The best results were achieved with a glass-epoxy cylinder when the operation was virtually quasi-sealed-off, i.e. without replacement of the active medium on 12C18O2 during 1—2 months (more than 105 pulses) without noticeable decrease of the laser energy. In addition, after long operation and before working gases replacement. the old mixture was pumped through liquid nitrogen traps to recover carbon dioxide for repeated use.

#### **7.2 Using a nonlinear crystal etalon for second harmonic generation from CO2 lasers**

The poor efficiency of the frequency conversion attributable on the whole to mid IR lasers can be compensated to a large degree by application of non-traditional optical schemes. Therefore, the problem remaining topical in the mid IR range along with creation of higherquality crystals applies to development of novel nonlinear conversion schemes and search for the laser operation modes which are optimal for frequency conversion. To this end and with the aim of reaching high conversion efficiency, we have performed some investigations on the basis of which it was possible to realize original optical frequency conversion schemes including intracavity versions.

CO2 Lasing on Non-Traditional Bands 127

the fixed temperature the etalon practically does not influence on oscillations of both lasers, as its bandwidth is much wider than longitudinal modes and comparable to the pressure broadened line width for the TEA laser. Therefore, it is easy to achieve a concurrence between maxima of the line shape function (for TEA and low-pressure longitudinaldischarge lasers) and transmittance bandwidth of the Fabry-Perot etalon by a small angular

However in real conditions a nonlinear crystal has a temperature drift due to the d*(nl)/*d*t* thermal expansion. For the used AgGaSe2 crystal according with the dates of Clevelend Crystals Inc. the factor of linear expansion (α) is 15x106 °C-1 and the thermo-optical factors (d*n0/*d*t* and d*ne/*d*t*) are ~50x10-6 °C-1. Our calculations (see Fig.11c) demonstrate the rather strong temperature drift of the crystal. It is especially important in the case of crystal operating for a low-pressure longitudinal-discharge CO2 laser. In our experiments the crystal was supported by a massive metal holder heated by a thermoelement and it was stabilized with accuracy <0.1°C. Besides it should be noted, that in our experiments the crystals having, the very small absorption (~0.01 cm-1) were used. This fact essentially simplifies process of temperature stabilization. Possible changes of the cavity losses because of the crystal temperature drift for a low-pressure longitudinal-discharge laser did not influence strongly on its output from the fact that we used a pulse-periodic regime of the

The optical crystal was used as a nonlinear output mirror of the TEA 12C18O2, laser. The cavity of the laser was formed by a 150 line/mm grating and an AgGaSe2 nonlinear crystal. A plate made of LiF was used to select second harmonic emission generated in the nonlinear crystal. A high-quality monocrystal sample made of AgGaSe2, with a 12 x 10-mm section *(L*  = 19 mm) was used as a nonlinear output mirror of the laser. The working faces of the crystal were mechanically polished and were not coated. The highly parallel faces (better than 10") caused the sample to operate as a Fabri-Perot etalon. The angle *Ө* (phase matching angle) was adjusted near 46°, and *φ* = 45°. The angle *Ө* is such that the highest efficiency of the second harmonic oscillation is observed at a normal incidence at line 9P(32) *(*λ = 9.06 µm) and at the neighboring line 9P(34) (λ = 9.05 µm) of the isotopic modifications 12C18O2 of

The cavity length was 1.1 m. Before the output mirror (AgGaSe2 crystal) there was in the cavity an iris diaphragm (diameter ~8 mm). In the case when the TEA module was filled with the mixture 12C16O2 : 12C16O18O : 12C18O2 : N2 : He = 104 : 32 : 64 : 200: 600 at a total pressure 500 Torr and a nonlinear crystal was used as an output mirror (~60% reflection), the output energy at lines 9P(32) and 9P(34) of carbon dioxide isotope 12C18O2, was ~0.8 J while the peak power was ~4MW. The diameter of the output beam was ~7 mm. The lasing spot had a good spatial distribution. The energy density of the output emission was ~2

Under above conditions the second harmonic generation energy *(E2ω)* was 52 mJ and the peak power *(P2ω)* was ~2 MW. The conversion efficiency reached almost 15%, and at the peak power it was ~50%. The efficiency was calculated by the standard method (*η= E2ω / E<sup>ω</sup> — for* the per pulse energy and *η= P2ω / Pω —* for peak power). *Eω,, Pω* and *E2<sup>ω</sup> , P2<sup>ω</sup> —* are

energy parameters of the laser emission in the ranges 9 and 4.5 µm, respectively.

**7.3 Second harmonic generation from a TEA 12C18O2 laser** 

tuning of the crystal.

lasing.

carbon dioxide.

J/cm2 (~10 MW/cm2).

In this work we used an original high-efficiency optical nonlinear conversion scheme without focusing optics developed by ourselves. An AgGaSe2 nonlinear crystal was acting as an Fabry-Perot etalon. In this case it could be placed in a laser cavity without reflectionreducing coating. However sonic problems connected with the spacing of its Fabry-Perot transmittance bandwidths and laser cavity modes can arise from it. To clarify these problems some calculations have been made (see Fig. 11).

The line shape function in Figs. 11a and 11b were calculated using the Foight and Lorentz expression, correspondingly. The intervals between the longitudinal modes for the lasers were calculated according with the condition *c/2L*, where *L* is the cavity length and c is the velocity of light. The curves in Fig. 11c are the Fabry-Perot etalon transmittance bandwidths calculated for different temperatures according with Airy's Formula for the etalon made from the AgGaSe2, crystal with the length of 17 mm.

Fig. 11. Line shape function for a low-pressure longitudinal-discharge СО2 laser (a) and for a ТЕА СО2 laser (b) and a transmittance bandwidth of the AgGaSe2 crystal acting as an Fabri-Perot etalon for different temperature variations (c).

In spite of the fact that the pressure broadened line width strongly differs for the TEA CO2 laser and the low-pressure longitudinal-discharge CO2 laser. For the first the full width at half maximum of the line shape function is about 3 GHz, and for the second ~0.l GHz. At

In this work we used an original high-efficiency optical nonlinear conversion scheme without focusing optics developed by ourselves. An AgGaSe2 nonlinear crystal was acting as an Fabry-Perot etalon. In this case it could be placed in a laser cavity without reflectionreducing coating. However sonic problems connected with the spacing of its Fabry-Perot transmittance bandwidths and laser cavity modes can arise from it. To clarify these

The line shape function in Figs. 11a and 11b were calculated using the Foight and Lorentz expression, correspondingly. The intervals between the longitudinal modes for the lasers were calculated according with the condition *c/2L*, where *L* is the cavity length and c is the velocity of light. The curves in Fig. 11c are the Fabry-Perot etalon transmittance bandwidths calculated for different temperatures according with Airy's Formula for the etalon made

Fig. 11. Line shape function for a low-pressure longitudinal-discharge СО2 laser (a) and for a ТЕА СО2 laser (b) and a transmittance bandwidth of the AgGaSe2 crystal acting as an Fabri-

In spite of the fact that the pressure broadened line width strongly differs for the TEA CO2 laser and the low-pressure longitudinal-discharge CO2 laser. For the first the full width at half maximum of the line shape function is about 3 GHz, and for the second ~0.l GHz. At

problems some calculations have been made (see Fig. 11).

from the AgGaSe2, crystal with the length of 17 mm.

Perot etalon for different temperature variations (c).

the fixed temperature the etalon practically does not influence on oscillations of both lasers, as its bandwidth is much wider than longitudinal modes and comparable to the pressure broadened line width for the TEA laser. Therefore, it is easy to achieve a concurrence between maxima of the line shape function (for TEA and low-pressure longitudinaldischarge lasers) and transmittance bandwidth of the Fabry-Perot etalon by a small angular tuning of the crystal.

However in real conditions a nonlinear crystal has a temperature drift due to the d*(nl)/*d*t* thermal expansion. For the used AgGaSe2 crystal according with the dates of Clevelend Crystals Inc. the factor of linear expansion (α) is 15x106 °C-1 and the thermo-optical factors (d*n0/*d*t* and d*ne/*d*t*) are ~50x10-6 °C-1. Our calculations (see Fig.11c) demonstrate the rather strong temperature drift of the crystal. It is especially important in the case of crystal operating for a low-pressure longitudinal-discharge CO2 laser. In our experiments the crystal was supported by a massive metal holder heated by a thermoelement and it was stabilized with accuracy <0.1°C. Besides it should be noted, that in our experiments the crystals having, the very small absorption (~0.01 cm-1) were used. This fact essentially simplifies process of temperature stabilization. Possible changes of the cavity losses because of the crystal temperature drift for a low-pressure longitudinal-discharge laser did not influence strongly on its output from the fact that we used a pulse-periodic regime of the lasing.

#### **7.3 Second harmonic generation from a TEA 12C18O2 laser**

The optical crystal was used as a nonlinear output mirror of the TEA 12C18O2, laser. The cavity of the laser was formed by a 150 line/mm grating and an AgGaSe2 nonlinear crystal. A plate made of LiF was used to select second harmonic emission generated in the nonlinear crystal. A high-quality monocrystal sample made of AgGaSe2, with a 12 x 10-mm section *(L*  = 19 mm) was used as a nonlinear output mirror of the laser. The working faces of the crystal were mechanically polished and were not coated. The highly parallel faces (better than 10") caused the sample to operate as a Fabri-Perot etalon. The angle *Ө* (phase matching angle) was adjusted near 46°, and *φ* = 45°. The angle *Ө* is such that the highest efficiency of the second harmonic oscillation is observed at a normal incidence at line 9P(32) *(*λ = 9.06 µm) and at the neighboring line 9P(34) (λ = 9.05 µm) of the isotopic modifications 12C18O2 of carbon dioxide.

The cavity length was 1.1 m. Before the output mirror (AgGaSe2 crystal) there was in the cavity an iris diaphragm (diameter ~8 mm). In the case when the TEA module was filled with the mixture 12C16O2 : 12C16O18O : 12C18O2 : N2 : He = 104 : 32 : 64 : 200: 600 at a total pressure 500 Torr and a nonlinear crystal was used as an output mirror (~60% reflection), the output energy at lines 9P(32) and 9P(34) of carbon dioxide isotope 12C18O2, was ~0.8 J while the peak power was ~4MW. The diameter of the output beam was ~7 mm. The lasing spot had a good spatial distribution. The energy density of the output emission was ~2 J/cm2 (~10 MW/cm2).

Under above conditions the second harmonic generation energy *(E2ω)* was 52 mJ and the peak power *(P2ω)* was ~2 MW. The conversion efficiency reached almost 15%, and at the peak power it was ~50%. The efficiency was calculated by the standard method (*η= E2ω / E<sup>ω</sup> — for* the per pulse energy and *η= P2ω / Pω —* for peak power). *Eω,, Pω* and *E2<sup>ω</sup> , P2<sup>ω</sup> —* are energy parameters of the laser emission in the ranges 9 and 4.5 µm, respectively.

CO2 Lasing on Non-Traditional Bands 129

more attractive for such lasers than for powerful TEA systems to place a nonlinear crystal

In our experiments a monocrystal sample made of AgGaSe2 and having a high optical quality (absorption factor ~0.0l cm-1) was used. The crystal was uncoated and had the rectangular 3.5 x 8.5-mm2 section. The length of the crystal *(l)* was 17mm. Highly parallel (~.4") working faces provided for a possibility to use the crystal as a Fabri-Perot etalon. The phase-matching angle was ~46°. When the incident pumping emission was normal to the crystal, the highest efficiency of second harmonic generation occurred at lines 9P(32) and

With the optimal radius of the spherical mirror and the focus of the coated lens it was possible to decrease the diameter of the laser beam passing through the crystal by more than one order and, therefore, to increase considerably the pumping density. Along with this we have provided for the pumping beam to be quasi-parallel in the nonlinear crystal. To couple out second harmonic (~75%), we used a Brewster window (GaAs). As the second harmonic polarization was orthogonal to pumping emission, its output was much more than that

A characteristic feature of the proposed system consists of application of the absolutely reflecting (with no out coupling) cavity for pumping emission, which even more increases its intensity. Our experiments showed the highest second harmonic peak power output of the cavity had been equal to 2 W. This is more than one order higher than the analogous parameters reached with the same laser operating with typical optical systems. It is important here to use high quality lens coating with a high damage threshold. This

The lidar apparatus complex is shown in Fig. 13. The CO2 laser was either TEA or low pressure as described previously. All optical elements CO2 laser, receiving telescope with the objective, photo-detectors, beam-splitting plates, etc. were fixed on a massive metal base to provide good repeatability of the experimental results. The load carrying base of the lidar complex was placed on a construction equipped with mechanisms rotating the system in horizontal (360°) and vertical (45°) directions for immediate and reliable targeting. The target is made visible using an optical sight (12 x 50). Comparatively low dimensions (1.4 x 0.7 x 1.2 m) and mass (~200 kg) give a possibility for development of a mobile version.

A schematic drawing of the receiver/transmitter is given in Fig. 14. The CO2 laser pulses are output through the beam splitter and are directed into the atmosphere using a transmitting telescope. The emission passed through the atmosphere and trapped by the telescope of the Cassegrain type and with a 250 mm aperture. It consists of two mirrors: front and rear made of sittal with a reflecting aluminum coating protected by corrosion-preventive film. The system uses additionally a ZnSe coated multi-lens objective. The optical configuration of the objective telescope provides for focusing in the focal plane of the detected emission with a 250-mm cross-section down to a diameter ~0.5 mm. After that the detected emission gets on the photodetector which has the sensitive area with a diameter ~1 mm. Optical signals are measured in two channels. Besides the measurement signal, there is a reference one not

intracavity optical system is simply adjusted and provides with high stable output.

into the cavity.

9P(34) which were emitted by the laser.

attainable in a typical conversion system.

**7.5 Laser detection of N2O** 

transmitted through the atmosphere.

#### **7.4 Low-pressure longitudinal-discharge 12C18O2 laser with frequency doubling in AgGaSe2 crystal**

There are two types of electric-discharge CO2, lasers which are promising to detect N2O content along a measurement path. First of them — low-pressure longitudinal-discharge excitation — is more efficient for small and average paths *(L* = 0.1 – 2.0 km). As a rule, it must operate with the laser beam reflection by a so-called corner reflector . The second— TEA—is suitable for long paths *(L >* 2 km) when the lidar operates either using the backscattering signal or pulses reflected by a topographic target]. This section considers the CO2 laser intended for gas analysis in small and average paths.

The laser the optical system of which is shown in Fig. 12 is automatic tunable and output stabilized as described early. The active element was a sealed-off gas-discharge tube like the industrial GL-50l (see Fig. 7) with the discharge gap of 1.2 m. Our experiments were performed with the 12C18O2 isotopic forms of carbon dioxide with the low enrichment factor with respect to 18O2 described earlier. It is known that when a gas-discharge tube is fed by a pulsed power supplier, the peak power in optimal regime may go up more than by one order as compared to cw electric pumping. This is of especial importance for lasers used in lidar systems. First, the length of the probing path increases up; secondly, pulse-periodic lasing at an optimal repetition rate (~1 kHz) are suitable for receiving and processing of optical and electrical signals and do not require additional devices for modulation.

Fig. 12. Optical scheme of the 12C18O2 laser with intracavity frequency doubling by nonlinear crystal.

Application of the pulse-periodic regime is of especial importance for second harmonic generation in nonlinear crystals. In this case the benefit in the conversion efficiency considerable at the peak power. Our experiments showed the output peak power of the laser to go up to ~l00 W (almost by one order as compared with cw lasing) at lines 9P(32) and 9P(34) of the 12C18O2 molecule (at each individual line in single-mode operation) when a pulsed power supply is applied.

It is very difficult for longitudinally excited CO2 lasers to obtain efficient frequency conversion in nonlinear crystals, as their output power is several orders lower than the peak value attainable in pulsed TEA CO2-systems. Thus, for the AgGaSe2 crystal, for instance, with a mean length *(l~* 2 cm) the second harmonic conversion efficiency attained by us with cw discharge was a little more than a tenth of a percent (in case of pulse-periodic discharge it was ~1%), which was a record-breaking value for such laser sources. Therefore, it is even

There are two types of electric-discharge CO2, lasers which are promising to detect N2O content along a measurement path. First of them — low-pressure longitudinal-discharge excitation — is more efficient for small and average paths *(L* = 0.1 – 2.0 km). As a rule, it must operate with the laser beam reflection by a so-called corner reflector . The second— TEA—is suitable for long paths *(L >* 2 km) when the lidar operates either using the backscattering signal or pulses reflected by a topographic target]. This section considers the

The laser the optical system of which is shown in Fig. 12 is automatic tunable and output stabilized as described early. The active element was a sealed-off gas-discharge tube like the industrial GL-50l (see Fig. 7) with the discharge gap of 1.2 m. Our experiments were performed with the 12C18O2 isotopic forms of carbon dioxide with the low enrichment factor with respect to 18O2 described earlier. It is known that when a gas-discharge tube is fed by a pulsed power supplier, the peak power in optimal regime may go up more than by one order as compared to cw electric pumping. This is of especial importance for lasers used in lidar systems. First, the length of the probing path increases up; secondly, pulse-periodic lasing at an optimal repetition rate (~1 kHz) are suitable for receiving and processing of

optical and electrical signals and do not require additional devices for modulation.

Fig. 12. Optical scheme of the 12C18O2 laser with intracavity frequency doubling by non-

Application of the pulse-periodic regime is of especial importance for second harmonic generation in nonlinear crystals. In this case the benefit in the conversion efficiency considerable at the peak power. Our experiments showed the output peak power of the laser to go up to ~l00 W (almost by one order as compared with cw lasing) at lines 9P(32) and 9P(34) of the 12C18O2 molecule (at each individual line in single-mode operation) when a

It is very difficult for longitudinally excited CO2 lasers to obtain efficient frequency conversion in nonlinear crystals, as their output power is several orders lower than the peak value attainable in pulsed TEA CO2-systems. Thus, for the AgGaSe2 crystal, for instance, with a mean length *(l~* 2 cm) the second harmonic conversion efficiency attained by us with cw discharge was a little more than a tenth of a percent (in case of pulse-periodic discharge it was ~1%), which was a record-breaking value for such laser sources. Therefore, it is even

**7.4 Low-pressure longitudinal-discharge 12C18O2 laser with frequency doubling in** 

CO2 laser intended for gas analysis in small and average paths.

**AgGaSe2 crystal** 

linear crystal.

pulsed power supply is applied.

more attractive for such lasers than for powerful TEA systems to place a nonlinear crystal into the cavity.

In our experiments a monocrystal sample made of AgGaSe2 and having a high optical quality (absorption factor ~0.0l cm-1) was used. The crystal was uncoated and had the rectangular 3.5 x 8.5-mm2 section. The length of the crystal *(l)* was 17mm. Highly parallel (~.4") working faces provided for a possibility to use the crystal as a Fabri-Perot etalon. The phase-matching angle was ~46°. When the incident pumping emission was normal to the crystal, the highest efficiency of second harmonic generation occurred at lines 9P(32) and 9P(34) which were emitted by the laser.

With the optimal radius of the spherical mirror and the focus of the coated lens it was possible to decrease the diameter of the laser beam passing through the crystal by more than one order and, therefore, to increase considerably the pumping density. Along with this we have provided for the pumping beam to be quasi-parallel in the nonlinear crystal. To couple out second harmonic (~75%), we used a Brewster window (GaAs). As the second harmonic polarization was orthogonal to pumping emission, its output was much more than that attainable in a typical conversion system.

A characteristic feature of the proposed system consists of application of the absolutely reflecting (with no out coupling) cavity for pumping emission, which even more increases its intensity. Our experiments showed the highest second harmonic peak power output of the cavity had been equal to 2 W. This is more than one order higher than the analogous parameters reached with the same laser operating with typical optical systems. It is important here to use high quality lens coating with a high damage threshold. This intracavity optical system is simply adjusted and provides with high stable output.

#### **7.5 Laser detection of N2O**

The lidar apparatus complex is shown in Fig. 13. The CO2 laser was either TEA or low pressure as described previously. All optical elements CO2 laser, receiving telescope with the objective, photo-detectors, beam-splitting plates, etc. were fixed on a massive metal base to provide good repeatability of the experimental results. The load carrying base of the lidar complex was placed on a construction equipped with mechanisms rotating the system in horizontal (360°) and vertical (45°) directions for immediate and reliable targeting. The target is made visible using an optical sight (12 x 50). Comparatively low dimensions (1.4 x 0.7 x 1.2 m) and mass (~200 kg) give a possibility for development of a mobile version.

A schematic drawing of the receiver/transmitter is given in Fig. 14. The CO2 laser pulses are output through the beam splitter and are directed into the atmosphere using a transmitting telescope. The emission passed through the atmosphere and trapped by the telescope of the Cassegrain type and with a 250 mm aperture. It consists of two mirrors: front and rear made of sittal with a reflecting aluminum coating protected by corrosion-preventive film. The system uses additionally a ZnSe coated multi-lens objective. The optical configuration of the objective telescope provides for focusing in the focal plane of the detected emission with a 250-mm cross-section down to a diameter ~0.5 mm. After that the detected emission gets on the photodetector which has the sensitive area with a diameter ~1 mm. Optical signals are measured in two channels. Besides the measurement signal, there is a reference one not transmitted through the atmosphere.

CO2 Lasing on Non-Traditional Bands 131

1 — output mirror of TEA CO2 laser; 2 — BaF2 beam-splitter; 3 — transmitting telescope; 4 — receiving telescope; 5, 6 — mirrors; 7 — receiving objective (ZnSe); 8 — photodetector (CdHgTe) of measurement channel; 9 — lens (ZnSe) of reference channel; 10 — photodetector (Ge:Au) of reference channel; 11 —

<sup>12</sup><sup>13</sup>

8 6 5

11 7

For monochromatic radiation propagating in homogeneous medium containing several

×

where *I0* and *Iλ,* are the intensities of the emission with the wavelength λ before and after its passage through a gas layer with length *L, τλ* = *L∑ik <sup>λ</sup>ic i* is the optical thickness, *k <sup>λ</sup>i* and *c i* are accordingly the absorption coefficient at the wavelength *λi* and the concentration of the *i*th

The analysis of the optical characteristics of the detected gases was performed using the differential absorption technique that is in wide use now for laser atmospheric probing. The probing is made at an on/off pair of laser emission lines. "On" line has the maximally possible resonance absorption, and "off"—minimal. The two-frequency differential absorption technique takes useful information only in the resonance absorption by a gas in question. The effects of such factors as water vapour continuum, non-resonance molecular and aerosol absorption, dust, smog, etc. scattering, atmospheric turbulence will be virtually absent due to the comparatively weak monotonic spectral dependence when "on" and "oil"

Prior to measuring N2O, the lidar complex was tested and calibrated for CO and H2O measurements using CO2 lasers both TEA and low pressure operating on the ordinary

 *exp(-τλ)* , (6)

4

3

Fig. 14. Schematic drawing of the receiver/transmitter of the lidar complex.

absorbing gases, the transmission *T<sup>λ</sup>* is described by the Buger law :

2

10

9

iris; 12 — ADC; 13 — personal computer

1

lines are located near each other.

absorbing gas.

 *Tλ =Iλ / I0*

1 — output mirror of CO2-laser; 2 — CO2-laser; 3 — horizontal rotation unit; 4 — vertical rotation unit; 5 — metallic base; 6 — receiver/transmitter

Fig. 13. Lidar complex.

The reference signal is produced using a 1-mm-thickness beam-splitter made of BaF2. Such a thin plate located at an angle ~50° introduces minimum loss for polarized radiation of the TEA CO2 laser. The loss in the reflection by both faces was no more than 2%. At the same time, only small portion of the emission would be reflected to provide the reference channel. Passing the focusing lens, the reflected portion comes to the sensitive area of the photodetector of the reference channel so organized that this allows automatic account of possible instability of the laser output by normalizing the measurement signal on the reference one, which essentially increases the measurement accuracy and reliability.

As photodetectors nitrogen-cooled photoresistors based on CdHgTe, InSb or germanium doped with gold (Ge:Au) were used. To increase the sensitivity in the measurement channel we used an amplifier. The photodetectors were placed on alignment units. This provided accurate adjustment of the sensitive area of the detector with respect to incident emission. Photodetector signals either arrive to a two-channel ADC or digital oscilloscope and then, via an interface unit, into a computer.

2

3

5

1 — output mirror of CO2-laser; 2 — CO2-laser; 3 — horizontal rotation unit; 4 — vertical rotation unit; 5

The reference signal is produced using a 1-mm-thickness beam-splitter made of BaF2. Such a thin plate located at an angle ~50° introduces minimum loss for polarized radiation of the TEA CO2 laser. The loss in the reflection by both faces was no more than 2%. At the same time, only small portion of the emission would be reflected to provide the reference channel. Passing the focusing lens, the reflected portion comes to the sensitive area of the photodetector of the reference channel so organized that this allows automatic account of possible instability of the laser output by normalizing the measurement signal on the

As photodetectors nitrogen-cooled photoresistors based on CdHgTe, InSb or germanium doped with gold (Ge:Au) were used. To increase the sensitivity in the measurement channel we used an amplifier. The photodetectors were placed on alignment units. This provided accurate adjustment of the sensitive area of the detector with respect to incident emission. Photodetector signals either arrive to a two-channel ADC or digital oscilloscope and then,

reference one, which essentially increases the measurement accuracy and reliability.

— metallic base; 6 — receiver/transmitter

1

4

via an interface unit, into a computer.

Fig. 13. Lidar complex.

1 — output mirror of TEA CO2 laser; 2 — BaF2 beam-splitter; 3 — transmitting telescope; 4 — receiving telescope; 5, 6 — mirrors; 7 — receiving objective (ZnSe); 8 — photodetector (CdHgTe) of measurement channel; 9 — lens (ZnSe) of reference channel; 10 — photodetector (Ge:Au) of reference channel; 11 iris; 12 — ADC; 13 — personal computer

Fig. 14. Schematic drawing of the receiver/transmitter of the lidar complex.

For monochromatic radiation propagating in homogeneous medium containing several absorbing gases, the transmission *T<sup>λ</sup>* is described by the Buger law :

$$\mathbf{T}\_{\lambda} = \mathbf{I}\_{\lambda} / I\_0 \times \exp(\mathbf{-}\mathbf{r}\lambda) \,. \tag{6}$$

where *I0* and *Iλ,* are the intensities of the emission with the wavelength λ before and after its passage through a gas layer with length *L, τλ* = *L∑ik <sup>λ</sup>ic i* is the optical thickness, *k <sup>λ</sup>i* and *c i* are accordingly the absorption coefficient at the wavelength *λi* and the concentration of the *i*th absorbing gas.

The analysis of the optical characteristics of the detected gases was performed using the differential absorption technique that is in wide use now for laser atmospheric probing. The probing is made at an on/off pair of laser emission lines. "On" line has the maximally possible resonance absorption, and "off"—minimal. The two-frequency differential absorption technique takes useful information only in the resonance absorption by a gas in question. The effects of such factors as water vapour continuum, non-resonance molecular and aerosol absorption, dust, smog, etc. scattering, atmospheric turbulence will be virtually absent due to the comparatively weak monotonic spectral dependence when "on" and "oil" lines are located near each other.

Prior to measuring N2O, the lidar complex was tested and calibrated for CO and H2O measurements using CO2 lasers both TEA and low pressure operating on the ordinary

CO2 Lasing on Non-Traditional Bands 133

Then, from the known concentration of H2O determined independently (for instance, using psychometric devices), it will be possible to calibrate the technique, i.e. obtain the evidence that the results of the laser atmospheric probing are reliable. We used the line 9P(22) that was almost fully absorbed by H2O as a reference one to check laser tuning at the selected lines. Based on such an original technique we have measured carbon dioxide and water vapour near a highway at a height about 10 m over the cart!, surface. The laser emission was reflected by a

The carbon monoxide concentration measured in autumn (500-600 p.m.) has varied from 0.8 to 1.2 ppm. The measured mean concentration of CO was ~1 ppm. The measurement

N2O measurements were performed with the same path *(2L =* 0.2 km) using tile lowpressure 12C18O2 laser with frequency doubling by a nonlinear crystal. As in the previous case, the emission was reflected by a metallized plywood sheet. Fig. 16 shows a calculated spectrum of the atmospheric gases absorption in the range of 4.5—4.55 μm. We select this spectral range as there are some doubled frequencies of efficient tines of the 12C18O2 laser. It is reasonable to select frequency doubled R(32) or R(40) as "on' line, and doubled frequencies of the neighboring R(34) or R(38)—as "off" line. It is important that the indicated lines do not coincide with the absorption lines of background gases H2O and CO which are always present in the atmosphere. In this way we carried out a number of measurements of N2O concentration along a researched path at various seasons and times of day. The analysis of the received data has shown that N2O content in the atmosphere varied considerably, and it is mainly caused by intensity of the transport movement. For example, our experiments performed in autumn in different times during a few days have shown that the N2O concentration in the path was from 0.35 to 0.5 ppm. The measurement accuracy is

We also have measured N2O for a longer path *(2L =* 1.4 km) using the frequency-doubling TEA 12C18O2 laser described earlier. In this case, the laser beam was reflected by a building wall. The averaged content of N2O was in a good agreement with the value obtained for the

The experimental investigations and the calculations carried out have proved conclusively the promising character of the technique developed for the determination of low nitrous oxide concentrations. The technique is based on the use of 12C18O2, lasers with effective

The research carried out has given a reliable technique for laser atmospheric probing of nitrous oxide and effective laser systems to implement this procedure. It is of importance that the path probing is made with a powerful molecular gas laser. Such lasers have narrow emission lines and high stability of spectral and energy output. These characteristics are achieved, as distinct from semiconductor and solid state lasers, naturally without any additional devices. Thus the laser system is simplified and the measurement accuracy increases. The 12C18O2 laser system with effective nonlinear frequency-doubling is much

A reliable procedure or remote high-accuracy laser detection of N2O as one of the principal destroyers of the protective ozone layer of the Earth has been developed. The procedure is based on using a CO2 laser system emitting efficiently in the ~4.5 μm range. In this case

promising for global network of lidar stations for atmosphere monitoring.

plywood sheet painted with a metallic color. The length of probing was 2L *=* 0.2 km.

accuracy determined from H2O calibrations was ~5%.

estimated to be better than 15%.

frequency doubling in nonlinear crystals.

shorter path.

12C16O2 with frequency doubling by a nonlinear AgGaSe2 crystal. Measurements of the CO and H2O concentrations also allowed us to account these gases as background for the N2O measurements.

The theoretical analysis of the absorption lines of CO and background gases (particularly, H2O) for a path with 2L = 200 m has shown that it is reasonable to select "on" line among the doubled frequencies of the 12C16O2, laser such as 9R(30) (at λ = 4.6099 µm the absorption is 50%/ppm). 9R(18) (λ= 4.6412 µm—45%/ppm) and 9P(24) (λ*=* 4.7931 µm—37%/ppm). Accordingly. the most suitable "off" line belongs to the same laser and are 9R(28) (λ*=* 4.6148 µm). 9R(20) (λ *=* 4.6357 µm) and 9P(26) (λ = 4.8018 µm) at which the absorption by carbon dioxide and background gases is virtually absent.

Fig. 15. Absorption spectrum of CO and background gases (H2O and CO2) in the range of 4.78 - 4.82 μm. The conditions: path length (2L)=200 m, P=1 atm, Т=287 К, gas contents: CO – 1 ppm, H2O – 10000 ppm, CO2 – 330 ppm.

Fig. 15 shows a calculated absorption spectrum of the atmospheric gases in the range of our investigations. We select this spectral range due to the following advantages. One of the four selected laser lines (9P(22)— 9P(28)), namely 9P(24) ("on line"), coincides well with the absorption peak of CO. Two of them (9P(22) and 9P(28)) coincides sufficiently well with the absorption lines of H2O, while 9P(26) demonstrating no absorption of both CO and H2O is quite suitable as the "off" line. In addition, there is no noticeable absorption by other atmospheric gases (CO2, for instance) at these lines. Then, carrying out consecutive measurements at these lines, it will be possible to measure concentrations of CO and H2O.

12C16O2 with frequency doubling by a nonlinear AgGaSe2 crystal. Measurements of the CO and H2O concentrations also allowed us to account these gases as background for the N2O

The theoretical analysis of the absorption lines of CO and background gases (particularly, H2O) for a path with 2L = 200 m has shown that it is reasonable to select "on" line among the doubled frequencies of the 12C16O2, laser such as 9R(30) (at λ = 4.6099 µm the absorption is 50%/ppm). 9R(18) (λ= 4.6412 µm—45%/ppm) and 9P(24) (λ*=* 4.7931 µm—37%/ppm). Accordingly. the most suitable "off" line belongs to the same laser and are 9R(28) (λ*=* 4.6148 µm). 9R(20) (λ *=* 4.6357 µm) and 9P(26) (λ = 4.8018 µm) at which the absorption by carbon

Fig. 15. Absorption spectrum of CO and background gases (H2O and CO2) in the range of 4.78 - 4.82 μm. The conditions: path length (2L)=200 m, P=1 atm, Т=287 К, gas contents:

Fig. 15 shows a calculated absorption spectrum of the atmospheric gases in the range of our investigations. We select this spectral range due to the following advantages. One of the four selected laser lines (9P(22)— 9P(28)), namely 9P(24) ("on line"), coincides well with the absorption peak of CO. Two of them (9P(22) and 9P(28)) coincides sufficiently well with the absorption lines of H2O, while 9P(26) demonstrating no absorption of both CO and H2O is quite suitable as the "off" line. In addition, there is no noticeable absorption by other atmospheric gases (CO2, for instance) at these lines. Then, carrying out consecutive measurements at these lines, it will be possible to measure concentrations of CO and H2O.

measurements.

dioxide and background gases is virtually absent.

CO – 1 ppm, H2O – 10000 ppm, CO2 – 330 ppm.

Then, from the known concentration of H2O determined independently (for instance, using psychometric devices), it will be possible to calibrate the technique, i.e. obtain the evidence that the results of the laser atmospheric probing are reliable. We used the line 9P(22) that was almost fully absorbed by H2O as a reference one to check laser tuning at the selected lines. Based on such an original technique we have measured carbon dioxide and water vapour near a highway at a height about 10 m over the cart!, surface. The laser emission was reflected by a plywood sheet painted with a metallic color. The length of probing was 2L *=* 0.2 km.

The carbon monoxide concentration measured in autumn (500-600 p.m.) has varied from 0.8 to 1.2 ppm. The measured mean concentration of CO was ~1 ppm. The measurement accuracy determined from H2O calibrations was ~5%.

N2O measurements were performed with the same path *(2L =* 0.2 km) using tile lowpressure 12C18O2 laser with frequency doubling by a nonlinear crystal. As in the previous case, the emission was reflected by a metallized plywood sheet. Fig. 16 shows a calculated spectrum of the atmospheric gases absorption in the range of 4.5—4.55 μm. We select this spectral range as there are some doubled frequencies of efficient tines of the 12C18O2 laser. It is reasonable to select frequency doubled R(32) or R(40) as "on' line, and doubled frequencies of the neighboring R(34) or R(38)—as "off" line. It is important that the indicated lines do not coincide with the absorption lines of background gases H2O and CO which are always present in the atmosphere. In this way we carried out a number of measurements of N2O concentration along a researched path at various seasons and times of day. The analysis of the received data has shown that N2O content in the atmosphere varied considerably, and it is mainly caused by intensity of the transport movement. For example, our experiments performed in autumn in different times during a few days have shown that the N2O concentration in the path was from 0.35 to 0.5 ppm. The measurement accuracy is estimated to be better than 15%.

We also have measured N2O for a longer path *(2L =* 1.4 km) using the frequency-doubling TEA 12C18O2 laser described earlier. In this case, the laser beam was reflected by a building wall. The averaged content of N2O was in a good agreement with the value obtained for the shorter path.

The experimental investigations and the calculations carried out have proved conclusively the promising character of the technique developed for the determination of low nitrous oxide concentrations. The technique is based on the use of 12C18O2, lasers with effective frequency doubling in nonlinear crystals.

The research carried out has given a reliable technique for laser atmospheric probing of nitrous oxide and effective laser systems to implement this procedure. It is of importance that the path probing is made with a powerful molecular gas laser. Such lasers have narrow emission lines and high stability of spectral and energy output. These characteristics are achieved, as distinct from semiconductor and solid state lasers, naturally without any additional devices. Thus the laser system is simplified and the measurement accuracy increases. The 12C18O2 laser system with effective nonlinear frequency-doubling is much promising for global network of lidar stations for atmosphere monitoring.

A reliable procedure or remote high-accuracy laser detection of N2O as one of the principal destroyers of the protective ozone layer of the Earth has been developed. The procedure is based on using a CO2 laser system emitting efficiently in the ~4.5 μm range. In this case

CO2 Lasing on Non-Traditional Bands 135

1110; (0221-1220, 0201-1200…) bands of CO2 molecule. To test the validity of the method, the experiment realization has been done for a low pressure CO2 laser with cw longitudinal discharge, that can oscillate on the lines of regular and nonregular lines. The good

We examined what kind of the small gain and the output energy can be attained in the TEA CO2 laser on the 16(14) µm 0201(1001)-0111 transitions. On tile basis of the experimentally determined vibrational temperatures *T3* and *T2* we calculated the small gain. The calculations shown that the small gain in the 0201(1001)-0111 band can attain a significant value (>1 m-1). The necessary conditions for the effective lasing have been determined. It is shown that in optimum conditions the output energy can reach *1.3* J/l at the peak power 5

The experimental investigations and the calculations carried out have proved conclusively the promising character of the technique developed for the determination of low nitrous oxide concentrations. The technique is based on the use of 12C18O2, lasers with effective frequency doubling in nonlinear crystals. The research carried out has given a reliable technique for laser atmospheric probing of nitrous oxide and effective laser systems to implement this procedure. It is of importance that the path probing is made with a powerful molecular gas laser. Such lasers have narrow emission lines and high stability of spectral and energy output. They were much promising for global network of lidar stations for

Aleinikov V.S. and Masychev V.I. (1990). *Carbon monoxide Lasers*, Radio Svyaz, Moscow, (in

Bertel I.M., Petukhov V.O., Stepanov B.I., Trushin S.A., Churakov V.V. (1982). Investigation

Bertel, I.M.; Petukhov V.V. et al. (1983) Diagnostics of active mediums of CO2 lasers with the

Bertel, I.M.; Petukhov, V.O.; Trushin, S.A. and Churakov, V.V. (1983). Study of the Gain and

Churakov, V.V.; Petukhov, V.O. and Tochitsky S.Ya. (1987). Two-color TEA CO2 laser oscillation on the lines of regular and hot hands. *Appl. Phis. B,* v .42, pp. 245-249. Crutzen, P.J. (1996). My life with O3, N2O, and other compounds, *Nobel Lecture,* Angew.

Gordiets B.F., Osipov A.I., and Shelepin L.A., (1980) Kinetic *Processes in Gases and Molecular* 

Gorobets, V.A,; Petukhov, V.O.; Tochitsky S.Ya. and V. V. Churakov. (1992) Method of

Gorobets, V.A.; Petikhov, V.O.; Tochitsky S.Ya. and Churakov V.V. (1995). Transversely

Tuning a CO2 laser on a Chosen Lasing Line, *Author's Certificate 1771367 SSSR*; MKI

excited CO2 lidar laser tunable over lines of regular and nontraditional bands.

*Preprint of the IF AN BSSR* No. 289*,* (in Russian), Minsk, Belarus

of the vibrational temperature kinetics in a TEA CO2 laser*. Sov. J Quantum Electron.*,

use of nontraditional transitions of molecule CO2, *Nonequilibrium Processes in Gas* 

the Conditions of Efficient Lasing on Lines of the Hot Band in a TEA CO2 laser,

agreement between calculation and experiment data has been observed

MW and at the full efficiency of 2 *%.* 

atmosphere monitoring.

Russian)

H 01 S 3/22

v. 12, No 8. pp. 1044-1049

*Dynamics*, (in Russian), Minsk, Belarus

Chem. Int. Ed. Engl. 35 1758—1777.

*Gas Lasers,* (in Russian), Moscow, Russia

*Quantum Electronics,* v. 25, No *5,* pp. 489-493.

**9. References** 

lasing from isotopic modification *12C18*O2 of carbon dioxide with its subsequent frequency doubling by a nonlinear crystal is used. With the object of reducing the price the composition of the active medium (both for TEA laser and low-pressure longitudinaldischarge excitation laser) has been optimized. New high-efficiency intracavity frequency doubling schemes based on nonlinear AgGaSe2 crystals have been developed for CO2 lasers of both types. Low concentrations of N2O and concentrations of the principal background gases CO and N2O have been measured under real atmosphere conditions with the aid of the lidar complex built around these lasers.

Fig. 16. Absorption spectrum of N2O and background gases (CO and H2O). The conditions: path length (2L)=0.2 km, P=1 atm, T=287 K, gas contens: N2O — 0.4 ppm, H2O — 10 000 ppm, CO — 1 ppm

#### **8. Conclusion**

Optimization of the gas content, pressure, discharge current and the cavity of a low-pressure laser with longitudinal discharge were carried out. Thus, after the above improvements the commercially available sealed-off laser oscillates on more than 30 lines of the P-branch of the 0111- 1110 band in the 10.9—11.3 µm range with output power no less than 0.5 W. On strong lines [P(16)—P(26)] output power was ~6W at efficiency ~3% which makes up ~ 40% of analogous laser parameters in the case of oscillation on the lines of regular bands 0001-1000 (0200) under optimum conditions.

The peak power on the strongest lines of the new bands (10°l-20°0(0400) with a lasing pulse was 30 W. The average output power reached 0.2 W. Lasing was achieved at a number of new transitions. More than 25 new lasing lines with λ = 11.1–11.4 μm, belonging to all the aforementioned bands, were observed in the spectral range studied.

The method of output optimization of cw CO2 lasers has been developed. The method is based on vibrational and translational temperatures determination by gain measurements on the ro-vibrational lines of regular (0001-1000, 0200) and nonregular (0002-1001, 0201; 0111-

lasing from isotopic modification *12C18*O2 of carbon dioxide with its subsequent frequency doubling by a nonlinear crystal is used. With the object of reducing the price the composition of the active medium (both for TEA laser and low-pressure longitudinaldischarge excitation laser) has been optimized. New high-efficiency intracavity frequency doubling schemes based on nonlinear AgGaSe2 crystals have been developed for CO2 lasers of both types. Low concentrations of N2O and concentrations of the principal background gases CO and N2O have been measured under real atmosphere conditions with the aid of

Fig. 16. Absorption spectrum of N2O and background gases (CO and H2O). The conditions:

Optimization of the gas content, pressure, discharge current and the cavity of a low-pressure laser with longitudinal discharge were carried out. Thus, after the above improvements the commercially available sealed-off laser oscillates on more than 30 lines of the P-branch of the 0111- 1110 band in the 10.9—11.3 µm range with output power no less than 0.5 W. On strong lines [P(16)—P(26)] output power was ~6W at efficiency ~3% which makes up ~ 40% of analogous laser parameters in the case of oscillation on the lines of regular bands 0001-1000

The peak power on the strongest lines of the new bands (10°l-20°0(0400) with a lasing pulse was 30 W. The average output power reached 0.2 W. Lasing was achieved at a number of new transitions. More than 25 new lasing lines with λ = 11.1–11.4 μm, belonging to all the

The method of output optimization of cw CO2 lasers has been developed. The method is based on vibrational and translational temperatures determination by gain measurements on the ro-vibrational lines of regular (0001-1000, 0200) and nonregular (0002-1001, 0201; 0111-

aforementioned bands, were observed in the spectral range studied.

path length (2L)=0.2 km, P=1 atm, T=287 K, gas contens: N2O — 0.4 ppm, H2O —

the lidar complex built around these lasers.

10 000 ppm, CO — 1 ppm

(0200) under optimum conditions.

**8. Conclusion** 

1110; (0221-1220, 0201-1200…) bands of CO2 molecule. To test the validity of the method, the experiment realization has been done for a low pressure CO2 laser with cw longitudinal discharge, that can oscillate on the lines of regular and nonregular lines. The good agreement between calculation and experiment data has been observed

We examined what kind of the small gain and the output energy can be attained in the TEA CO2 laser on the 16(14) µm 0201(1001)-0111 transitions. On tile basis of the experimentally determined vibrational temperatures *T3* and *T2* we calculated the small gain. The calculations shown that the small gain in the 0201(1001)-0111 band can attain a significant value (>1 m-1). The necessary conditions for the effective lasing have been determined. It is shown that in optimum conditions the output energy can reach *1.3* J/l at the peak power 5 MW and at the full efficiency of 2 *%.* 

The experimental investigations and the calculations carried out have proved conclusively the promising character of the technique developed for the determination of low nitrous oxide concentrations. The technique is based on the use of 12C18O2, lasers with effective frequency doubling in nonlinear crystals. The research carried out has given a reliable technique for laser atmospheric probing of nitrous oxide and effective laser systems to implement this procedure. It is of importance that the path probing is made with a powerful molecular gas laser. Such lasers have narrow emission lines and high stability of spectral and energy output. They were much promising for global network of lidar stations for atmosphere monitoring.

#### **9. References**


**Part 2** 

**New Systems**


## **Part 2**

**New Systems**

CO2 136 Laser – Optimisation and Application

Gorobets, V.A.; Petukhov, V.O. and Churakov V.V. (1990) Optimization of the Output

Petukhov, V.O. et al. (1985). Fizicheskaya Gazodinamika: Eksperimental 'noe

Smith, K. and Thompson R. (1981). *Numerical Modeling of Gas Lasers,* (in Russian), Moscow,

Wexler, B.E.; Manuccia T.J. and Waynant R. (1987). CW and improved pulsed operation of the 14 µm and 16 µm CO2 lasers, *Appl. Phys. Lett,* v.31, No 11, pp. 730-732. Witteman, W. (1987). The CO2 Laser, *Springer-Verlag*, Berlin, Heidelberg, New York, London,

*AN BSSR No. 608*, (in Russian), Minsk, Belarus

Russia

Paris, Tokyo

*Diagnostic).* IHMT AS BSSR, (in Russian), Minsk, Belarus

Power of a Continuous CO2 Lasing on Unconventional Transitions, *Preprint of the IF* 

Modelirovanie, *Diagnostika (Physical Gas Dynamics: Experimental Modeling and* 

**4** 

*USA* 

**Ultrashort Pulses** 

*Brookhaven National Laboratory* 

Mikhail N. Polyanskiy and Marcus Babzien

Ultrashort pulses usually are defined as those lasting less than a nanosecond. Low-energetic ultrashort pulses can be used, for instance, as a probe for studying the dynamics of ultrafast processes. Amplifying these pulses can deliver extremely high peak power, allowing applications such as laser particle acceleration, or γ-ray generation via Compton scattering on relativistic electrons. Existing laser systems can provide pulses as brief as hundreds of attoseconds (10-18 s) and as powerful as tens of petawatts (1015 W); more advanced ones are being constructed or are planned (Corkum & Krausz, 2007,

Virtually all modern ultrashort-pulse lasers are based on solid-state technology and usually operate at ~1 µm wavelength. Nevertheless, these applications relying not only on the ultrashort duration or the extreme power of the laser pulse, but also on its wavelength, leave a niche for laser systems utilizing different types of active medium. The 10-micron

To demonstrate the potential of ultrashort, mid-IR pulses, we consider their employment for laser ion acceleration, presently one of the main drivers for developing ultrashort-pulse CO2 lasers (Palmer et al., 2011, Norreys, 2011). The motivation underlying the search for alternatives to conventional accelerators, wherein a system of electrodes and magnets creates the accelerating field, is the need to reduce the size and the cost of these devices. Acceleration in the electromagnetic field of a laser beam is a promising alternative for traditional acceleration schemes. In laser ion acceleration, an intense laser pulse focused on a target first ionizes it and then accelerates the charged particles from the resulting plasma. Usually this target is a metal foil, and a ~1 µm, multi-TW peak power, solid-state laser provides the ionizing/accelerating field. A very efficient acceleration regime called *Radiation Pressure Acceleration* (RPA) featuring a narrow energy-spectrum of the accelerated ions is reached when laser pulse interacts with plasma having a near-critical density (Esirkepov et al., 2004). The following formula defines critical plasma density, *Nc* (the density at which

> -3 <sup>21</sup> [cm ] 1.115 10 [μm] *<sup>c</sup> <sup>n</sup> <sup>N</sup>*

≈ ×

2

, (1)

λ

wavelength of the CO2 laser particularly is beneficial for some usages.

**1. Introduction** 

Korzhimanov et al., 2011).

plasma becomes opaque):

**1.1 Niche for ultrashort-pulse CO2 lasers** 

### **Ultrashort Pulses**

Mikhail N. Polyanskiy and Marcus Babzien *Brookhaven National Laboratory USA* 

#### **1. Introduction**

#### **1.1 Niche for ultrashort-pulse CO2 lasers**

Ultrashort pulses usually are defined as those lasting less than a nanosecond. Low-energetic ultrashort pulses can be used, for instance, as a probe for studying the dynamics of ultrafast processes. Amplifying these pulses can deliver extremely high peak power, allowing applications such as laser particle acceleration, or γ-ray generation via Compton scattering on relativistic electrons. Existing laser systems can provide pulses as brief as hundreds of attoseconds (10-18 s) and as powerful as tens of petawatts (1015 W); more advanced ones are being constructed or are planned (Corkum & Krausz, 2007, Korzhimanov et al., 2011).

Virtually all modern ultrashort-pulse lasers are based on solid-state technology and usually operate at ~1 µm wavelength. Nevertheless, these applications relying not only on the ultrashort duration or the extreme power of the laser pulse, but also on its wavelength, leave a niche for laser systems utilizing different types of active medium. The 10-micron wavelength of the CO2 laser particularly is beneficial for some usages.

To demonstrate the potential of ultrashort, mid-IR pulses, we consider their employment for laser ion acceleration, presently one of the main drivers for developing ultrashort-pulse CO2 lasers (Palmer et al., 2011, Norreys, 2011). The motivation underlying the search for alternatives to conventional accelerators, wherein a system of electrodes and magnets creates the accelerating field, is the need to reduce the size and the cost of these devices. Acceleration in the electromagnetic field of a laser beam is a promising alternative for traditional acceleration schemes. In laser ion acceleration, an intense laser pulse focused on a target first ionizes it and then accelerates the charged particles from the resulting plasma. Usually this target is a metal foil, and a ~1 µm, multi-TW peak power, solid-state laser provides the ionizing/accelerating field. A very efficient acceleration regime called *Radiation Pressure Acceleration* (RPA) featuring a narrow energy-spectrum of the accelerated ions is reached when laser pulse interacts with plasma having a near-critical density (Esirkepov et al., 2004). The following formula defines critical plasma density, *Nc* (the density at which plasma becomes opaque):

$$N\_c \text{[cm}^{-3}] = 1.115 \times 10^{21} \left(\frac{n}{\mathcal{A} \text{[\mu m]}}\right)^2,\tag{1}$$

Ultrashort Pulses 141

where *P* is the total gas pressure, and *Ψx* is the relative concentration of the component *x*. Eq. (3) yields *Δνpressure*≈3.8 GHz at 1 bar of a typical mixture [CO2]:[N2]:[He]=1:1:8. Although direct substituting this bandwidth in Eq. (2) gives *τp*≈120 ps, in reality the pulse's spectrum is narrower than the gain bandwidth, and, correspondingly, the pulse's duration is longer. The latter fact is comprehensible by realizing that amplification is the strongest in the center of the laser line, and thus, upon amplification, the ratio between the intensity at the central frequency and that at the wing of the gain-spectrum line increases, thus narrowing the pulse's spectrum. Consequently, the minimum achievable duration of the pulse for an atmospheric-pressure CO2 laser is about 1 ns (Abrams & Wood, 1971). Pressure can be increased to broaden the gain bandwidth, and thus somewhat reduce the pulse's duration. However, the complete overlap of rotational lines separated by 55 GHz (P-) or 40 GHz (Rbranches) that would allow using an entire rotational branch, does not occur below 20- 25 bar; this is not feasible in discharge-pumped lasers having a ~10 bar practical pressure

Fig. 2. Simulated normalized gain spectra at different gas pressures. 10P, 10R, 9P, and 9R: Rotational P- and R-branches of the two vibrational transitions supporting lasing at ~10 µm

Another important consequence of the rotational structure of the CO2 gain spectrum relates to the amplification of the ultrashort pulses. The spectrum of a few-picosecond-long pulse, according to Eq. (2), overlaps several rotational lines of the gain spectrum. Hence, upon amplification, the pulse's spectrum acquires the corresponding periodic structure. In the

limit.

and ~9 µm respectively.

[ ] [ ] ( ) Δ *pressure* GHz bar 5.79 4.25 3.55 *CO*2 2 *<sup>N</sup> He ν* ≈ ⋅ Ψ + Ψ+ Ψ *P* , (3)

where *n* is the refractive index, and *λ* the laser wavelength. According to the Eq. (1), *Nc* is ~1021 cm-3 for the 1-µm lasers, and ~1019 cm-3 for the 10-µm lasers. These densities are much lower than that of solid materials. The critical density at 10 µm is comparable with the density of gases (~2.7×1019 cm-3 at 1 bar); thus, it readily is achievable for the CO2 laser's wavelength when the gas jet is used as a target. On the other hand, realizing the criticaldensity jet for 1-µm solid-state lasers is challenging. Another advantage of the longer wavelength for ion acceleration in the RPA regime is the λ2 scaling of the ponderomotive force, implying that a 100x lower intensity of the CO2 laser field will suffice for reaching a given ion energy compared with a solid-state laser.

Yet another simple consideration favors CO2 lasers for certain applications: A 10-µm laser pulse carries 10x more photons than a 1-µm pulse of the same energy. Photon density is important for applications such as γ-ray generation by Compton scattering on relativistic electrons (Yakimenko & Pogorelsky, 2006).

#### **1.2 Challenge of high peak power**

The minimum achievable duration of the pulse is defined by the bandwidth of the gain spectrum. In the simplest case of the absence of chirping (frequency variation with time), the spectrum of a pulse is the Fourier transform of its temporal profile. The pulse then is called transform-limited, and its duration, *τp*, is inversely proportional to its spectral width, *Δνp*. The following expression is valid for a transform-limited Gaussian pulse (Paschotta, 2008):

$$
\sigma\_p = \frac{0.44}{\Delta \nu\_p} \,\prime\tag{2}
$$

where *τp* and *Δνp* are defined as full-width at half-maximum (FWHM). The duration of a chirped pulse is longer than that of a transform-limited pulse of the same shape and spectral width. Fig. 1 shows the spectra of several femto- and pico-second transform-limited Gaussian pulses. Fig. 2 compares them with the gain spectrum of a typical CO2 laser mixture, clearly revealing the challenge of generating and amplifying ultrashort pulses in a CO2 laser.

Fig. 1. Spectra of transform-limited Gaussian pulses. Durations are full-width at halfmaximum (FWHM).

At low pressures (less than a few bars), the gain spectrum consists of individual rotational lines whose bandwidth (FWHM) is given by the following expression (Brimacombe & Reid, 1983):

where *n* is the refractive index, and *λ* the laser wavelength. According to the Eq. (1), *Nc* is ~1021 cm-3 for the 1-µm lasers, and ~1019 cm-3 for the 10-µm lasers. These densities are much lower than that of solid materials. The critical density at 10 µm is comparable with the density of gases (~2.7×1019 cm-3 at 1 bar); thus, it readily is achievable for the CO2 laser's wavelength when the gas jet is used as a target. On the other hand, realizing the criticaldensity jet for 1-µm solid-state lasers is challenging. Another advantage of the longer wavelength for ion acceleration in the RPA regime is the λ2 scaling of the ponderomotive force, implying that a 100x lower intensity of the CO2 laser field will suffice for reaching a

Yet another simple consideration favors CO2 lasers for certain applications: A 10-µm laser pulse carries 10x more photons than a 1-µm pulse of the same energy. Photon density is important for applications such as γ-ray generation by Compton scattering on relativistic

The minimum achievable duration of the pulse is defined by the bandwidth of the gain spectrum. In the simplest case of the absence of chirping (frequency variation with time), the spectrum of a pulse is the Fourier transform of its temporal profile. The pulse then is called transform-limited, and its duration, *τp*, is inversely proportional to its spectral width, *Δνp*. The following expression is valid for a transform-limited Gaussian pulse (Paschotta, 2008):

0.44

ν

where *τp* and *Δνp* are defined as full-width at half-maximum (FWHM). The duration of a chirped pulse is longer than that of a transform-limited pulse of the same shape and spectral width. Fig. 1 shows the spectra of several femto- and pico-second transform-limited Gaussian pulses. Fig. 2 compares them with the gain spectrum of a typical CO2 laser mixture, clearly revealing the challenge of generating and amplifying ultrashort pulses in a

*p*

<sup>≈</sup> <sup>Δ</sup> , (2)

*p*

Fig. 1. Spectra of transform-limited Gaussian pulses. Durations are full-width at half-

At low pressures (less than a few bars), the gain spectrum consists of individual rotational lines whose bandwidth (FWHM) is given by the following expression (Brimacombe & Reid,

τ

given ion energy compared with a solid-state laser.

electrons (Yakimenko & Pogorelsky, 2006).

**1.2 Challenge of high peak power** 

CO2 laser.

maximum (FWHM).

1983):

$$
\Delta\nu\_{\text{pressure}}\,\text{[GHz]} = P\,\text{[bar]} \cdot \left( \text{5.79}\,\text{\textdegree C}\_{\text{CO2}} + \text{4.25}\,\text{\textdegree N}\_{N2} + \text{3.55}\,\text{\textdegree N}\_{\text{H}} \right), \tag{3}
$$

where *P* is the total gas pressure, and *Ψx* is the relative concentration of the component *x*. Eq. (3) yields *Δνpressure*≈3.8 GHz at 1 bar of a typical mixture [CO2]:[N2]:[He]=1:1:8. Although direct substituting this bandwidth in Eq. (2) gives *τp*≈120 ps, in reality the pulse's spectrum is narrower than the gain bandwidth, and, correspondingly, the pulse's duration is longer. The latter fact is comprehensible by realizing that amplification is the strongest in the center of the laser line, and thus, upon amplification, the ratio between the intensity at the central frequency and that at the wing of the gain-spectrum line increases, thus narrowing the pulse's spectrum. Consequently, the minimum achievable duration of the pulse for an atmospheric-pressure CO2 laser is about 1 ns (Abrams & Wood, 1971). Pressure can be increased to broaden the gain bandwidth, and thus somewhat reduce the pulse's duration. However, the complete overlap of rotational lines separated by 55 GHz (P-) or 40 GHz (Rbranches) that would allow using an entire rotational branch, does not occur below 20- 25 bar; this is not feasible in discharge-pumped lasers having a ~10 bar practical pressure limit.

Fig. 2. Simulated normalized gain spectra at different gas pressures. 10P, 10R, 9P, and 9R: Rotational P- and R-branches of the two vibrational transitions supporting lasing at ~10 µm and ~9 µm respectively.

Another important consequence of the rotational structure of the CO2 gain spectrum relates to the amplification of the ultrashort pulses. The spectrum of a few-picosecond-long pulse, according to Eq. (2), overlaps several rotational lines of the gain spectrum. Hence, upon amplification, the pulse's spectrum acquires the corresponding periodic structure. In the

Ultrashort Pulses 143

frequency (i.e., a multiple of the inter-mode distance), and individual pulse's duration is

The minimum pulse duration achievable via mode-locking is related to the bandwidth, *Δν,* (FWHM) of the gain spectrum according the following expression (Siegman & Kuizenga,

> 1/4 1/2 0.45 *<sup>p</sup> <sup>g</sup> <sup>f</sup> <sup>M</sup>*

where *g≡2αL* is the saturated round-trip excess gain (*α* – excess gain per unit length, *L* – resonator length), *M* is the modulation, and *f=c/2L* is its frequency. For a typical transversely excited atmospheric pressure (TEA) CO2 laser (*g*=1; *M*=1; *f*=150 MHz; *Δν*=3.8 GHz) the duration is *τp*≈600 ps. Wood et al. describe their technical realization of the mode-locked TEA CO2 laser (Wood et al., 1970, Abrams & Wood, 1971). A 10-bar mode-locked system was reported by Houtman and Meyer (Houtman & Meyer, 1987). Application of modelocking is limited in 10-micron systems by relatively long (hundreds of picoseconds) pulse

Passive self-mode-locking often occurs in TEA CO2 lasers producing a comb pulse-structure unless special countermeasures are taken. This effect is believed to be due to gain saturation (Kovalev, 1996). When a smooth pulse is required, the laser must be forced to operate at a single cavity mode that usually is achieved by using a low-pressure intra-cavity CW discharge cell ("smoothing tube"). Such a laser, combining two gain sections in a single resonator; viz., main atmospheric-pressure and a low-pressure one for spectrum narrowing, is called *hybrid* laser. Fig. 4 is an example of a hybrid TEA CO2 lasers' pulse profile with and without discharge in the smoothing tube. As Fig. 4a shows, self-mode-locking occurring when the smoothing tube not activated results in modulation at a frequency that is a multiple (here, double) of the inter-mode spacing. Activating the smoothing tube eliminates

Fig. 4. Temporal structure of the output of a hybrid TEA CO2 laser with smoothing tube discharge OFF (a), and ON (b). Resonator round-trip time is 12 ns; self-mode-locking occurs

<sup>−</sup>

( )

 ν

≈ ⋅ ⋅Δ , (4)

inversely proportional to the total extent of the spectrum.

duration achievable via this technique.

the modulation, Fig. 4b.

at the doubled round-trip frequency.

τ

1969):

time-domain (inverse Fourier-transform of the spectrum), this is equivalent to a pulse train with pulse-to-pulse distance equal to the inverse separation of the spectral lines (18 ps in the P-, and 25 ps in the R-branches). Fig. 3 demonstrates this effect for a 5-ps pulse amplified in a 10-bar active medium.

Fig. *3*. Simulated dynamics of a 5-ps (FWHM) pulse spectrum (a), and its temporal structure normalized by the total energy in the train (b) amplified in a 10-bar CO2 amplifier. Dashed line: normalized gain spectrum.

We discuss below different approaches to overcome these difficulties.

#### **2. Generating the seed pulse**

In all modern schemes for producing ultrahigh-power laser pulses there are at least two major stages: (1) Generation of a low-power, ultrashort seed pulse, and, (2) amplification of the pulse. In this section, we consider different methods of creating ultrashort 10-µm pulses. Section 3, following, discusses the amplification stage.

#### **2.1 Mode-locking**

Mode-locking is the primary technique of generating ultrashort pulses in solid-state systems. In this approach, cavity modes present in the spectrum of the laser field are synchronized (locked) by modulating the cavity's Q-factor at a frequency that is a multiple of the inverse of the resonator's round-trip time, either actively (e.g., with an intra-cavity acousto-optical modulator), or passively (e.g., with a saturable absorber). Without synchronization, each mode is independent and defines its own pulse; thus, the pulse's duration is only limited by the relatively narrow bandwidth of an individual mode. However, after mode-locking, the time structure of the laser field is defined by the entire spectrum comprising *all* active modes. For the periodic spectrum of longitudinal modes, this structure is a periodic train of pulses; the pulse's repetition rate is equal to the lock-in

time-domain (inverse Fourier-transform of the spectrum), this is equivalent to a pulse train with pulse-to-pulse distance equal to the inverse separation of the spectral lines (18 ps in the P-, and 25 ps in the R-branches). Fig. 3 demonstrates this effect for a 5-ps pulse amplified in

Fig. *3*. Simulated dynamics of a 5-ps (FWHM) pulse spectrum (a), and its temporal structure normalized by the total energy in the train (b) amplified in a 10-bar CO2 amplifier. Dashed

In all modern schemes for producing ultrahigh-power laser pulses there are at least two major stages: (1) Generation of a low-power, ultrashort seed pulse, and, (2) amplification of the pulse. In this section, we consider different methods of creating ultrashort 10-µm pulses.

Mode-locking is the primary technique of generating ultrashort pulses in solid-state systems. In this approach, cavity modes present in the spectrum of the laser field are synchronized (locked) by modulating the cavity's Q-factor at a frequency that is a multiple of the inverse of the resonator's round-trip time, either actively (e.g., with an intra-cavity acousto-optical modulator), or passively (e.g., with a saturable absorber). Without synchronization, each mode is independent and defines its own pulse; thus, the pulse's duration is only limited by the relatively narrow bandwidth of an individual mode. However, after mode-locking, the time structure of the laser field is defined by the entire spectrum comprising *all* active modes. For the periodic spectrum of longitudinal modes, this structure is a periodic train of pulses; the pulse's repetition rate is equal to the lock-in

We discuss below different approaches to overcome these difficulties.

Section 3, following, discusses the amplification stage.

a 10-bar active medium.

line: normalized gain spectrum.

**2. Generating the seed pulse** 

**2.1 Mode-locking** 

frequency (i.e., a multiple of the inter-mode distance), and individual pulse's duration is inversely proportional to the total extent of the spectrum.

The minimum pulse duration achievable via mode-locking is related to the bandwidth, *Δν,* (FWHM) of the gain spectrum according the following expression (Siegman & Kuizenga, 1969):

$$
\sigma\_p = 0.45 \cdot \left(\frac{\text{g}}{\text{M}}\right)^{1/4} \left(f \cdot \Delta \nu\right)^{-1/2} \text{ }\tag{4}
$$

where *g≡2αL* is the saturated round-trip excess gain (*α* – excess gain per unit length, *L* – resonator length), *M* is the modulation, and *f=c/2L* is its frequency. For a typical transversely excited atmospheric pressure (TEA) CO2 laser (*g*=1; *M*=1; *f*=150 MHz; *Δν*=3.8 GHz) the duration is *τp*≈600 ps. Wood et al. describe their technical realization of the mode-locked TEA CO2 laser (Wood et al., 1970, Abrams & Wood, 1971). A 10-bar mode-locked system was reported by Houtman and Meyer (Houtman & Meyer, 1987). Application of modelocking is limited in 10-micron systems by relatively long (hundreds of picoseconds) pulse duration achievable via this technique.

Passive self-mode-locking often occurs in TEA CO2 lasers producing a comb pulse-structure unless special countermeasures are taken. This effect is believed to be due to gain saturation (Kovalev, 1996). When a smooth pulse is required, the laser must be forced to operate at a single cavity mode that usually is achieved by using a low-pressure intra-cavity CW discharge cell ("smoothing tube"). Such a laser, combining two gain sections in a single resonator; viz., main atmospheric-pressure and a low-pressure one for spectrum narrowing, is called *hybrid* laser. Fig. 4 is an example of a hybrid TEA CO2 lasers' pulse profile with and without discharge in the smoothing tube. As Fig. 4a shows, self-mode-locking occurring when the smoothing tube not activated results in modulation at a frequency that is a multiple (here, double) of the inter-mode spacing. Activating the smoothing tube eliminates the modulation, Fig. 4b.

Fig. 4. Temporal structure of the output of a hybrid TEA CO2 laser with smoothing tube discharge OFF (a), and ON (b). Resonator round-trip time is 12 ns; self-mode-locking occurs at the doubled round-trip frequency.

Ultrashort Pulses 145

inverse-quadratic relationship between *Nc* and the laser's wavelength (Eq. (1)) allows our realization of a scheme wherein a relatively low-energy pulse from a solid-state laser controls a high-power CO2-laser pulse. Combining two semiconductor switches, the first of which operates in a reflection- and the second in the transmission- configuration (Fig. 6) enables us to slice a CO2 pulse on both edges, thus producing one whose duration is limited

Fig. 6. Combination of reflection- and transmission- semiconductor switches to generate an

Reportedly, Rolland & Corkum, (1986) achieved a 130-fs pulse via this technique. Germanium is the commonest material used in semiconductor switches; silicon and

The laser-stimulated birefringence employed in the Kerr-cell technique has the advantage of low inertness, so supporting the production of an ultrashort pulse in a single step. Its minimum achievable duration is limited by that of the control pulse, and the relaxation speed of the induced birefringence. The Kerr cell depicted in Fig. 5b rotates the polarization of the CO2 laser-beam while it is being irradiated by the control pulse. A polarization filter on the cell output separates the part of the pulse with rotated polarization from the main pulse. Liquid carbon disulphide (CS2) featuring ~2 ps relaxation time usually serves as the active medium in the optical Kerr cell for slicing the CO2 laser pulses. For optimum switching efficiency, the phase angle between the control- and the CO2 laser- pulses must be

Currently, pulse-slicing is the main method of producing low-energy ultrashort (few-

Solid-state ultrafast oscillators producing several-cycle and longer optical pulses in the nearinfrared spectral region are a well-established technology. Using frequency conversion via *optical parametric amplification* (OPA) one can generate an ultrashort mid-IR pulse. One of the earliest theoretical treatments of parametric amplification was by Armstrong, Bloembergen, Ducuing, and Pershan (Armstrong et al., 1962). Using a resonant cavity to enhance output, Giordmaine and Miller demonstrated the principle (Giordmaine and Miller, 1965). Okorogu et al. demonstrated efficient, single-stage difference frequency downconversion from near-

only by the rise-time of the control pulse.

cadmium telluride also proved usable in this application.

ultrashort pulse.

equal to *π/4*.

picosecond) 10-micron seed pulses.

**2.4 All-solid-state systems** 

#### **2.2 Plasma shutter and optical free-induction decay**

Highly intense laser pulses focused in gas media can initiate avalanche ionization (laser breakdown). If gas density is high enough, overcritical plasma forms, blocking the trailing part of the laser pulse, partially absorbing and partially reflecting it. This effect itself, usually termed *plasma shutter*, can be used to cut the tail of the pulse thus reducing its overall duration. However, it is not sufficient for producing an ultrashort pulse because the front part of the initial pulse passes the plasma shutter unchanged. The possibility of generating a pulse as short as a few optical cycles lies in the fact that the fast switching-out of the laser field by plasma entails a very rapid variation in the field spectra. Essentially, we can approximate the spectrum of the transmitted pulse by the Fourier-transform of a step function. Frequencies different from those present in the original pulse briefly appear in the spectrum. If we now filter-out the frequency of the initial pulse from the resulting spectrum, we end up with a very short pulse (Yablonovich, 1973, 1974a, 1974b). Free-induction decay technique is relatively simple to realize and can allow achieving ~20 ps pulse duration at the expense of large losses and strong alteration of the spectrum.

#### **2.3 Pulse-slicing techniques**

Another possibility for producing a low-energy ultrashort pulse is to slice a small fraction out of a longer one (for instance, a hundred-nanosecond output of a hybrid TEA CO2 laser similar to that in Fig. 4b) using a fast optical switch. Here, the switching speed limits the duration of the resulting pulse. Two techniques often employed for this purpose are a semiconductor optical switch (Alcock & Corkum, 1979), or a Kerr cell (Filip et al., 2002). Both rely on an ultrashort pulse of another laser (usually a solid-state one) to trigger the switch by inducing a short-living "plasma mirror" in the case of a semiconductor switch, or birefringence in that of the Kerr cell. Fig. 5 illustrates the principles of these two techniques.

Fig. 5. Simplified schematics of the techniques for pulse slicing by (a) the semiconductor switch, and, (b) the Kerr cell.

A powerful laser pulse irradiating the surface of a semiconductor partially ionizes it creating a "plasma" of free charge carriers. If the plasma's density exceeds the critical one (*Nc*), the semiconductor surface turns into a mirror, reflecting the entering laser beam. At belowcritical densities, the beam is attenuated mostly by free-carrier absorption. The duration of the reflection is determined mainly by that of the control pulse, and the speed of free carrier diffusion (typically hundreds of picoseconds). Absorption generally lasts longer (hundreds of nanoseconds), and its persistence is defined by the free carrier's recombination time. The

Highly intense laser pulses focused in gas media can initiate avalanche ionization (laser breakdown). If gas density is high enough, overcritical plasma forms, blocking the trailing part of the laser pulse, partially absorbing and partially reflecting it. This effect itself, usually termed *plasma shutter*, can be used to cut the tail of the pulse thus reducing its overall duration. However, it is not sufficient for producing an ultrashort pulse because the front part of the initial pulse passes the plasma shutter unchanged. The possibility of generating a pulse as short as a few optical cycles lies in the fact that the fast switching-out of the laser field by plasma entails a very rapid variation in the field spectra. Essentially, we can approximate the spectrum of the transmitted pulse by the Fourier-transform of a step function. Frequencies different from those present in the original pulse briefly appear in the spectrum. If we now filter-out the frequency of the initial pulse from the resulting spectrum, we end up with a very short pulse (Yablonovich, 1973, 1974a, 1974b). Free-induction decay technique is relatively simple to realize and can allow achieving ~20 ps pulse duration at the

Another possibility for producing a low-energy ultrashort pulse is to slice a small fraction out of a longer one (for instance, a hundred-nanosecond output of a hybrid TEA CO2 laser similar to that in Fig. 4b) using a fast optical switch. Here, the switching speed limits the duration of the resulting pulse. Two techniques often employed for this purpose are a semiconductor optical switch (Alcock & Corkum, 1979), or a Kerr cell (Filip et al., 2002). Both rely on an ultrashort pulse of another laser (usually a solid-state one) to trigger the switch by inducing a short-living "plasma mirror" in the case of a semiconductor switch, or birefringence in that of the Kerr cell. Fig. 5 illustrates the principles of these two techniques.

Fig. 5. Simplified schematics of the techniques for pulse slicing by (a) the semiconductor

A powerful laser pulse irradiating the surface of a semiconductor partially ionizes it creating a "plasma" of free charge carriers. If the plasma's density exceeds the critical one (*Nc*), the semiconductor surface turns into a mirror, reflecting the entering laser beam. At belowcritical densities, the beam is attenuated mostly by free-carrier absorption. The duration of the reflection is determined mainly by that of the control pulse, and the speed of free carrier diffusion (typically hundreds of picoseconds). Absorption generally lasts longer (hundreds of nanoseconds), and its persistence is defined by the free carrier's recombination time. The

**2.2 Plasma shutter and optical free-induction decay** 

expense of large losses and strong alteration of the spectrum.

**2.3 Pulse-slicing techniques** 

switch, and, (b) the Kerr cell.

inverse-quadratic relationship between *Nc* and the laser's wavelength (Eq. (1)) allows our realization of a scheme wherein a relatively low-energy pulse from a solid-state laser controls a high-power CO2-laser pulse. Combining two semiconductor switches, the first of which operates in a reflection- and the second in the transmission- configuration (Fig. 6) enables us to slice a CO2 pulse on both edges, thus producing one whose duration is limited only by the rise-time of the control pulse.

Fig. 6. Combination of reflection- and transmission- semiconductor switches to generate an ultrashort pulse.

Reportedly, Rolland & Corkum, (1986) achieved a 130-fs pulse via this technique. Germanium is the commonest material used in semiconductor switches; silicon and cadmium telluride also proved usable in this application.

The laser-stimulated birefringence employed in the Kerr-cell technique has the advantage of low inertness, so supporting the production of an ultrashort pulse in a single step. Its minimum achievable duration is limited by that of the control pulse, and the relaxation speed of the induced birefringence. The Kerr cell depicted in Fig. 5b rotates the polarization of the CO2 laser-beam while it is being irradiated by the control pulse. A polarization filter on the cell output separates the part of the pulse with rotated polarization from the main pulse. Liquid carbon disulphide (CS2) featuring ~2 ps relaxation time usually serves as the active medium in the optical Kerr cell for slicing the CO2 laser pulses. For optimum switching efficiency, the phase angle between the control- and the CO2 laser- pulses must be equal to *π/4*.

Currently, pulse-slicing is the main method of producing low-energy ultrashort (fewpicosecond) 10-micron seed pulses.

#### **2.4 All-solid-state systems**

Solid-state ultrafast oscillators producing several-cycle and longer optical pulses in the nearinfrared spectral region are a well-established technology. Using frequency conversion via *optical parametric amplification* (OPA) one can generate an ultrashort mid-IR pulse. One of the earliest theoretical treatments of parametric amplification was by Armstrong, Bloembergen, Ducuing, and Pershan (Armstrong et al., 1962). Using a resonant cavity to enhance output, Giordmaine and Miller demonstrated the principle (Giordmaine and Miller, 1965). Okorogu et al. demonstrated efficient, single-stage difference frequency downconversion from near-

Ultrashort Pulses 147

These cascaded nonlinear processes allow stable, repeatable conversion of the ultrafast pump pulses from the near- to the mid-IR region, while providing broad bandwidth, wavelength tunability, and ultrashort duration. The theoretical maximum energy conversion efficiency from 0.8 to 10 micron via this cascaded three-photon mixing is near 3.5%, however when real beams which are non-uniform in time and space are considered, as well as losses on the large number of optical elements required, the realized efficiency is approximately an order of magnitude lower. Pulsewidths under 500 fs are easily achievable,

All-solid-state systems provide good control of pulse synchronization and shape, but are much more elaborate than the other techniques used for ultrashort mid-IR pulse generation.

A major problem in seamlessly amplifying picosecond pulses is the discrete rotational-line structure of the gain spectrum, causing modulation of the pulse spectrum and pulse splitting. The gain spectrum's modulation can be smeared either by broadening individual rotational lines, thus assuring their better overlap, or by increasing their density. In the first case, we can use pressure- (collision-) and/or field- (power-) broadening effects. Several approaches increase line density: (1) Using an R-branch of a laser transition having a 1.4 times denser line structure than a conventional P-branch; (2) isotopic enrichment of the CO2 molecules, wherein the superposition of the slightly shifted spectra of different isotopic species (*isotopologues*) generates a denser effective spectrum; and, (3) combining the *sequence* bands of laser transition with regular ones. We briefly overview these approaches next.

*Pressure broadening.* As discussed in the Section 1.2, increasing the pressure lowers modulation in the gain spectrum. Complete suppression occurs when collisionally broadened bandwidths of the rotational lines become about twice the interline distance. However, the 20-25 bar pressure required for this, according to the Eq. (3), is impractical due to difficulties in arranging the uniform electric-discharge pumping the large volume of active gas required for building a high-power CO2 laser amplifier. Replacing discharge- with optical- pumping may afford using a pure-CO2 active medium and increased working pressure, thus considerably extending the pressure broadening effect. Rapid progress in the solid-state laser technology might well lead to the availability of a reliable source for optical excitation of CO2 active medium in the near future. Gordienko & Platonenko, (2010)

*Field broadening.* We can approximate the magnitude of line broadening (FWHM) appearing in the intense laser field due to the Autler-Townes (or dynamic Stark) effect (Autler &

transition dipole momentum, *E* is the laser field, and *h* is Plank's constant. Substituting the laser field with its expression through the intensity, *I*, and using the numerical values of the

*d E <sup>=</sup> <sup>h</sup>*

<sup>2</sup> Δ [GHz] 0.02764 [D] [W/cm ] *field ν* ≈ *d I* (5)

= Ω <sup>⋅</sup> , where *d* is the

consider that here the ErCr:YSGG (2.79 µm) laser is a promising candidate.

Townes, 1955) by the doubled Rabi frequency *Ω*: Δ 2 2 *field ν*

involved constants, we get the following equation:

as well as bandwidth covering any single branch of the CO2 gain spectrum.

**3. Amplification** 

**3.1 "Smoothing" the gain spectrum** 

to mid-IR (Okorogu et al., 1998). The combination of compact size, various free-space or fiber-based configurations, and efficient pump sources provide an advantageous starting point for CO2 laser seed sources. One method used for frequency conversion is covered below with attention toward stable and reliable operation as a sub-component of a larger CO2 laser system.

Titanium-doped sapphire is now the dominant laser system in many industrial and research fields such as physical chemistry, materials science and processing, and strong-field physics. Therefore, a large commercial infrastructure exists for producing reliable amplifiers delivering high energy pulses suitable for nonlinear conversion. Diode-pumped Neodymium lasers which are frequency-doubled for pumping the broadband Ti:Al2O3 gain medium are turn-key and have lifetimes on the order of 10 000 hours. Many amplifier systems are available producing pulse energies above 5 mJ near 1 kHz repetition rates. In such a configuration, the pump pulses have energy stability better than 1% because the energy is removed on a time scale comparable to the upper-state lifetime, and a quasisteady-state exists between pumping and energy extraction.

After amplification to high energy, the use of OPA provides a path for the generation of significant seed energies at 10 µm with the full bandwidth and tunability to cover the entire gain spectrum of CO2. One such commercial approach is shown in Fig. 7.

Fig. 7. Commercially-available frequency conversion system from 0.8 to 10 microns

In this configuration, the pulses from the Ti:Al2O3 amplifier are used in three separate nonlinear processes. The first is white light continuum generation in sapphire. This process creates an ultra-broadband spectrum spanning the entire visible and near-IR region while preserving the phase and temporal structure of the original pulses. This broadband radiation makes an ideal seed source for the following sections as it allows free tuning to the desired wavelengths. Because the next section uses three-wave mixing, this seed power also eliminates instabilities that would be encountered from quantum fluctuations in a pure parametric generator.

The next two stages rely on standard nonlinear crystals and act as simple parametric amplifiers that are angle-tuned to achieve gain at the desired signal and idler wavelengths. For conversion from 0.8 to 10 micron, these are approximately 1.5 and 1.7 micron, respectively. By utilizing two stages, the gain of each section can be optimized while preserving bandwidth that would be limited by a longer single crystal. The second parametric amplification stage therefore utilizes most of the pulse energy delivered from the Ti:Al2O3 amplifier.

In the final section, the signal and idler from the previous stages generate a difference frequency pulse in another nonlinear material that has transparency in the mid-IR region.

to mid-IR (Okorogu et al., 1998). The combination of compact size, various free-space or fiber-based configurations, and efficient pump sources provide an advantageous starting point for CO2 laser seed sources. One method used for frequency conversion is covered below with attention toward stable and reliable operation as a sub-component of a larger

Titanium-doped sapphire is now the dominant laser system in many industrial and research fields such as physical chemistry, materials science and processing, and strong-field physics. Therefore, a large commercial infrastructure exists for producing reliable amplifiers delivering high energy pulses suitable for nonlinear conversion. Diode-pumped Neodymium lasers which are frequency-doubled for pumping the broadband Ti:Al2O3 gain medium are turn-key and have lifetimes on the order of 10 000 hours. Many amplifier systems are available producing pulse energies above 5 mJ near 1 kHz repetition rates. In such a configuration, the pump pulses have energy stability better than 1% because the energy is removed on a time scale comparable to the upper-state lifetime, and a quasi-

After amplification to high energy, the use of OPA provides a path for the generation of significant seed energies at 10 µm with the full bandwidth and tunability to cover the entire

steady-state exists between pumping and energy extraction.

gain spectrum of CO2. One such commercial approach is shown in Fig. 7.

Fig. 7. Commercially-available frequency conversion system from 0.8 to 10 microns

In this configuration, the pulses from the Ti:Al2O3 amplifier are used in three separate nonlinear processes. The first is white light continuum generation in sapphire. This process creates an ultra-broadband spectrum spanning the entire visible and near-IR region while preserving the phase and temporal structure of the original pulses. This broadband radiation makes an ideal seed source for the following sections as it allows free tuning to the desired wavelengths. Because the next section uses three-wave mixing, this seed power also eliminates instabilities that would be encountered from quantum fluctuations in a pure

The next two stages rely on standard nonlinear crystals and act as simple parametric amplifiers that are angle-tuned to achieve gain at the desired signal and idler wavelengths. For conversion from 0.8 to 10 micron, these are approximately 1.5 and 1.7 micron, respectively. By utilizing two stages, the gain of each section can be optimized while preserving bandwidth that would be limited by a longer single crystal. The second parametric amplification stage therefore utilizes most of the pulse energy delivered from the

In the final section, the signal and idler from the previous stages generate a difference frequency pulse in another nonlinear material that has transparency in the mid-IR region.

CO2 laser system.

parametric generator.

Ti:Al2O3 amplifier.

These cascaded nonlinear processes allow stable, repeatable conversion of the ultrafast pump pulses from the near- to the mid-IR region, while providing broad bandwidth, wavelength tunability, and ultrashort duration. The theoretical maximum energy conversion efficiency from 0.8 to 10 micron via this cascaded three-photon mixing is near 3.5%, however when real beams which are non-uniform in time and space are considered, as well as losses on the large number of optical elements required, the realized efficiency is approximately an order of magnitude lower. Pulsewidths under 500 fs are easily achievable, as well as bandwidth covering any single branch of the CO2 gain spectrum.

All-solid-state systems provide good control of pulse synchronization and shape, but are much more elaborate than the other techniques used for ultrashort mid-IR pulse generation.

#### **3. Amplification**

#### **3.1 "Smoothing" the gain spectrum**

A major problem in seamlessly amplifying picosecond pulses is the discrete rotational-line structure of the gain spectrum, causing modulation of the pulse spectrum and pulse splitting. The gain spectrum's modulation can be smeared either by broadening individual rotational lines, thus assuring their better overlap, or by increasing their density. In the first case, we can use pressure- (collision-) and/or field- (power-) broadening effects. Several approaches increase line density: (1) Using an R-branch of a laser transition having a 1.4 times denser line structure than a conventional P-branch; (2) isotopic enrichment of the CO2 molecules, wherein the superposition of the slightly shifted spectra of different isotopic species (*isotopologues*) generates a denser effective spectrum; and, (3) combining the *sequence* bands of laser transition with regular ones. We briefly overview these approaches next.

*Pressure broadening.* As discussed in the Section 1.2, increasing the pressure lowers modulation in the gain spectrum. Complete suppression occurs when collisionally broadened bandwidths of the rotational lines become about twice the interline distance. However, the 20-25 bar pressure required for this, according to the Eq. (3), is impractical due to difficulties in arranging the uniform electric-discharge pumping the large volume of active gas required for building a high-power CO2 laser amplifier. Replacing discharge- with optical- pumping may afford using a pure-CO2 active medium and increased working pressure, thus considerably extending the pressure broadening effect. Rapid progress in the solid-state laser technology might well lead to the availability of a reliable source for optical excitation of CO2 active medium in the near future. Gordienko & Platonenko, (2010) consider that here the ErCr:YSGG (2.79 µm) laser is a promising candidate.

*Field broadening.* We can approximate the magnitude of line broadening (FWHM) appearing in the intense laser field due to the Autler-Townes (or dynamic Stark) effect (Autler & Townes, 1955) by the doubled Rabi frequency *Ω*: Δ 2 2 *field ν d E <sup>=</sup> <sup>h</sup>* = Ω <sup>⋅</sup> , where *d* is the transition dipole momentum, *E* is the laser field, and *h* is Plank's constant. Substituting the laser field with its expression through the intensity, *I*, and using the numerical values of the involved constants, we get the following equation:

$$
\Delta\nu\_{\text{field}}[\text{GHz}] = 0.02764 \, d[\text{D}] \, \sqrt{l[\text{W}/\text{cm}^2]} \tag{5}
$$

Ultrashort Pulses 149

For a given proportion [16O]:[18O], independent of the initial distribution of 16O and 18O between the CO2 molecules, statistical equilibration via intermolecular isotope-exchange leads to [626]:[628]:[828]= [16O]2:2[16O] [18O]:[18O]2. We note that due to the broken symmetry of the 628 molecule, it has twice as many rotational lines in each rotational branch compared to more symmetric 626- and 828- isotopologues. The combination of three CO2 isotopologues, as depicted in Fig. 8, results in a smooth spectrum already apparent at 10 bar. The gain of the isotopic mixture in the 10-micron branches at this pressure is 1.4 times lower than that of the regular gas, mainly reflecting the relatively low gain of the 828 CO2 isotopologue. Thus, a longer path through an active medium or a higher CO2 concentration is needed to maintain the same net amplification. The isotope-based approach is practically implemented in the CO2 laser of Accelerator Test Facility at Brookhaven National

*Sequence bands.* Transitions between high-lying vibrational overtones of the CO2 molecule can contribute considerably to the high-pressure amplifier gain. In this case, the rotational spectra of the regular- and sequence- bands overlap, so providing a denser effective spectrum. Exploiting the sequence band for smoothing the gain spectrum seems especially promising for the 10R branch wherein the rotational lines belonging to the sequence band 0002-[1001,0201]I fall very close to the centers of the gaps between the lines of the regular band 0001-[1000,0200]I. Simple estimation of the ratio of gains of the sequence- and the regular- band, assuming the Boltzmann energy distribution within a vibrational mode (Reid

*G G seq reg* / 2 exp( / ) 3 3 = −*h kT*

where *T3* and *ν3* are the vibrational temperature and frequency of the asymmetric stretchmode of the CO2 molecule, and *h* and *k* respectively are the Plank's and Boltzmann's constants, show that sequence band's gain reaches 50% of the regular band's gain at

To assure highly intense laser fields, special attention must be given to properly selecting and utilizing the optical elements, and to accounting for their influence on the laser field. This especially is challenging in the 10-μm spectral region because of the dearth of optical materials compared to the visible or near-IR diapasons, and lack of data on the materials' behavior under ultrashort mid-IR pulses. Below, we summarize the properties of optical materials most important for using in the high-peak-power 10-μm laser field. Table 1 gives numerical data on the refractive indices and dispersion of some popular IR materials used in

*Chromatic dispersion* plays an important role due to the hundreds of GHz-wide spectrum of (sub-) picosecond 10-μm pulses that may entail considerable pulse stretching. For example, a pulse of 1 ps (FWHM) spreads to 1.27 ps after a single pass through a 10-cm NaCl window. Accordingly, the amount and thickness of optical elements should be minimized,

*Nonlinear index, B-integral*. A high-power laser pulse propagating through a medium

*T3*=2500 K, viz., comparable to the conditions of high-pressure CO2 amplifiers.

and/or a grating compensator added for recompressing the pulse.

changes its refractive index *n* (the *Kerr effect*):

ν

, (6)

Laboratory (Section 6.1).

& Siemsen, 1976):

CO2 lasers.

**3.2 Effects in optical materials** 

With Eq. (5), and the known value of the laser's transition dipole momentum *d*=0.0275 D (the value for the 10P(20) line from HITRAN database (Rothman et al., 2009)), we find that field broadening is sufficient to completely suppress modulation at a laser intensity 15-20 GW/cm2; this is reachable in the modern high-power picosecond CO2 laser systems. Capitalizing on this approach supported the attainment of 15 TW peak power in the CO2 laser system of Neptune Laboratory of the University of California, Loss Angeles (Section 6.2).

*R-branch.* The R-branches of the CO2 laser transitions have a rotational structure 1.4 times denser than the more often used P-branches (Witteman, 1987); thus, they offer better overlap between collisionally broadened lines, and, hence, yield a smoother gain spectrum (Fig. 2). Interestingly, under high-pressure conditions, such as 10 bar or higher, the overlap between rotational lines increases the peak intensity of the R-branch compared to that of the P-branch that otherwise prevails in conventional low-pressure lasers.

*Isotopic CO2.* By partially substituting the 16O atoms in CO2 gas with another stable 18O isotope, we obtain almost perfectly smooth combined spectrum after superimposing the spectra of three CO2 isotopologues (molecules with different isotopic composition): 16O-12C-16O, 16O-12C-18O, and 18O-12C-18O (Fig. 8). They often are denoted as 626, 628, and 828 wherein 2, 6, and 8, respectively, represent 12C, 16O and 18O.

Fig. 8. Simulated gain spectra of three CO2 isotopologues with different combinations of oxygen-16 and oxygen-18 atoms (no enrichment in carbon isotopes), and the effective spectrum of their mixture in the proportion [626]:[628]:[828]=0.16:0.48:0.36 (statistical equilibrium in the case of [16O]:[18O]=0.4:0.6). Total gas pressure is 10 bar.

With Eq. (5), and the known value of the laser's transition dipole momentum *d*=0.0275 D (the value for the 10P(20) line from HITRAN database (Rothman et al., 2009)), we find that field broadening is sufficient to completely suppress modulation at a laser intensity 15-20 GW/cm2; this is reachable in the modern high-power picosecond CO2 laser systems. Capitalizing on this approach supported the attainment of 15 TW peak power in the CO2 laser system of Neptune Laboratory of the University of California, Loss Angeles (Section 6.2).

*R-branch.* The R-branches of the CO2 laser transitions have a rotational structure 1.4 times denser than the more often used P-branches (Witteman, 1987); thus, they offer better overlap between collisionally broadened lines, and, hence, yield a smoother gain spectrum (Fig. 2). Interestingly, under high-pressure conditions, such as 10 bar or higher, the overlap between rotational lines increases the peak intensity of the R-branch compared to that of the P-branch

*Isotopic CO2.* By partially substituting the 16O atoms in CO2 gas with another stable 18O isotope, we obtain almost perfectly smooth combined spectrum after superimposing the spectra of three CO2 isotopologues (molecules with different isotopic composition): 16O-12C-16O, 16O-12C-18O, and 18O-12C-18O (Fig. 8). They often are denoted as 626, 628, and 828

Fig. 8. Simulated gain spectra of three CO2 isotopologues with different combinations of oxygen-16 and oxygen-18 atoms (no enrichment in carbon isotopes), and the effective spectrum of their mixture in the proportion [626]:[628]:[828]=0.16:0.48:0.36 (statistical

equilibrium in the case of [16O]:[18O]=0.4:0.6). Total gas pressure is 10 bar.

that otherwise prevails in conventional low-pressure lasers.

wherein 2, 6, and 8, respectively, represent 12C, 16O and 18O.

For a given proportion [16O]:[18O], independent of the initial distribution of 16O and 18O between the CO2 molecules, statistical equilibration via intermolecular isotope-exchange leads to [626]:[628]:[828]= [16O]2:2[16O] [18O]:[18O]2. We note that due to the broken symmetry of the 628 molecule, it has twice as many rotational lines in each rotational branch compared to more symmetric 626- and 828- isotopologues. The combination of three CO2 isotopologues, as depicted in Fig. 8, results in a smooth spectrum already apparent at 10 bar. The gain of the isotopic mixture in the 10-micron branches at this pressure is 1.4 times lower than that of the regular gas, mainly reflecting the relatively low gain of the 828 CO2 isotopologue. Thus, a longer path through an active medium or a higher CO2 concentration is needed to maintain the same net amplification. The isotope-based approach is practically implemented in the CO2 laser of Accelerator Test Facility at Brookhaven National Laboratory (Section 6.1).

*Sequence bands.* Transitions between high-lying vibrational overtones of the CO2 molecule can contribute considerably to the high-pressure amplifier gain. In this case, the rotational spectra of the regular- and sequence- bands overlap, so providing a denser effective spectrum. Exploiting the sequence band for smoothing the gain spectrum seems especially promising for the 10R branch wherein the rotational lines belonging to the sequence band 0002-[1001,0201]I fall very close to the centers of the gaps between the lines of the regular band 0001-[1000,0200]I. Simple estimation of the ratio of gains of the sequence- and the regular- band, assuming the Boltzmann energy distribution within a vibrational mode (Reid & Siemsen, 1976):

$$\mathcal{G}\_{\text{sq}} \;/ \; G\_{\text{reg}} = 2 \exp(-h\nu\_{\text{s}} \;/ \; kT\_{\text{s}}) \; \prime \tag{6}$$

where *T3* and *ν3* are the vibrational temperature and frequency of the asymmetric stretchmode of the CO2 molecule, and *h* and *k* respectively are the Plank's and Boltzmann's constants, show that sequence band's gain reaches 50% of the regular band's gain at *T3*=2500 K, viz., comparable to the conditions of high-pressure CO2 amplifiers.

#### **3.2 Effects in optical materials**

To assure highly intense laser fields, special attention must be given to properly selecting and utilizing the optical elements, and to accounting for their influence on the laser field. This especially is challenging in the 10-μm spectral region because of the dearth of optical materials compared to the visible or near-IR diapasons, and lack of data on the materials' behavior under ultrashort mid-IR pulses. Below, we summarize the properties of optical materials most important for using in the high-peak-power 10-μm laser field. Table 1 gives numerical data on the refractive indices and dispersion of some popular IR materials used in CO2 lasers.

*Chromatic dispersion* plays an important role due to the hundreds of GHz-wide spectrum of (sub-) picosecond 10-μm pulses that may entail considerable pulse stretching. For example, a pulse of 1 ps (FWHM) spreads to 1.27 ps after a single pass through a 10-cm NaCl window. Accordingly, the amount and thickness of optical elements should be minimized, and/or a grating compensator added for recompressing the pulse.

*Nonlinear index, B-integral*. A high-power laser pulse propagating through a medium changes its refractive index *n* (the *Kerr effect*):

Ultrashort Pulses 151

formation. Assuming a similar behavior in mid-IR, we conclude there is relatively small variation of the breakdown threshold fluence as a function of pulse duration for pulses of a few picoseconds or shorter; thus, as a guideline in system design, in most cases we can

We can minimize the high-power effects in optical materials on the pulse by employing the method of chirped-pulse amplification (CPA), the principle of which is illustrated in Fig. 9.

Fig. 9. Chirped-pulse amplification schematic (Perry et al., 1995). Reproduced with

Before being amplified, an ultrashort pulse is *chirped*: A wavelength-dependent delay is introduced in the pulse using a *stretcher* consisting of a couple of gratings and lenses, as shown in the Fig. 9. Because ultrashort pulses have broad spectral bandwidth, inversely proportional to their duration (Eq. (2)), it is relatively straightforward to stretch them by a few orders-of-magnitude. The chirped pulse carries virtually the same energy as the original one, but its peak power is reduced in inverse proportion to the stretching factor. The chirped pulse can be amplified to energies much higher than that achievable by directly amplifying ultrashort pulses wherein high-power effects in optical materials and active medium appear earlier. After amplification, the pulse is re-compressed in another two-grating device (the

The invention of CPA for reducing light intensity during ultrashort pulse amplification was a dramatic breakthrough in solid-state laser technology. Although implementing the CPA technique in a (sub-)picosecond CO2 laser remains to be done (the corresponding project is

permission, courtesy of the Lawrence Livermore National Laboratory.

adopt 0.5 J/cm2 for transparent optics, and 1 J/cm2 for mirrors.

**3.3 Chirped-pulse amplification** 

*compressor*).

$$m = n\_0 + n\_2 I \,, \tag{7}$$

where *n0* is the linear (low-intensity) refractive index, *n2* the nonlinear index, and *I* the optical intensity. Variation of refractive index across the beam's cross-section degrades its quality. For instance, lensing (*Kerr lensing*) occurs when phase-shift in the center of the beam is considerably larger than on its edge. The additional phase-retardation introduced to the beam after propagating through an optical element due to the nonlinear index (*B-integral*) is the accepted parameter for quantifying this effect (Paschotta):

2 <sup>2</sup> *B n I z dz* ( ) π λ<sup>=</sup> , (8)

where *λ* is the wavelength, *I(z)* the optical intensity along the beam's axis, and, *z* the position in the beam's direction. Usually, a noticeable self-focusing occurs if the B-integral exceeds 3- 5. Strong wave-front distortion and eventually catastrophic filamentation may occur at larger values of the B-integral. An estimate of the B-integral using the *n2* index from the Table 1 yields *B* = 13.4 for a 1 ps (FWHM), 500 mJ/cm2 pulse passing through a 10 cm of NaCl. Expectedly, the effect will be much stronger for other materials, implying that special care must be taken in selecting materials and controlling the fluence through the optical elements. The Kerr effect also is responsible for self-chirping due to temporal variation of the phase shift defined by the pulse's temporal structure (see Section 4.1).


Table 1. Linear refractive index *n0*, chromatic dispersion *dn0/dν*, and nonlinear index *n2* of some IR materials. (a) RefractiveIndex.INFO; (b) Sheik-Bahae et al., 1991; (c) Bristow et al., 2007.

*Optical breakdown threshold*. We know far less about the ultrashort-pulse breakdown thresholds for mid-IR wavelengths and the materials used at these wavelengths than we do for visible light and near-IR. Reportedly, the values are ~0.5 J/cm2 for NaCl, and 1-2 J/cm2 for gold-coated stainless-steel mirrors for 2-ps, 10-μm pulse (Corkum, 1983). Variations in the breakdown threshold with pulse duration are best studied for fused silica at a wavelength of ~800 nm (Du et al., 1994, Stuart et al., 1996, Tien et al., 1999). Jia et al. (2006) also explored the wavelength dependence of the damage threshold over 250-2000 nm for 150 fs pulses; they concluded that there was a relatively small variation in the threshold at wavelengths above 800 nm. At pulses <10 ps, the damage threshold decreases slow with declining duration of the pulse, rather than displaying the *τ<sup>p</sup>* 1/2 dependence valid for longer pulses; this difference is explained by the gradual transition from a thermally dominated damage regime to one dominated by collisional- and multi-photon- ionization and plasma

where *n0* is the linear (low-intensity) refractive index, *n2* the nonlinear index, and *I* the optical intensity. Variation of refractive index across the beam's cross-section degrades its quality. For instance, lensing (*Kerr lensing*) occurs when phase-shift in the center of the beam is considerably larger than on its edge. The additional phase-retardation introduced to the beam after propagating through an optical element due to the nonlinear index (*B-integral*) is

> 2 <sup>2</sup> *B n I z dz* ( ) π

where *λ* is the wavelength, *I(z)* the optical intensity along the beam's axis, and, *z* the position in the beam's direction. Usually, a noticeable self-focusing occurs if the B-integral exceeds 3- 5. Strong wave-front distortion and eventually catastrophic filamentation may occur at larger values of the B-integral. An estimate of the B-integral using the *n2* index from the Table 1 yields *B* = 13.4 for a 1 ps (FWHM), 500 mJ/cm2 pulse passing through a 10 cm of NaCl. Expectedly, the effect will be much stronger for other materials, implying that special care must be taken in selecting materials and controlling the fluence through the optical elements. The Kerr effect also is responsible for self-chirping due to temporal variation of

*n0* **@ 10.6 µm (a)** *dn0/dν* **@10.6 µm** 

Table 1. Linear refractive index *n0*, chromatic dispersion *dn0/dν*, and nonlinear index *n2* of some IR materials. (a) RefractiveIndex.INFO; (b) Sheik-Bahae et al., 1991; (c) Bristow et al., 2007.

*Optical breakdown threshold*. We know far less about the ultrashort-pulse breakdown thresholds for mid-IR wavelengths and the materials used at these wavelengths than we do for visible light and near-IR. Reportedly, the values are ~0.5 J/cm2 for NaCl, and 1-2 J/cm2 for gold-coated stainless-steel mirrors for 2-ps, 10-μm pulse (Corkum, 1983). Variations in the breakdown threshold with pulse duration are best studied for fused silica at a wavelength of ~800 nm (Du et al., 1994, Stuart et al., 1996, Tien et al., 1999). Jia et al. (2006) also explored the wavelength dependence of the damage threshold over 250-2000 nm for 150 fs pulses; they concluded that there was a relatively small variation in the threshold at wavelengths above 800 nm. At pulses <10 ps, the damage threshold decreases slow with declining duration of the pulse, rather than displaying the *τp*1/2 dependence valid for longer pulses; this difference is explained by the gradual transition from a thermally dominated damage regime to one dominated by collisional- and multi-photon- ionization and plasma

KCl 1.45 1.51 5.7 @ 1.06 µm NaCl 1.49 2.64 4.4 @ 1.06 µm ZnSe 2.40 2.44 290 @ 1.06 µm CdTe 2.67 1.04 -3000 @ 1.06 µm Si 3.42 0.0914 1000 @ 2.2 µm(c) Ge 4.00 0.293 2800 @ 10.6 µm

λ

the phase shift defined by the pulse's temporal structure (see Section 4.1).

the accepted parameter for quantifying this effect (Paschotta):

*n n nI* = +0 2 , (7)

<sup>=</sup> , (8)

**(10-3 THz-1) (a)** *n2* **(10-16 cm2/W) (b)**

formation. Assuming a similar behavior in mid-IR, we conclude there is relatively small variation of the breakdown threshold fluence as a function of pulse duration for pulses of a few picoseconds or shorter; thus, as a guideline in system design, in most cases we can adopt 0.5 J/cm2 for transparent optics, and 1 J/cm2 for mirrors.

#### **3.3 Chirped-pulse amplification**

We can minimize the high-power effects in optical materials on the pulse by employing the method of chirped-pulse amplification (CPA), the principle of which is illustrated in Fig. 9.

Fig. 9. Chirped-pulse amplification schematic (Perry et al., 1995). Reproduced with permission, courtesy of the Lawrence Livermore National Laboratory.

Before being amplified, an ultrashort pulse is *chirped*: A wavelength-dependent delay is introduced in the pulse using a *stretcher* consisting of a couple of gratings and lenses, as shown in the Fig. 9. Because ultrashort pulses have broad spectral bandwidth, inversely proportional to their duration (Eq. (2)), it is relatively straightforward to stretch them by a few orders-of-magnitude. The chirped pulse carries virtually the same energy as the original one, but its peak power is reduced in inverse proportion to the stretching factor. The chirped pulse can be amplified to energies much higher than that achievable by directly amplifying ultrashort pulses wherein high-power effects in optical materials and active medium appear earlier. After amplification, the pulse is re-compressed in another two-grating device (the *compressor*).

The invention of CPA for reducing light intensity during ultrashort pulse amplification was a dramatic breakthrough in solid-state laser technology. Although implementing the CPA technique in a (sub-)picosecond CO2 laser remains to be done (the corresponding project is

Ultrashort Pulses 153

rotational lines to the ~0.5 THz necessary for this regime. (3) The spectrum of the pulse covers the entire rotational branch, as happens when the pulse duration is ≤1 ps (Eq. (2)).

Despite the usual attempts researchers take in trying to avoid the undesirable effects of the nonlinear response on the high-power pulses, it might be possible to employ these phenomena to further compress ultrashort pulses. When an optical pulse propagates through a media, the refractive index of the latter changes according to Eq. (7), following the intensity of the optical field (the Kerr effect). Phase velocity, *vp=c/n,* varies accordingly. The field frequency of the pulse, whose phase velocity continuously changes, shifts proportionally to its derivative *dvp/dt*, so generating pulse chirping. Fig. 10 illustrates this

Fig. 10. Self-chirping of a pulse propagating through a nonlinear media. Top: Pulse intensity profile (leading edge is on the left); bottom dashed: Phase velocity derivative; bottom solid:

It is important to realize the difference between the chirping, as in the CPA, and chirping, as in self-chirping. In the first case, the pulse's spectrum is unchanged whereas its duration increases; in the second, the spectrum broadens while pulse duration does not change. A dispersive compressor similar to that utilized in the CPA can be arranged to shrink the self-

Self-chirping in plasma essentially is a variation of the self-chirping in nonlinear media. The distinctive feature of this case is that the variation in refractive index is caused by laser-

The last regime is preferable if the aim is to keep pulse's span as brief as possible.

**4. Pulse compression** 

process.

**4.1 Self-chirping in nonlinear media** 

Wave-packet of the chirped pulse.

**4.2 Self-chirping in plasma** 

chirped pulse well below its original duration.

planned at the Accelerator Test Facility of the Brookhaven National Laboratory), it is reasonable to expect that the outcome will comparably be valuable.

#### **3.4 Energy extraction efficiency**

Optimal use of the energy stored in the active medium is a key characteristic of a mature laser design. The difficulty in efficiently extracting excitation energy from gaseous active media via an ultrashort pulse arises from the fact that the pulse's duration is either shorter than, or comparable to the characteristic times of the involved excitation- and relaxationprocesses. Below, we briefly consider these processes and their influence on the efficiency of extracting energy.

*Excitation and vibrational relaxation*. In a typical CO2 laser, an electric discharge is used to create population inversion. Fast electrons accelerated by electric field collide with CO2 and N2 molecules, so exciting their upper vibrational states. Nitrogen serves as reservoir for storing the excitation energy which is then transferred to CO2 via vibrational relaxation. The typical duration of discharge in a pulsed CO2 laser is about a microsecond, and vibrational relaxation times range from 1-10 ns·bar. This implies that a (sub-)picosecond laser pulse only extracts energy already available at the upper vibrational laser-level, with negligible energy deposition from the discharge or from redistribution from other vibrational levels during pulse propagation. To maximize extraction, wherever possible a regenerative amplification scheme is used, wherein the pulse passes the amplifier medium many times allowing repopulation of the upper vibrational level of the laser transition between the passes. However, realizing this scheme practically is problematic for high-energy pulses when beam must be wide to increase the active volume and avoid damaging optical elements. Thus, two-stage amplification usually is adopted (see Section 6); a regenerative amplifier providing amplification up to millijoules level is followed by a final high-energy amplifier arranged either in a single-pass configuration, or several passes are only partially overlapped. Slow pumping and vibrational relaxation limit energy extraction in the final amplification stage. A possible solution is replacing pumping by electric discharge, with optical pumping by a short laser pulse that quickly and directly excites the upper laser level, and eliminates the need for redistributing vibrational energy.

*Rotational relaxation*. Rotational relaxation processes limit the fraction of energy extractable from the upper vibrational laser level in a single pass through the active medium. The laser pulse interacts only with a limited number of rotational transitions that is defined by the overlap between the pulse's spectrum and the amplification band. At high pressure, when collisionally broadened rotational lines overlap, or for a very short pulse, when pulse's spectrum covers several rotational lines, energy is extracted from several rotational sublevels. Otherwise, energy is extracted only from a single sub-level containing about 1/15th of the entire energy stored in that vibrational level. Three scenarios support the complete emptying of the vibrational level: (1) The pulse is long enough to provide time for repopulation of the active rotational levels. Typical rotational relaxation times are ~100 ps·bar; about 15 collisions are required effectively to empty all rotational sub-levels through a single active rotational transition. Thus, the minimum required pulse duration is ~1.5 ns·bar (e.g., 150 ps at 10 bar). (2) Pressure broadening allows all rotational transitions to interact with the laser field. Using Eq. (3) we find that ~100 bar is needed to broaden the

planned at the Accelerator Test Facility of the Brookhaven National Laboratory), it is

Optimal use of the energy stored in the active medium is a key characteristic of a mature laser design. The difficulty in efficiently extracting excitation energy from gaseous active media via an ultrashort pulse arises from the fact that the pulse's duration is either shorter than, or comparable to the characteristic times of the involved excitation- and relaxationprocesses. Below, we briefly consider these processes and their influence on the efficiency of

*Excitation and vibrational relaxation*. In a typical CO2 laser, an electric discharge is used to create population inversion. Fast electrons accelerated by electric field collide with CO2 and N2 molecules, so exciting their upper vibrational states. Nitrogen serves as reservoir for storing the excitation energy which is then transferred to CO2 via vibrational relaxation. The typical duration of discharge in a pulsed CO2 laser is about a microsecond, and vibrational relaxation times range from 1-10 ns·bar. This implies that a (sub-)picosecond laser pulse only extracts energy already available at the upper vibrational laser-level, with negligible energy deposition from the discharge or from redistribution from other vibrational levels during pulse propagation. To maximize extraction, wherever possible a regenerative amplification scheme is used, wherein the pulse passes the amplifier medium many times allowing repopulation of the upper vibrational level of the laser transition between the passes. However, realizing this scheme practically is problematic for high-energy pulses when beam must be wide to increase the active volume and avoid damaging optical elements. Thus, two-stage amplification usually is adopted (see Section 6); a regenerative amplifier providing amplification up to millijoules level is followed by a final high-energy amplifier arranged either in a single-pass configuration, or several passes are only partially overlapped. Slow pumping and vibrational relaxation limit energy extraction in the final amplification stage. A possible solution is replacing pumping by electric discharge, with optical pumping by a short laser pulse that quickly and directly excites the upper laser level,

*Rotational relaxation*. Rotational relaxation processes limit the fraction of energy extractable from the upper vibrational laser level in a single pass through the active medium. The laser pulse interacts only with a limited number of rotational transitions that is defined by the overlap between the pulse's spectrum and the amplification band. At high pressure, when collisionally broadened rotational lines overlap, or for a very short pulse, when pulse's spectrum covers several rotational lines, energy is extracted from several rotational sublevels. Otherwise, energy is extracted only from a single sub-level containing about 1/15th of the entire energy stored in that vibrational level. Three scenarios support the complete emptying of the vibrational level: (1) The pulse is long enough to provide time for repopulation of the active rotational levels. Typical rotational relaxation times are ~100 ps·bar; about 15 collisions are required effectively to empty all rotational sub-levels through a single active rotational transition. Thus, the minimum required pulse duration is ~1.5 ns·bar (e.g., 150 ps at 10 bar). (2) Pressure broadening allows all rotational transitions to interact with the laser field. Using Eq. (3) we find that ~100 bar is needed to broaden the

reasonable to expect that the outcome will comparably be valuable.

and eliminates the need for redistributing vibrational energy.

**3.4 Energy extraction efficiency** 

extracting energy.

rotational lines to the ~0.5 THz necessary for this regime. (3) The spectrum of the pulse covers the entire rotational branch, as happens when the pulse duration is ≤1 ps (Eq. (2)). The last regime is preferable if the aim is to keep pulse's span as brief as possible.

#### **4. Pulse compression**

#### **4.1 Self-chirping in nonlinear media**

Despite the usual attempts researchers take in trying to avoid the undesirable effects of the nonlinear response on the high-power pulses, it might be possible to employ these phenomena to further compress ultrashort pulses. When an optical pulse propagates through a media, the refractive index of the latter changes according to Eq. (7), following the intensity of the optical field (the Kerr effect). Phase velocity, *vp=c/n,* varies accordingly. The field frequency of the pulse, whose phase velocity continuously changes, shifts proportionally to its derivative *dvp/dt*, so generating pulse chirping. Fig. 10 illustrates this process.

Fig. 10. Self-chirping of a pulse propagating through a nonlinear media. Top: Pulse intensity profile (leading edge is on the left); bottom dashed: Phase velocity derivative; bottom solid: Wave-packet of the chirped pulse.

It is important to realize the difference between the chirping, as in the CPA, and chirping, as in self-chirping. In the first case, the pulse's spectrum is unchanged whereas its duration increases; in the second, the spectrum broadens while pulse duration does not change. A dispersive compressor similar to that utilized in the CPA can be arranged to shrink the selfchirped pulse well below its original duration.

#### **4.2 Self-chirping in plasma**

Self-chirping in plasma essentially is a variation of the self-chirping in nonlinear media. The distinctive feature of this case is that the variation in refractive index is caused by laser-

Ultrashort Pulses 155

chirping in the partially ionized active media, and compression in the material of the cavity windows. Controlled shortening was realized using an external gas cell by Tochitsky et al.

Measuring the temporal structure of ultrashort 10-µm pulses is not fundamentally different from measuring visible or near-IR pulses. However, due to low demand, there are very few commercial diagnostic instruments (e.g., Frequency Resolved Optical Gating, FROG) suitable for direct use in the mid-IR region. Several techniques used for diagnosing CO2

Fig. 12. Apparatuses for ultrashort mid-IR pulse diagnostics. (a) Streak camera;

band not included in the simulations); and, (c) Autocorrelator.

spectrometer can be arranged similar to that shown in Fig. 12b.

(b) Spectrometer (additional peaks in the measured spectrum are attributed to a sequence

A *streak camera* is a convenient tool for monitoring the pulse structure, providing a resolution of 1-2 ps. Because photocathodes used in streak cameras are insensitive to the mid-IR wavelengths, a frequency conversion technique must be used to shift the pulse wavelength to the visible- or near-IR- diapason. For this purpose, either a differencefrequency mixing in a nonlinear crystal (Fig. 12a), or a Kerr-cell-based optical switch where the CO2 laser's pulse controls a visible or mid-IR beam is suitable. The resolution of the streak camera is sufficient for measuring pulse splitting due to modulation on the rotational gain spectrum. However, the accuracy of measuring the duration of individual pulses is

A *spectrometer* can be used for indirect measurement of the pulse's duration. In the absence of chirping, the total bandwidth of the spectrum is inversely proportional to the duration of the individual pulses (Eq. (2)). If the beam's quality is good enough, a simple grating

(Tochitsky et al., 2001).

**5. Pulse diagnostics** 

limited by 1-2 ps.

laser pulses are schematically represented in Fig. 12.

induced gas-ionization rather than the Kerr effect. Refractive index of the ionized gas is determined by the linear refractive index of the media, *n0*, and the plasma density, *Ne*:

$$n = n\_0 \left(1 - \frac{N\_c}{N\_c}\right)^{1/2} \tag{9}$$

where *Nc* is the critical density (Eq. (1)). Unlike the Kerr effect, where refractive index usually *increases* with laser intensity, strong ionization in high-intensity fields *decreases* the refractive index. Therefore, the direction of chirping is reversed: The field frequency of the leading edge of the pulse is higher than that of the trailing one (*blue chirp*), allowing the compression of the chirped pulse via the linear dispersion in an optical material. By sending the pulse through a window of a properly selected thickness, made of a material with negative group velocity dispersion (e.g., NaCl), we can delay the blue-shifted leading edge of the pulse more than the trailing edge, thus shrinking the pulse.

Inert gases (e.g., xenon) are considered promising candidates for the role of nonlinear media for CO2 laser pulse self-chirping (Gordienko et al., 2009). A complication arises because the field intensity is not constant across the beam; thus, self-chirping that is pronounced in the center of the beam becomes negligible at its edges. The beam can be homogenized using a hollow waveguide (Nisoli et al., 1997, Voronin et al., 2010), or a filamentation regime (Couairon et al., 2006, Gordienko et al., 2009). Fig. 11 shows the results of simulations of an 1.2-ps pulse compression via self-chirping in xenon in filamentation regime followed by a NaCl compressor.

Fig. 11. Simulated 1.2-ps (FWHM) pulse before (solid) and after (dashed) compression via self-chirping in xenon plasma and dispersive compression in NaCl (Gordienko et al., 2009). Time is measured in optical cycles (1 o.c.≈35 fs); P is power and Pcr is critical self-focusing power in xenon: Pcr≈λ2/4πn0n2. Reprinted by permission of Turpion Ltd.

Corcum observed unintentional pulse shortening due to plasma chirping in a picosecond CO2 amplifier (Corcum, 1985). The suggested explanation capitalized on the pulse's self-

induced gas-ionization rather than the Kerr effect. Refractive index of the ionized gas is determined by the linear refractive index of the media, *n0*, and the plasma density, *Ne*:

> <sup>0</sup> 1 *<sup>e</sup> c N*

where *Nc* is the critical density (Eq. (1)). Unlike the Kerr effect, where refractive index usually *increases* with laser intensity, strong ionization in high-intensity fields *decreases* the refractive index. Therefore, the direction of chirping is reversed: The field frequency of the leading edge of the pulse is higher than that of the trailing one (*blue chirp*), allowing the compression of the chirped pulse via the linear dispersion in an optical material. By sending the pulse through a window of a properly selected thickness, made of a material with negative group velocity dispersion (e.g., NaCl), we can delay the blue-shifted leading edge

Inert gases (e.g., xenon) are considered promising candidates for the role of nonlinear media for CO2 laser pulse self-chirping (Gordienko et al., 2009). A complication arises because the field intensity is not constant across the beam; thus, self-chirping that is pronounced in the center of the beam becomes negligible at its edges. The beam can be homogenized using a hollow waveguide (Nisoli et al., 1997, Voronin et al., 2010), or a filamentation regime (Couairon et al., 2006, Gordienko et al., 2009). Fig. 11 shows the results of simulations of an 1.2-ps pulse compression via self-chirping in xenon in filamentation regime followed by a

Fig. 11. Simulated 1.2-ps (FWHM) pulse before (solid) and after (dashed) compression via self-chirping in xenon plasma and dispersive compression in NaCl (Gordienko et al., 2009). Time is measured in optical cycles (1 o.c.≈35 fs); P is power and Pcr is critical self-focusing

Corcum observed unintentional pulse shortening due to plasma chirping in a picosecond CO2 amplifier (Corcum, 1985). The suggested explanation capitalized on the pulse's self-

power in xenon: Pcr≈λ2/4πn0n2. Reprinted by permission of Turpion Ltd.

*N* = − 

*n n*

of the pulse more than the trailing edge, thus shrinking the pulse.

NaCl compressor.

1/2

, (9)

chirping in the partially ionized active media, and compression in the material of the cavity windows. Controlled shortening was realized using an external gas cell by Tochitsky et al. (Tochitsky et al., 2001).

#### **5. Pulse diagnostics**

Measuring the temporal structure of ultrashort 10-µm pulses is not fundamentally different from measuring visible or near-IR pulses. However, due to low demand, there are very few commercial diagnostic instruments (e.g., Frequency Resolved Optical Gating, FROG) suitable for direct use in the mid-IR region. Several techniques used for diagnosing CO2 laser pulses are schematically represented in Fig. 12.

Fig. 12. Apparatuses for ultrashort mid-IR pulse diagnostics. (a) Streak camera; (b) Spectrometer (additional peaks in the measured spectrum are attributed to a sequence band not included in the simulations); and, (c) Autocorrelator.

A *streak camera* is a convenient tool for monitoring the pulse structure, providing a resolution of 1-2 ps. Because photocathodes used in streak cameras are insensitive to the mid-IR wavelengths, a frequency conversion technique must be used to shift the pulse wavelength to the visible- or near-IR- diapason. For this purpose, either a differencefrequency mixing in a nonlinear crystal (Fig. 12a), or a Kerr-cell-based optical switch where the CO2 laser's pulse controls a visible or mid-IR beam is suitable. The resolution of the streak camera is sufficient for measuring pulse splitting due to modulation on the rotational gain spectrum. However, the accuracy of measuring the duration of individual pulses is limited by 1-2 ps.

A *spectrometer* can be used for indirect measurement of the pulse's duration. In the absence of chirping, the total bandwidth of the spectrum is inversely proportional to the duration of the individual pulses (Eq. (2)). If the beam's quality is good enough, a simple grating spectrometer can be arranged similar to that shown in Fig. 12b.

Ultrashort Pulses 157

Fig. 13. Layout and pulse dynamics in the BNL-ATF CO2 laser system; PS: Polarizing

Working pressure 10 bar 8 bar Gas mixture: [CO2]:[N2]:[He] 1:1:18 (isotopic CO2) 2:1:28 Active volume 1×1×80 cm3 8×10×100 cm3 Small-signal gain 1-2 %/cm 1.5-2 %/cm Number of passes 8-12 round-trips 6 passes Net amplification 105 103

Fig. 14 is a scheme of the CO2 laser system of the UCLA's Neptune Laboratory operating at 10.6 µm wavelength (10P branch). The 3-ps injection pulse is produced by slicing a portion of the output of a hybrid TEA CO2 laser (comprising a low-pressure smoothing tube to suppress energy modulation caused by self-mode-locking). The slicing is realized as a single-step process, using a CS2-filled Kerr cell controlled by a 3-ps pulse of a solid-state laser. The nanojoule injection pulse first is amplified in an 8-bar regenerative amplifier,

Table 2. Parameters of BNL-ATF laser amplifiers.

**6.2 15-TW system at UCLA's Neptune Laboratory** 

**Regenerative amplifier Final amplifier** 

splitter.

An *autocorrelator* technique must be established to attain the most reliable results. For instance, it can be used to periodically validate the measurements from the streak camera and the spectrometer. An autocorrelator splits the measured beam into two, and recombines it on an active element where the pulses interact, providing a measurable signal that is a function of the temporal overlap. By recording the interaction signal as a function of the time-delay between pulses, we obtain information about the temporal profile of the pulse. Usually, a nonlinear crystal is used as the active element, generating a harmonic frequency when the two pulses overlap in time. In a simpler design, the pulses' temporal overlap is evaluated by measuring the modulation of the interference pattern resulting from the interaction of the two beams. In the autocorrelator design shown in the Fig. 12c an intentionally induced slight misalignment of the interferometer's arms generates an interference pattern on the pyroelectric camera's sensor. The interference contrast serves as a measure of the temporal overlap between the pulses; the maximum modulation corresponds to zero delay, whereas the complete separation of the pulses in time entails the disappearance of interference. With this technique, we can study both the duration of individual pulses and the train's structure, which results in the periodic appearance of the interference pattern with gradually reduced modulation at delays that are multiples of the pulse-splitting period.

#### **6. Existing terawatt CO2 lasers**

Two systems worldwide now can generate terawatt peak-power, 10-µm pulses: One at the Accelerator Test Facility of the Brookhaven National Laboratory (BNL) (Polyanskiy et al., 2011); and, the other at the Neptune Laboratory of the University of California, Loss Angeles (UCLA) (Haberberger et al., 2010). These systems are described briefly below.

#### **6.1 1-TW system at BNL's Accelerator Test Facility (BNL-ATF)**

The CO2 laser system depicted in the Fig. 13 consists of a picosecond pulse-generator that produces a linear-polarized 0.1-μJ, 5-ps pulse, along with two high-pressure amplifiers that ultimately boost the laser pulses' energy to the ~5 J level.

In this system, a 5-ps pulse is sliced by the sequence of optical switches from the 200-ns, 20 mJ output of a hybrid TEA CO2 laser tuned to the 10R(14) line (10.3 μm). First, a 10-ns pulse is cut off the initial pulse with a Pockels cell, and intensified in a 3-bar UV-pre-ionized electric-discharge pre-amplifier. Then, a semiconductor optical switch, which is controlled by a 14-ps YAG laser, slices off a ~200 ps part of the pulse. Finally, the 200-ps pulse is sent through a CS2 Kerr cell controlled by a co-propagating, 5-ps, frequency-doubled YAG laserpulse. A polarization filter placed after the Kerr cell selects a 0.1-μJ, 5-ps seed pulse that then is raised to 10 mJ in multiple round-trip passes through a regenerative amplifier filled with a gas mixture featuring *isotopically enriched* carbon dioxide to prevent pulse splitting upon amplification. The amplifier is energized with UV-pre-ionized transverse electric discharge. Further amplification to 5 J is attained in 6 passes through a large-aperture (8x10 cm2), x-ray pre-ionized final amplifier. Field broadening prevents pulse splitting in the final amplifier despite using regular CO2 gas therein. The output is a single 5-ps pulse implying ~1 TW peak power. Table 2 summarizes the technical details of these two amplification stages.

An *autocorrelator* technique must be established to attain the most reliable results. For instance, it can be used to periodically validate the measurements from the streak camera and the spectrometer. An autocorrelator splits the measured beam into two, and recombines it on an active element where the pulses interact, providing a measurable signal that is a function of the temporal overlap. By recording the interaction signal as a function of the time-delay between pulses, we obtain information about the temporal profile of the pulse. Usually, a nonlinear crystal is used as the active element, generating a harmonic frequency when the two pulses overlap in time. In a simpler design, the pulses' temporal overlap is evaluated by measuring the modulation of the interference pattern resulting from the interaction of the two beams. In the autocorrelator design shown in the Fig. 12c an intentionally induced slight misalignment of the interferometer's arms generates an interference pattern on the pyroelectric camera's sensor. The interference contrast serves as a measure of the temporal overlap between the pulses; the maximum modulation corresponds to zero delay, whereas the complete separation of the pulses in time entails the disappearance of interference. With this technique, we can study both the duration of individual pulses and the train's structure, which results in the periodic appearance of the interference pattern with gradually reduced modulation at delays that are multiples of the

Two systems worldwide now can generate terawatt peak-power, 10-µm pulses: One at the Accelerator Test Facility of the Brookhaven National Laboratory (BNL) (Polyanskiy et al., 2011); and, the other at the Neptune Laboratory of the University of California, Loss Angeles

The CO2 laser system depicted in the Fig. 13 consists of a picosecond pulse-generator that produces a linear-polarized 0.1-μJ, 5-ps pulse, along with two high-pressure amplifiers that

In this system, a 5-ps pulse is sliced by the sequence of optical switches from the 200-ns, 20 mJ output of a hybrid TEA CO2 laser tuned to the 10R(14) line (10.3 μm). First, a 10-ns pulse is cut off the initial pulse with a Pockels cell, and intensified in a 3-bar UV-pre-ionized electric-discharge pre-amplifier. Then, a semiconductor optical switch, which is controlled by a 14-ps YAG laser, slices off a ~200 ps part of the pulse. Finally, the 200-ps pulse is sent through a CS2 Kerr cell controlled by a co-propagating, 5-ps, frequency-doubled YAG laserpulse. A polarization filter placed after the Kerr cell selects a 0.1-μJ, 5-ps seed pulse that then is raised to 10 mJ in multiple round-trip passes through a regenerative amplifier filled with a gas mixture featuring *isotopically enriched* carbon dioxide to prevent pulse splitting upon amplification. The amplifier is energized with UV-pre-ionized transverse electric discharge. Further amplification to 5 J is attained in 6 passes through a large-aperture (8x10 cm2), x-ray pre-ionized final amplifier. Field broadening prevents pulse splitting in the final amplifier despite using regular CO2 gas therein. The output is a single 5-ps pulse implying ~1 TW peak power. Table 2 summarizes the technical details of these two

(UCLA) (Haberberger et al., 2010). These systems are described briefly below.

**6.1 1-TW system at BNL's Accelerator Test Facility (BNL-ATF)** 

ultimately boost the laser pulses' energy to the ~5 J level.

pulse-splitting period.

amplification stages.

**6. Existing terawatt CO2 lasers** 

Fig. 13. Layout and pulse dynamics in the BNL-ATF CO2 laser system; PS: Polarizing splitter.


Table 2. Parameters of BNL-ATF laser amplifiers.

#### **6.2 15-TW system at UCLA's Neptune Laboratory**

Fig. 14 is a scheme of the CO2 laser system of the UCLA's Neptune Laboratory operating at 10.6 µm wavelength (10P branch). The 3-ps injection pulse is produced by slicing a portion of the output of a hybrid TEA CO2 laser (comprising a low-pressure smoothing tube to suppress energy modulation caused by self-mode-locking). The slicing is realized as a single-step process, using a CS2-filled Kerr cell controlled by a 3-ps pulse of a solid-state laser. The nanojoule injection pulse first is amplified in an 8-bar regenerative amplifier,

Ultrashort Pulses 159

which are the high-energy physics experiments and the proton acceleration for cancer

Achievements in solid-state laser technology can help the further development of ultrashort-pulse, high-peak-power CO2 laser systems. Modern solid-state lasers can be directly used in mid-IR systems, e.g., for controlling optical switches, pumping CO2 laser transition, or generating the ultrashort 10-µm seed pulses via nonlinear frequency conversion and parametric amplification. Apart from that, the advanced techniques initially developed for solid-state lasers (e.g. chirped pulse amplification) can be adopted

This work is supported by the US DOE contract DE-AC02-98CH10886 and by the BNL Laboratory Directed R&D (LDRD) grant #07-004. The authors are thankful to Sergei Tochitsky from UCLA's Neptune Laboratory for providing information on the Neptune's

Abrams, R. L. & Wood, O. R. (1971). Characteristics of a mode-locked TEA CO2 laser. *Appl. Phys. Lett.,* Vol.19, No.12, (December 1971), pp. 518-520, ISSN 0003-6951 Alcock, A. J. & Corkum, P. B. (1979). Ultra-fast switching of infrared radiation by laser-

Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. (1962). Interactions between

Autler, S. H. & Townes, C. H. (1955). Stark effect in rapidly varying fields. *Phys. Rev.*,

Brimacombe, R. K. & Reid, J. (1983). Accurate measurements of pressure-broadened

Bristow, A. D., Rotenberg, N., & van Driel, H. M. (2007). Two-photon absorption and Kerr

Corkum, P. B. & Krausz, F. (2007). Attosecond science. *Nature Physics.,* Vol.3, No.6, (June

Corkum, P. B. (1983). High-power, subpicosecond 10-μm pulse generation. *Opt. Lett.*, Vol.8,

Corkum, P. B. (1985). Amplification of picosecond 10 µm pulses in multiatmosphere CO2

Couairon, A., Biegert, J., Hauri, C. P., Kornelis, W., Helbing, F. W., Keller, U. & Mysyrowicz,

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No.10, (October 1983), pp. 514-516, ISSN 0146-9592

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produced carriers in semiconductors. *Can. J. Phys.,* Vol.57, No.9, (September 1979),

light waves in a nonlinear dielectric. *Phys. Rev.*, Vol.127,No.6, (September 1962), pp.

linewidths in a transversely excited CO2 discharge. *IEEE J. Quantum Electron.,* 

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A., F. (2006). Self-compression of ultra-short laser pulses down to one optical cycle by filamentation. *J. Modern Opt.,* Vol.53, No.1-2, (January 2006), pp. 75-85, ISSN

therapy, call for even higher peak power.

pp. 1280-1290, ISSN 0008-4204

1918-1939, ISSN 1943-2879

p. 191104, ISSN 0003-6951

0018-9197

0950–0340

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in CO2 laser systems.

CO2 laser.

**9. References** 

**8. Acknowledgements** 

reaching milijoules energy and splitting into a train of ~7 sub-pulses separated by 18-ps intervals. The final 2.5-bar amplifier boosts the pulse energy up to 100 J, and simultaneously mostly suppresses splitting via the field-broadening effect. The output pulse consists of 2-3 sub-pulses with ~45% energy in the first of them, implying ~15 TW peak power.

Fig. 14. Layout and pulse dynamics of the UCLA's Neptune Laboratory laser system (Haberberger et al., 2010). Reproduced with permission.

Table 3 summarizes the parameters of this system's amplifiers.


Table 3. Parameters of UCLA's Neptune Laboratory laser amplifiers.

#### **7. Conclusion**

We overviewed the underlying physics and technical approaches to generating and amplifying ultrashort 10-µm pulses. Modern CO2 laser systems can generate pulses as brief as few picoseconds and as powerful as several terawatt. Potential applications, among

reaching milijoules energy and splitting into a train of ~7 sub-pulses separated by 18-ps intervals. The final 2.5-bar amplifier boosts the pulse energy up to 100 J, and simultaneously mostly suppresses splitting via the field-broadening effect. The output pulse consists of 2-3

sub-pulses with ~45% energy in the first of them, implying ~15 TW peak power.

Fig. 14. Layout and pulse dynamics of the UCLA's Neptune Laboratory laser system

Working pressure 8 bar 2.5 bar Gas mixture: [CO2]:[N2]:[He] 1:1:14 4:1:0

Active volume 1×1×60 cm3 20×35×250 cm3 Small-signal gain - 2.6 %/cm Number of passes - 3 passes Net amplification 107 105

We overviewed the underlying physics and technical approaches to generating and amplifying ultrashort 10-µm pulses. Modern CO2 laser systems can generate pulses as brief as few picoseconds and as powerful as several terawatt. Potential applications, among

**Regenerative amplifier Final amplifier** 

(Haberberger et al., 2010). Reproduced with permission.

Table 3 summarizes the parameters of this system's amplifiers.

Table 3. Parameters of UCLA's Neptune Laboratory laser amplifiers.

**7. Conclusion** 

which are the high-energy physics experiments and the proton acceleration for cancer therapy, call for even higher peak power.

Achievements in solid-state laser technology can help the further development of ultrashort-pulse, high-peak-power CO2 laser systems. Modern solid-state lasers can be directly used in mid-IR systems, e.g., for controlling optical switches, pumping CO2 laser transition, or generating the ultrashort 10-µm seed pulses via nonlinear frequency conversion and parametric amplification. Apart from that, the advanced techniques initially developed for solid-state lasers (e.g. chirped pulse amplification) can be adopted in CO2 laser systems.

#### **8. Acknowledgements**

This work is supported by the US DOE contract DE-AC02-98CH10886 and by the BNL Laboratory Directed R&D (LDRD) grant #07-004. The authors are thankful to Sergei Tochitsky from UCLA's Neptune Laboratory for providing information on the Neptune's CO2 laser.

#### **9. References**


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**5** 

Akira Endo

*Japan* 

**High Average Power Pulsed CO2 Laser** 

*Research Institute for Science and Engineering, Waseda University, Tokyo* 

Increase of average power of pulsed CO2 laser was required by strong demand of the semiconductor industry, in pursue of the next generation of lithography light source at 13.5nm (Endo, et.al, 2006). The target average EUV power was increased from 10W level in the beginning to several 100W levels in the recent maturing period. No existing solid state laser technology satisfies the demand of the average power as the laser driver, by counting the laser-EUV conversion efficiency around 1%. Intensive research of one decade also showed that opacity, namely self absorption of the generated EUV light is less significant in high Z plasma, driven by a longer wavelength laser. CO2 laser produced Tin plasma showed more than 4% conversion efficiency in practical target geometry. Details are recently reviewed by A.Endo (Endo, 2010) and V.Y.Banine (Banine et.al, 2011). Interested readers are advised to refer to these articles. The established architecture is shown in Fig.1 as the laser produced Tin plasma which is generated from mist target of 300μm diameter, irradiated by 15ns CO2 laser pulse. The mist target is produced from a 10μm Tin droplet after irradiation

The conversion efficiency (CE), from the input laser pulse energy to the generated EUV pulse energy at 13.5nm (2% bandwidth, 2*π* sr), is the major parameter for improvement in high average power EUV light source for better economy. Low repetition rate pulsed CO2 laser was composed of transverse discharge modules, and often employed in laser plasma

**1. Introduction** 

**1.1 Background of the emerging technology** 

by a solid state laser with smaller pulse energy.

Fig. 1. Schematic of Tin plasma by double pulse method

 **for Short Wavelength Light Sources** 


### **High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources**

Akira Endo

*Research Institute for Science and Engineering, Waseda University, Tokyo Japan* 

#### **1. Introduction**

162 CO2 Laser – Optimisation and Application

Yablonovich, E. (1973). Spectral broadening in the light transmitted through a rapidly

Yablonovich, E. (1974a). Short CO2 laser pulse generation by optical free induction decay. *Appl. Phys. Lett.,* Vol.25, No.10, (November 1974), pp. 580-582, ISSN 0003-6951 Yablonovich, E. (1974b). Self-phase modulation and short-pulse generation from laser-

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in a laser cavity. *Phys. Rev. ST Accel. Beams,* Vol.9, No.9, (September 2006), p.

#### **1.1 Background of the emerging technology**

Increase of average power of pulsed CO2 laser was required by strong demand of the semiconductor industry, in pursue of the next generation of lithography light source at 13.5nm (Endo, et.al, 2006). The target average EUV power was increased from 10W level in the beginning to several 100W levels in the recent maturing period. No existing solid state laser technology satisfies the demand of the average power as the laser driver, by counting the laser-EUV conversion efficiency around 1%. Intensive research of one decade also showed that opacity, namely self absorption of the generated EUV light is less significant in high Z plasma, driven by a longer wavelength laser. CO2 laser produced Tin plasma showed more than 4% conversion efficiency in practical target geometry. Details are recently reviewed by A.Endo (Endo, 2010) and V.Y.Banine (Banine et.al, 2011). Interested readers are advised to refer to these articles. The established architecture is shown in Fig.1 as the laser produced Tin plasma which is generated from mist target of 300μm diameter, irradiated by 15ns CO2 laser pulse. The mist target is produced from a 10μm Tin droplet after irradiation by a solid state laser with smaller pulse energy.

Fig. 1. Schematic of Tin plasma by double pulse method

The conversion efficiency (CE), from the input laser pulse energy to the generated EUV pulse energy at 13.5nm (2% bandwidth, 2*π* sr), is the major parameter for improvement in high average power EUV light source for better economy. Low repetition rate pulsed CO2 laser was composed of transverse discharge modules, and often employed in laser plasma

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 165

power from the main amplifier was 7kW, but the experimentally obtained power of 5kW

The laser beam quality was measured with a ZnSe lens of 508mm focal length and a slit-scan type beam profiler (Photon Inc., NanoScan). The laser beam size at the lens focus was measured for the oscillator and amplifier, resulting in a beam quality factor M2 as 1.1. Especially, the laser beam size was identical before and after amplification, i.e. the amplification did not cause any phase distortion. Fig.3 shows a typical spatial beam profile. Fig.4 shows the temporal laser pulse profile of the amplified laser output. The pulse duration was 20 ns (FWHM) and the pedestal was below 10% of the total pulse energy. A pedestal and/or tail of the seed laser pulse could be amplified and reduce the laser gain. Back scattering light from Tin mist target is experimentally less than 10% of the input laser energy, and backward amplification must be carefully avoided by full depletion of residual laser gain.

indicated many factors for further improvement.

Fig. 3. CO2 laser beam of M2=1.1

Fig. 4. CO2 laser pulse with low pedestal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Intensity

Intensity

Tim e 50 ns/div.

Time 50 ns/div.

Fig. 2. Schematic diagram of multi stage MOPA, short pulse CO2 laser

experiments until 90's, but gradually disappeared from laboratories after improvements of solid state pulsed lasers. It was once employed as a driver of a plasma X-ray laser from a carbon target (Suckewer, et.al., 1983).

Medium average power pulsed CO2 laser systems are very successful tools for various applications ranging from material processing of metals, glass, ceramics and epoxy, paint removal and medical or spectroscopic applications, to the generation of laser produced plasmas as UV, EUV and soft X-ray sources. One drawback is the limited repetition rate of TEA CO2 laser based source, another drawback is limited controllability of the pulse width in low pressure microwave excited lasers. Attempts were reported in early 90's to operate microwave excited CO2 laser modules in a Q-switched oscillator mode of CW 2kW device (Sakai et.al., 1994) and an oscillator-amplifier mode of CW 7kW system (Bielesch et.al., 1992). Typical performances were at the repetition rate of 4 kHz with output average power of 680 W with pulse energy of 170 mJ and pulse width in full width half maximum (FWHM) of 250 ns, and at the repetition rate of 10 kHz with average power of 800W, with pulse energy of 70 mJ, and 35 ns pulse width, respectively. Laser extraction efficiencies, however, were not very high in both cases in the short pulse mode. Commercially available short pulse CO2 laser oscillator was known typically as EOM-10 from De Maria Electro Optics Systems, Inc (now Coherent Inc). The specification was average power of 10W at 100 kHz repetition rate with 15ns pulse width. The design guideline of a multi kW short pulse CO2 laser system is characterized by high repetition rate, high pulse energy, high amplification efficiency and high beam quality. The system is based on commercial high average power CW CO2 laser modules as amplifiers.

A short pulse oscillator was installed in our laboratory as the seeder for the amplifiers. The laser was an EO Q-switched, pulse length of 15~30 ns, single P(20) line, RF pumped waveguide CO2 laser with 60 W output at a repetition rate of 100 kHz. The repetition rate was tunable as 10~140 kHz. Commercial 5 kW and 15 kW CW CO2 lasers were employed as amplifiers. Every unit was 13.56 MHz RF-excited, fast axial flow lasers from Trumpf Inc. Lasers were modified as amplifiers by replacing both cavity mirror with ZnSe windows. The 5 kW laser used a standard gas composition of CO2:N2:He=5:29:66 at 120 Torr gas pressure. The axial gas flow speed was sufficiently high to keep the laser gas temperature low inside the operational condition. The length of a single gain region was 15 cm, and 16 cylindrical gain regions were connected in series in one laser unit; the tube inner diameter was 17mm. The total length of the optical pass inside the laser was 590 cm. The laser operated at 5 kW CW output power with a M2 =1.8 beam quality. The electrical input power was 36 kW. The 15 kW laser as the main amplifier, used a standard gas composition of CO2:N2:He=2:10:48 at 150 Torr gas pressure. The length of a single gain region was 28 cm, and 16 active cylindrical gain regions were connected in series; the tube inner diameter was 30 mm. The total length of the optical pass inside the laser was 890 cm. The maximum electrical input power was 88 kW. The key parameters of the amplifier are the extraction efficiency and beam quality. A series of experiments were performed to clarify these parameters to estimate the final possible values (Hoshino et.al., 2008).

The experimental setup is shown as Fig.2 with expected output power of 10kW. The maximum average output power of 8 kW was experimentally obtained at a repetition rate of 100 kHz with 3kW input power to the main amplifier. Parasitic oscillations and/or optical coupling between amplifier modules were not significant in burst mode. It was successful to extract 5kW power in pulsed mode from CW 15kW laser. The extraction efficiency (output power-input power/ CW output power) was over 30%. Initial estimation of extractable

experiments until 90's, but gradually disappeared from laboratories after improvements of solid state pulsed lasers. It was once employed as a driver of a plasma X-ray laser from a

Medium average power pulsed CO2 laser systems are very successful tools for various applications ranging from material processing of metals, glass, ceramics and epoxy, paint removal and medical or spectroscopic applications, to the generation of laser produced plasmas as UV, EUV and soft X-ray sources. One drawback is the limited repetition rate of TEA CO2 laser based source, another drawback is limited controllability of the pulse width in low pressure microwave excited lasers. Attempts were reported in early 90's to operate microwave excited CO2 laser modules in a Q-switched oscillator mode of CW 2kW device (Sakai et.al., 1994) and an oscillator-amplifier mode of CW 7kW system (Bielesch et.al., 1992). Typical performances were at the repetition rate of 4 kHz with output average power of 680 W with pulse energy of 170 mJ and pulse width in full width half maximum (FWHM) of 250 ns, and at the repetition rate of 10 kHz with average power of 800W, with pulse energy of 70 mJ, and 35 ns pulse width, respectively. Laser extraction efficiencies, however, were not very high in both cases in the short pulse mode. Commercially available short pulse CO2 laser oscillator was known typically as EOM-10 from De Maria Electro Optics Systems, Inc (now Coherent Inc). The specification was average power of 10W at 100 kHz repetition rate with 15ns pulse width. The design guideline of a multi kW short pulse CO2 laser system is characterized by high repetition rate, high pulse energy, high amplification efficiency and high beam quality. The system is based on commercial high average power CW CO2 laser modules as amplifiers. A short pulse oscillator was installed in our laboratory as the seeder for the amplifiers. The laser was an EO Q-switched, pulse length of 15~30 ns, single P(20) line, RF pumped waveguide CO2 laser with 60 W output at a repetition rate of 100 kHz. The repetition rate was tunable as 10~140 kHz. Commercial 5 kW and 15 kW CW CO2 lasers were employed as amplifiers. Every unit was 13.56 MHz RF-excited, fast axial flow lasers from Trumpf Inc. Lasers were modified as amplifiers by replacing both cavity mirror with ZnSe windows. The 5 kW laser used a standard gas composition of CO2:N2:He=5:29:66 at 120 Torr gas pressure. The axial gas flow speed was sufficiently high to keep the laser gas temperature low inside the operational condition. The length of a single gain region was 15 cm, and 16 cylindrical gain regions were connected in series in one laser unit; the tube inner diameter was 17mm. The total length of the optical pass inside the laser was 590 cm. The laser operated at 5 kW CW output power with a M2 =1.8 beam quality. The electrical input power was 36 kW. The 15 kW laser as the main amplifier, used a standard gas composition of CO2:N2:He=2:10:48 at 150 Torr gas pressure. The length of a single gain region was 28 cm, and 16 active cylindrical gain regions were connected in series; the tube inner diameter was 30 mm. The total length of the optical pass inside the laser was 890 cm. The maximum electrical input power was 88 kW. The key parameters of the amplifier are the extraction efficiency and beam quality. A series of experiments were performed to clarify these parameters to estimate the final

The experimental setup is shown as Fig.2 with expected output power of 10kW. The maximum average output power of 8 kW was experimentally obtained at a repetition rate of 100 kHz with 3kW input power to the main amplifier. Parasitic oscillations and/or optical coupling between amplifier modules were not significant in burst mode. It was successful to extract 5kW power in pulsed mode from CW 15kW laser. The extraction efficiency (output power-input power/ CW output power) was over 30%. Initial estimation of extractable

carbon target (Suckewer, et.al., 1983).

possible values (Hoshino et.al., 2008).

power from the main amplifier was 7kW, but the experimentally obtained power of 5kW indicated many factors for further improvement.

Fig. 2. Schematic diagram of multi stage MOPA, short pulse CO2 laser

The laser beam quality was measured with a ZnSe lens of 508mm focal length and a slit-scan type beam profiler (Photon Inc., NanoScan). The laser beam size at the lens focus was measured for the oscillator and amplifier, resulting in a beam quality factor M2 as 1.1. Especially, the laser beam size was identical before and after amplification, i.e. the amplification did not cause any phase distortion. Fig.3 shows a typical spatial beam profile. Fig.4 shows the temporal laser pulse profile of the amplified laser output. The pulse duration was 20 ns (FWHM) and the pedestal was below 10% of the total pulse energy. A pedestal and/or tail of the seed laser pulse could be amplified and reduce the laser gain. Back scattering light from Tin mist target is experimentally less than 10% of the input laser energy, and backward amplification must be carefully avoided by full depletion of residual laser gain.

Fig. 3. CO2 laser beam of M2=1.1

Fig. 4. CO2 laser pulse with low pedestal

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 167

1975). The rotational relaxation time is calculated as τr = 2.3ns for 100 Torr and a 4500C medium, while the typical laser pulse width in the example is τp = 15ns. The characteristic number τp /τr is 6.5 for 100 Torr medium, and the work of F.Rheaut deals with the case of

As a parameter study, small signal gain coefficient g0 is tentatively assumed as 1%/cm, and the saturation fluence is as 10mJ/cm2 for a 100 Torr RF pumped CO2 laser amplifier. The maximum fluence Em is then given as 10mJ/cm2 for L=1m gain length. Figure 6 shows one early experimental result of 15ns pulse amplification at 100 kHz of an axial flow CW 15kW laser. The average beam diameter was ~ 15mm, and amplification parameters were calculated as g0=0.43%/cm, and Es=8.0mJ/cm2, by numerical fitting of the experimental data to the equation (1). The fitting gave reasonable results in spite of the τp ≳τr condition (Ariga, 2007). It was concluded that the Frantz-Nodvik equation was practically usable in this semiintermediate region for characterization of the amplifier parameters. It seems reasonable by accounting the measured Es, together with an effort to increase g0 to 1%/cm,to obtain 100mJ pulse energy from the amplifier once the gain cross section A is 10cm2, or the gain length L is 10m with A=1cm2. The cross section A is depending on the amplifier design, and the gain

Fig. 6. Short pulse amplification data of 15kW CW output power module with 15ns pulse width at 100 kHz. The results were best fitted by the Frantz-Nodvik equation to give the

A short pulse amplifier is characterized by its medium gain diameter, D and gain length, L. The most common limitation of the available gain is set by the amplified spontaneous emission (ASE) on the optical axis, which deteriorates the pulse signal to noise ratio (SN), and depletes the available gain. A general mathematical formula on this phenomenon has been reported by Lowenthal et.al. (Lowental et.al,1986). On axis ASE flux is given by equation (11) from this work, for the purpose of numerical calculation. Figure 16 of the paper shows the achieved g0L with parameters L/D. It is generally advised to keep g0L less than 3 for a single pass amplifier, especially for storage lasers which have no coherent flux to extract gain simultaneously with pumping (short pulse amplification in cw pumped medium). A short pulse CO2 laser amplifier has a typical gain diameter of 1cm, an optical gain length of 1m and an aspect ratio L/D large enough to consider the configuration as one dimensional. The gain depletion effect is less significant compared to the cubic gain medium previously reported (Lowenthal, et.al. 1986), but the on axis ASE effect is similar. Parasitic

almost the same ratio for 1 atmosphere.

length L is limited by self oscillation of the amplifier.

effective value of g0 and Es.

#### **2. 10ns, 100 kHz operation of CO2 laser at 10kW average power**

CO2 molecular dynamics is the fundamental subject to understand the operational parameters of pulsed CO2 laser. Figure 5 shows a typical energy diagram of CO2 laser active medium.

Fig. 5. Energy level diagram of active CO2 laser medium

Short pulse, high repetition operational CO2 laser is the most suitable laser technology to meet the requirements of HVM EUV source. Free electron lasers (FEL) are also capable of realizing high average power, short pulse coherent beam, based on the emerging superconducting energy recovery linac (sERL) technology (Krafft, 2006). However, the pulse energy is in sub mJ range with a few ps pulse width at 75MHz repetition rate, which does not match to the plasma production specifications for EUV sources.

Short pulse CO2 laser technology was well studied by TEA discharge oscillator-amplifier configuration up until the 1990's (Decker, et.al, 1991). There were two major limitations on this scheme, namely, a low repetition rate up to 10Hz and backscatter amplification in nonsaturated amplifier medium. The gain medium in the RF pumped CO2 laser is a CO2/N2/He mixture of typically 100 Torr pressure. The CO2 molecule stores energy in the rotational-vibration mode from electric collision excitation in the 0001 band, and the typical relaxation time for the vibration is 0.5μsec, which is shorter than the pulse interval time of 10μsec for 100kHz repetition rate. The amplification that is described in this case is short pulse amplification and expressed by the Frantz-Nodvik equation (Rheaut, et.al, 1973), where Ein is the input fluence in mJ/cm2, Eout is the output fluence, Es is the saturation fluence, g0 is the small signal gain coefficient in cm-1, L is the gain medium length in cm. Maximum available fluence after single pass amplification Em is given by g0·L·Es in mJ/cm2. g0 and Es are functions of medium parameters proportional to the upper state molecule numbers as, σN\*, and inversely proportional to the radiative cross section as hν/2σ , each other. The Frantz-Nodvik equation describes the short pulse amplification as,

$$E\_{out} = E\_s \cdot \ln[1 + \exp(\mathbf{g}\_0 \cdot L)[\exp(\frac{E\_{in}}{E\_s}) - 1]] \tag{1}$$

and the equation is valid provided that the pulse duration τp is long compared to the rotational relaxation time τr , or short, namely in the case of τp τr or τp τr . CO2 laser amplification in the intermediate region, namely in the case τp ≈τr , is treated by rotational reservoir model calculations, which requires non practical numerical solutions (Harrach,

CO2 molecular dynamics is the fundamental subject to understand the operational parameters of pulsed CO2 laser. Figure 5 shows a typical energy diagram of CO2 laser active medium.

Short pulse, high repetition operational CO2 laser is the most suitable laser technology to meet the requirements of HVM EUV source. Free electron lasers (FEL) are also capable of realizing high average power, short pulse coherent beam, based on the emerging superconducting energy recovery linac (sERL) technology (Krafft, 2006). However, the pulse energy is in sub mJ range with a few ps pulse width at 75MHz repetition rate, which does

Short pulse CO2 laser technology was well studied by TEA discharge oscillator-amplifier configuration up until the 1990's (Decker, et.al, 1991). There were two major limitations on this scheme, namely, a low repetition rate up to 10Hz and backscatter amplification in nonsaturated amplifier medium. The gain medium in the RF pumped CO2 laser is a CO2/N2/He mixture of typically 100 Torr pressure. The CO2 molecule stores energy in the rotational-vibration mode from electric collision excitation in the 0001 band, and the typical relaxation time for the vibration is 0.5μsec, which is shorter than the pulse interval time of 10μsec for 100kHz repetition rate. The amplification that is described in this case is short pulse amplification and expressed by the Frantz-Nodvik equation (Rheaut, et.al, 1973), where Ein is the input fluence in mJ/cm2, Eout is the output fluence, Es is the saturation fluence, g0 is the small signal gain coefficient in cm-1, L is the gain medium length in cm. Maximum available fluence after single pass amplification Em is given by g0·L·Es in mJ/cm2. g0 and Es are functions of medium parameters proportional to the upper state molecule numbers as, σN\*, and inversely proportional to the radiative cross section as hν/2σ , each

**2. 10ns, 100 kHz operation of CO2 laser at 10kW average power** 

Fig. 5. Energy level diagram of active CO2 laser medium

not match to the plasma production specifications for EUV sources.

other. The Frantz-Nodvik equation describes the short pulse amplification as,

*<sup>E</sup> E E gL <sup>E</sup>*

and the equation is valid provided that the pulse duration τp is long compared to the rotational relaxation time τr , or short, namely in the case of τp τr or τp τr . CO2 laser amplification in the intermediate region, namely in the case τp ≈τr , is treated by rotational reservoir model calculations, which requires non practical numerical solutions (Harrach,

*out s*

<sup>0</sup> ln[1 exp( )[exp( ) 1]] *in*

*s*

=⋅ + ⋅ − (1)

1975). The rotational relaxation time is calculated as τr = 2.3ns for 100 Torr and a 4500C medium, while the typical laser pulse width in the example is τp = 15ns. The characteristic number τp /τr is 6.5 for 100 Torr medium, and the work of F.Rheaut deals with the case of almost the same ratio for 1 atmosphere.

As a parameter study, small signal gain coefficient g0 is tentatively assumed as 1%/cm, and the saturation fluence is as 10mJ/cm2 for a 100 Torr RF pumped CO2 laser amplifier. The maximum fluence Em is then given as 10mJ/cm2 for L=1m gain length. Figure 6 shows one early experimental result of 15ns pulse amplification at 100 kHz of an axial flow CW 15kW laser. The average beam diameter was ~ 15mm, and amplification parameters were calculated as g0=0.43%/cm, and Es=8.0mJ/cm2, by numerical fitting of the experimental data to the equation (1). The fitting gave reasonable results in spite of the τp ≳τr condition (Ariga, 2007). It was concluded that the Frantz-Nodvik equation was practically usable in this semiintermediate region for characterization of the amplifier parameters. It seems reasonable by accounting the measured Es, together with an effort to increase g0 to 1%/cm,to obtain 100mJ pulse energy from the amplifier once the gain cross section A is 10cm2, or the gain length L is 10m with A=1cm2. The cross section A is depending on the amplifier design, and the gain length L is limited by self oscillation of the amplifier.

Fig. 6. Short pulse amplification data of 15kW CW output power module with 15ns pulse width at 100 kHz. The results were best fitted by the Frantz-Nodvik equation to give the effective value of g0 and Es.

A short pulse amplifier is characterized by its medium gain diameter, D and gain length, L. The most common limitation of the available gain is set by the amplified spontaneous emission (ASE) on the optical axis, which deteriorates the pulse signal to noise ratio (SN), and depletes the available gain. A general mathematical formula on this phenomenon has been reported by Lowenthal et.al. (Lowental et.al,1986). On axis ASE flux is given by equation (11) from this work, for the purpose of numerical calculation. Figure 16 of the paper shows the achieved g0L with parameters L/D. It is generally advised to keep g0L less than 3 for a single pass amplifier, especially for storage lasers which have no coherent flux to extract gain simultaneously with pumping (short pulse amplification in cw pumped medium). A short pulse CO2 laser amplifier has a typical gain diameter of 1cm, an optical gain length of 1m and an aspect ratio L/D large enough to consider the configuration as one dimensional. The gain depletion effect is less significant compared to the cubic gain medium previously reported (Lowenthal, et.al. 1986), but the on axis ASE effect is similar. Parasitic

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 169

It is indicated that the thermal lens effect is not deterministic at low duty operation (2%), but significant at 100% duty operation. Filling factor Φ, is the parameter used to measure the

This is reduced at higher duty operation due to a shorter thermal lens focus length, and amplification saturation is lower at higher duty operation with reduced Φ. Specifically designed active feedback control is necessary to stabilize the beam propagation at high duty operation. Figure 8 shows an experimental example of the beam diameter at the amplifier exit, with and without active beam control (Nowak, et.al, 2008). Lower spatial quality oscillator beam causes micro lens effects in the transparent optical components, and leads to chaotic beam amplification with a higher M2 number. Design of a controlled spectrum oscillator with high quality spatial profile is important for better amplified beam quality,

Fig. 8. Measured beam diameter after output window with and without active optical

Precise control of the amplification depends on the quality of the oscillator pulse. Recent development of two different IR source technologies, namely OPA(Optical Parametric Amplifier) and QCL(Quantum Cascade Laser) are reviewed in this paragraph. Compact slab CO2 laser is employed as the gain medium of regenerative amplifier to boost the weak initial IR beam. OPA and QCL are potentially controllable in its pulse width even in the pico

Laser beam is characterized by its spectrum, and the low pressure CO2 laser medium is composed of many vibration-rotational lines. The P(20) line is the single laser line in normal oscillation conditions at 10.6μm wavelength. The rotational relaxation time is calculated as τr = 2.3ns for a 100 Torr and 4500C medium, which is not negligibly small compared to the typical laser pulse width τp = 15ns. Electrically excited energy distributes in many other rotational modes of CO2 molecules, and collisional relaxation to the P(20) line is limited

Φ= beam volume/gain volume (3)

usability of the gain region by the propagating beam,

**3. New generation oscillator technologies** 

and efficient amplification.

feedback.

second range.

oscillation is experienced in actual experiments and this is often the practical limit for full amplification. The phenomena are strictly dependant on the device design, namely partial reflection from laser wall, optics holders or leakage through isolators. It is an issue to be treated for each laser system, but the physical fundamental is the same as the double pass case by Lowenthal et.al.

It is preferable to employ gaseous saturable absorbers like SF6 in the multi stage amplifiers, to avoid damage to solid-state saturable absorbers like p-doped Germanium (Haglund, et.al. 1981). The typical switching threshold in the gaseous saturable absorbers is 10mJ/cm2. Also, the optical beam delivery system requires optimization to efficiently depress pulse pedestal. An electro optical switch, which uses solid-state material like CdTe, is employed in the lower average power stage to realize better noise depression (Slattery, et.al. 1975). The damage threshold is dependant on the laser parameters such as pulse width, fluence, average power and beam uniformity. Laser beam containing hot spots can cause damage to the material surface even at much lower fluence. Solid-state materials suffer stronger thermal lens effects as shown by the following formula (Koechner, 1999).

$$f = \frac{KA}{P\_a} \left(\frac{1}{2}\frac{dn}{dT} + \alpha C\_{r,\theta} n\_0^3 + \frac{\alpha r\_0 \left(n\_0 - 1\right)}{L}\right)^{-1} \tag{2}$$

The first term is the temperature dependant refractive index change, the second term is stress induced refractive index change, and the final term is temperature dependant surface modification. Thermal lensing is the most significant phenomenon in the power amplifier stage with optical components, especially for ZnSe or Diamond windows. The effective focus depends on the beam power, and active feedback is necessary to realize stable beam propagation throughout the whole laser optical path. Figure 7 shows a model calculation of the thermal loading effect to the beam propagation through 2 stage amplifiers of axial flow type of 5kW CW output, with an input of pulses in 20ns at 100 kHz repetition rate input with 60W average power (Nowak, et.al, 2008).

Fig. 7. Calculated results of the amplified beam diameter behavior depending on the operational duty. Input power is 60W at a distance of 0m, and the output optics of the first 5kW amplifier is at a distance of 10m. The input optics of the second module is at a distance of 11m. These windows suffer from strong thermal lensing effects which lead to beam diameter fluctuation.

oscillation is experienced in actual experiments and this is often the practical limit for full amplification. The phenomena are strictly dependant on the device design, namely partial reflection from laser wall, optics holders or leakage through isolators. It is an issue to be treated for each laser system, but the physical fundamental is the same as the double pass

It is preferable to employ gaseous saturable absorbers like SF6 in the multi stage amplifiers, to avoid damage to solid-state saturable absorbers like p-doped Germanium (Haglund, et.al. 1981). The typical switching threshold in the gaseous saturable absorbers is 10mJ/cm2. Also, the optical beam delivery system requires optimization to efficiently depress pulse pedestal. An electro optical switch, which uses solid-state material like CdTe, is employed in the lower average power stage to realize better noise depression (Slattery, et.al. 1975). The damage threshold is dependant on the laser parameters such as pulse width, fluence, average power and beam uniformity. Laser beam containing hot spots can cause damage to the material surface even at much lower fluence. Solid-state materials suffer stronger

3 0 0

−

(2)

, 0 1 1

φ α − = +α + 

The first term is the temperature dependant refractive index change, the second term is stress induced refractive index change, and the final term is temperature dependant surface modification. Thermal lensing is the most significant phenomenon in the power amplifier stage with optical components, especially for ZnSe or Diamond windows. The effective focus depends on the beam power, and active feedback is necessary to realize stable beam propagation throughout the whole laser optical path. Figure 7 shows a model calculation of the thermal loading effect to the beam propagation through 2 stage amplifiers of axial flow type of 5kW CW output, with an input of pulses in 20ns at 100 kHz repetition rate input

thermal lens effects as shown by the following formula (Koechner, 1999).

2 *<sup>r</sup>*

Fig. 7. Calculated results of the amplified beam diameter behavior depending on the operational duty. Input power is 60W at a distance of 0m, and the output optics of the first 5kW amplifier is at a distance of 10m. The input optics of the second module is at a distance of 11m. These windows suffer from strong thermal lensing effects which lead to beam

*f C n*

*KA dn r n*

*P dT L*

( ) <sup>1</sup>

*a*

with 60W average power (Nowak, et.al, 2008).

diameter fluctuation.

case by Lowenthal et.al.

It is indicated that the thermal lens effect is not deterministic at low duty operation (2%), but significant at 100% duty operation. Filling factor Φ, is the parameter used to measure the usability of the gain region by the propagating beam,

$$\spadesuit = \textbf{beam volume} / \text{gain volume} \tag{3}$$

This is reduced at higher duty operation due to a shorter thermal lens focus length, and amplification saturation is lower at higher duty operation with reduced Φ. Specifically designed active feedback control is necessary to stabilize the beam propagation at high duty operation. Figure 8 shows an experimental example of the beam diameter at the amplifier exit, with and without active beam control (Nowak, et.al, 2008). Lower spatial quality oscillator beam causes micro lens effects in the transparent optical components, and leads to chaotic beam amplification with a higher M2 number. Design of a controlled spectrum oscillator with high quality spatial profile is important for better amplified beam quality, and efficient amplification.

Fig. 8. Measured beam diameter after output window with and without active optical feedback.

#### **3. New generation oscillator technologies**

Precise control of the amplification depends on the quality of the oscillator pulse. Recent development of two different IR source technologies, namely OPA(Optical Parametric Amplifier) and QCL(Quantum Cascade Laser) are reviewed in this paragraph. Compact slab CO2 laser is employed as the gain medium of regenerative amplifier to boost the weak initial IR beam. OPA and QCL are potentially controllable in its pulse width even in the pico second range.

Laser beam is characterized by its spectrum, and the low pressure CO2 laser medium is composed of many vibration-rotational lines. The P(20) line is the single laser line in normal oscillation conditions at 10.6μm wavelength. The rotational relaxation time is calculated as τr = 2.3ns for a 100 Torr and 4500C medium, which is not negligibly small compared to the typical laser pulse width τp = 15ns. Electrically excited energy distributes in many other rotational modes of CO2 molecules, and collisional relaxation to the P(20) line is limited

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 171

Fig. 10. Absolute (●,▼) and relative (X) energy extraction from a main amplifier tube pumped by a CW RF discharge with discharge power 88 kW. The input beam shape is Gaussian with diameter D=18mm. The energy extraction is plotted to the input pulse energy. The symbol -X- is the relative gain ratio of single P20 line to 4 lines (P16-P22)

It is understood that the high conversion efficiency of EUV light comes from the UTA (unresolved transition arrays) of highly ionized high Z plasma. The peak wavelength of the UTA is depending on the Z number, and further shorter wavelength plasma has a similar physical behavior (Li, et.al. 2011). The first generation EUV source at 13.5nm wavelength works well up to 11nm node of semiconductor mass production within the next one decade. A possibility to switch to a shorter wavelength (BEUV: beyond EUV) is required to be studied in advance (Banine, et.al, 2010). Availability of high reflectivity mirror at 6.x nm region initiated basic research to find candidate heavy elements with high UTA emission in this wavelength region (Churilov, et.al, 2009). Intensive research has revealed that the UTA emission has peak intensity from Gadolinium at 6.7nm wavelength comparably efficient to that of Tin at 13.5nm. Lower density plasma is favorable for less opacity effect, and short pulse CO2 laser is again the best driver (Higashiguchi et.al, 2011). The optimum plasma temperature increases from 40eV for Sn at 13.5nm, to 150eV for Gd at 6.x nm. The laser

 T ∝ ( I0 λ2 ) 2/3 (4) where I0 is the laser peak intensity, and λ is the laser wavelength (Ramis et.al, 1983). It is understood that a short pulse CO2 laser is better fitted to higher plasma temperature due to its longer wavelength. Optimum laser pulse width for highest CE for Sn at 13.5nm is typically 15nsec, but higher temperature Gd plasma dissipates faster, and shorter pulse length may be required for highest CE. Minimum sustainable pulse width in low pressure CO2 laser amplifier is estimated from rotational gain bandwidth Δν(Abrams, 1974) as,

Δν = 7.58 ( φCO2 + 0.73φN2 + 0.64φHe ) x P(300/T)1/2 (5)

amplification

**4. Further developments** 

plasma temperature is expressed as

during the amplified pulse period. Figure 9 shows the spectrum structure of the laser lines, with a broad continuous spectrum from a solid state seeder overlapped, to fully extract the stored energy. Recent advanced nonlinear laser technology is at the stage of operating a broad band optical parametric oscillator (OPA) at the center wavelength of 10.6μm, with more than 10mW at 150kHz (Light Conversion, "ORPHEUS", 2011). This specification is enough to seed a single transverse mode CO2 laser oscillator.

Fig. 9. CO2 laser spectrum structure overlapped with a broad OPA seeder spectrum

Multiline amplification was calculated to evaluate the effectiveness of the low pressure CO2 laser at 15kW CW output power. The beam diameter was assumed to be 18mm. Numerical result shows the amplification enhancement, with 4 lines composed of P(16,18,20,22) as 1.3 times higher than the single P(20) amplification case. Figure 10 shows the calculation result of the gain Γ. Emerging quantum cascade lasers (QCL) are available, which can generate specific lines of the P band of the CO2 laser (Cascade Technologies, LS03D, 2009) and possibly seed a CO2 laser oscillator with a discrete spectrum. QCL lasers are thus ideal as compact and robust seed sources. They can be accurately tuned to particular gain lines of the CO2 medium with sufficient accuracy. QCL lasers are capable of tens of mW output power at typical pulse durations of 10ns, providing good bandwidth matching to a lasing line in a typical CO2 medium. A QCL can provide at least 3 orders of magnitude higher power per self oscillation lines of a small oscillator, thus relaxing the requirement of the roundtrip gain and the number of roundtrips in the seeded oscillator, thereby improving power output and stability. The theoretical prediction of Fig.10 was recently confirmed by QCL multiline seeded pulses in a large slab amplifier (Nowak, 2011).

Multiline amplification effectively enhances small signal gain g0 compared to CW gain, and saturation fluence Es, by improving the spectrum factor, and this leads to the enhancement of maximum available flux Em. The final optical limit, typically 1J/cm2, is given by the optical damage of the output window, which is more than one magnitude higher than the available Em. The small signal gain g0 and saturation fluence Es are the two basic parameters to characterize for any amplifiers (DeaAutels, et.al. 2003). It is reasonable to expect double enhancement of Em to 20mJ/cm2 after optimization of amplifier parameters, and the available beam energy as 200mJ with the effective gain volume as LA = 1000 cm3 (1 litter). Typical repetition rate of 100 kHz gives the average output power as 20kW, after meeting all requirements described in this article.

Fig. 10. Absolute (●,▼) and relative (X) energy extraction from a main amplifier tube pumped by a CW RF discharge with discharge power 88 kW. The input beam shape is Gaussian with diameter D=18mm. The energy extraction is plotted to the input pulse energy. The symbol -X- is the relative gain ratio of single P20 line to 4 lines (P16-P22) amplification

#### **4. Further developments**

170 CO2 Laser – Optimisation and Application

during the amplified pulse period. Figure 9 shows the spectrum structure of the laser lines, with a broad continuous spectrum from a solid state seeder overlapped, to fully extract the stored energy. Recent advanced nonlinear laser technology is at the stage of operating a broad band optical parametric oscillator (OPA) at the center wavelength of 10.6μm, with more than 10mW at 150kHz (Light Conversion, "ORPHEUS", 2011). This specification is

Fig. 9. CO2 laser spectrum structure overlapped with a broad OPA seeder spectrum

QCL multiline seeded pulses in a large slab amplifier (Nowak, 2011).

requirements described in this article.

Multiline amplification was calculated to evaluate the effectiveness of the low pressure CO2 laser at 15kW CW output power. The beam diameter was assumed to be 18mm. Numerical result shows the amplification enhancement, with 4 lines composed of P(16,18,20,22) as 1.3 times higher than the single P(20) amplification case. Figure 10 shows the calculation result of the gain Γ. Emerging quantum cascade lasers (QCL) are available, which can generate specific lines of the P band of the CO2 laser (Cascade Technologies, LS03D, 2009) and possibly seed a CO2 laser oscillator with a discrete spectrum. QCL lasers are thus ideal as compact and robust seed sources. They can be accurately tuned to particular gain lines of the CO2 medium with sufficient accuracy. QCL lasers are capable of tens of mW output power at typical pulse durations of 10ns, providing good bandwidth matching to a lasing line in a typical CO2 medium. A QCL can provide at least 3 orders of magnitude higher power per self oscillation lines of a small oscillator, thus relaxing the requirement of the roundtrip gain and the number of roundtrips in the seeded oscillator, thereby improving power output and stability. The theoretical prediction of Fig.10 was recently confirmed by

Multiline amplification effectively enhances small signal gain g0 compared to CW gain, and saturation fluence Es, by improving the spectrum factor, and this leads to the enhancement of maximum available flux Em. The final optical limit, typically 1J/cm2, is given by the optical damage of the output window, which is more than one magnitude higher than the available Em. The small signal gain g0 and saturation fluence Es are the two basic parameters to characterize for any amplifiers (DeaAutels, et.al. 2003). It is reasonable to expect double enhancement of Em to 20mJ/cm2 after optimization of amplifier parameters, and the available beam energy as 200mJ with the effective gain volume as LA = 1000 cm3 (1 litter). Typical repetition rate of 100 kHz gives the average output power as 20kW, after meeting all

enough to seed a single transverse mode CO2 laser oscillator.

It is understood that the high conversion efficiency of EUV light comes from the UTA (unresolved transition arrays) of highly ionized high Z plasma. The peak wavelength of the UTA is depending on the Z number, and further shorter wavelength plasma has a similar physical behavior (Li, et.al. 2011). The first generation EUV source at 13.5nm wavelength works well up to 11nm node of semiconductor mass production within the next one decade. A possibility to switch to a shorter wavelength (BEUV: beyond EUV) is required to be studied in advance (Banine, et.al, 2010). Availability of high reflectivity mirror at 6.x nm region initiated basic research to find candidate heavy elements with high UTA emission in this wavelength region (Churilov, et.al, 2009). Intensive research has revealed that the UTA emission has peak intensity from Gadolinium at 6.7nm wavelength comparably efficient to that of Tin at 13.5nm. Lower density plasma is favorable for less opacity effect, and short pulse CO2 laser is again the best driver (Higashiguchi et.al, 2011). The optimum plasma temperature increases from 40eV for Sn at 13.5nm, to 150eV for Gd at 6.x nm. The laser plasma temperature is expressed as

$$\mathbf{T} \ll \left(\mathbf{I}\_0 \lambda^2\right) 2^{\mathbf{\upbeta}} \tag{4}$$

where I0 is the laser peak intensity, and λ is the laser wavelength (Ramis et.al, 1983). It is understood that a short pulse CO2 laser is better fitted to higher plasma temperature due to its longer wavelength. Optimum laser pulse width for highest CE for Sn at 13.5nm is typically 15nsec, but higher temperature Gd plasma dissipates faster, and shorter pulse length may be required for highest CE. Minimum sustainable pulse width in low pressure CO2 laser amplifier is estimated from rotational gain bandwidth Δν(Abrams, 1974) as,

$$
\Delta \mathbf{v} = 7.58 \left( \mathbf{q}\_{\rm CO2} + 0.73 \mathbf{q}\_{\rm N2} + 0.64 \mathbf{q}\_{\rm He} \right) \times \mathbf{P} (\mathbf{300}/\mathbf{T})^{1/2} \tag{5}
$$

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 173

Laser-Compton scattering photon spectrum has a peak in the forward direction at a

2

γ

λ

*L*

where γ and β are Lorentz factors, λL the laser undulation period (laser wavelength), K the K parameter of the undulator which is equivalent to the laser intensity parameter, and Φ the colliding angle. The spectrum depends on the angular distribution; the wavelength λ is

<sup>1</sup> <sup>θ</sup> *<sup>p</sup>*

It is seen that higher γ electron beam produces less divergent light. Figure 12 shows the relationship between electron beam energy and maximum (forward) photon energy for both laser wavelengths by Nd:YAG laser (1.06µm) and CO2 laser (10.6µm). As a result of Fig. 12, the required electron beam energy is 3.2MeV (1.06µm) and 10.2MeV (10.6µm) in order to produce 6.7nm SXR. It makes large difference to treat such a low energy electron beam. The Lorentz factor γ is 6.3 and 20.0, respectively, which means 3 times better directivity with

The general formula of obtainable photon flux N0 is calculated in the normal collision by the

*c e N Np <sup>N</sup> r* <sup>σ</sup> <sup>∝</sup> <sup>π</sup>

where σc is the Compton cross section (6.7 x 10-25 cm2), Ne the total electron number, Np the

Fig. 12. Laser-Compton photon energy vs electron beam energy. Comparison 1064nm

(Nd:YAG) with 10600nm (CO2) wavelength as the photon target.

2

*cos*

<sup>=</sup> + (9)

λ−λ <sup>=</sup> γ λ (10)

(11)

*K*

*p*

(1 ) <sup>2</sup> 2 (1 )

+

 βφ

*p*

λ

wavelength;

emitted at

10.6µm laser than that of 1.06µm.

<sup>0</sup> <sup>2</sup> <sup>4</sup>

total photon number, and r the interaction area radius.

following expression.

where φ is the partial ratio of each component gas, P is the total pressure in Torr, and T is the gas temperature in K. Δν is given as

$$
\Delta \mathbf{v} = 424 \text{ MHz} \tag{6}
$$

for typical gas parameters as

$$\begin{array}{l} \text{CO}\_{2}: \text{N}\_{2}: \text{He} = 1:1:8 \\\\ \text{P} = 100 \text{ Torr} \\\\ \text{T} = \text{ 450 K} \end{array} \tag{7}$$

The minimum pulse width is estimated from the Fourier transform limit of a Gaussian pulse as

$$
\Delta \mathbf{v} \cdot \Delta \mathbf{t} = 0.44 \tag{8}
$$

and the resulting Δt is around 1 nsec. The present oscillator is a QCL seeded Q-switched, cavity dumped laser based on a RF pumped low pressure CO2 laser. Typical out put pulse width is 15nsec at 100 kHz repetition rate with 5W average power. Shorter pulse width is available by various methods like electro-optical or laser pulse slicing, depending on the requirement from future plasma experiments. Careful optical design of amplifiers can sustain the amplified pulse width for the requirement by dispersion compensation.

Another important field where 10μm wavelength is effective for short wavelength light generation, is the laser Compton X-ray generation. It is already well studied on the optimization of the laser-Compton hard X-ray source by single shot base (John, 1998, Endo, 2001). Experimental results agreed well with theoretical predictions. Highest peak brightness is obtained in the case of counter propagating laser pulse and electron beam bunch, in the minimum focusing before nonlinear threshold. The new short wavelength light source is now well matured to demonstrate single-shot phase contrast bio imaging in hard X-ray region (Oliva, et.al, 2010).

The major challenge of the laser Compton source in the EUV/SXR region is the lower electron beam voltage, which in turn results in a larger interaction cross section. Figure 11 describes the schematic of the laser-Compton interaction between electron beam and laser.

Fig. 11. Schematic of laser-Compton scattering process

172 CO2 Laser – Optimisation and Application

where φ is the partial ratio of each component gas, P is the total pressure in Torr, and T is

CO2 : N2 : He = 1:1:8

T = 450 K The minimum pulse width is estimated from the Fourier transform limit of a Gaussian pulse

and the resulting Δt is around 1 nsec. The present oscillator is a QCL seeded Q-switched, cavity dumped laser based on a RF pumped low pressure CO2 laser. Typical out put pulse width is 15nsec at 100 kHz repetition rate with 5W average power. Shorter pulse width is available by various methods like electro-optical or laser pulse slicing, depending on the requirement from future plasma experiments. Careful optical design of amplifiers can

Another important field where 10μm wavelength is effective for short wavelength light generation, is the laser Compton X-ray generation. It is already well studied on the optimization of the laser-Compton hard X-ray source by single shot base (John, 1998, Endo, 2001). Experimental results agreed well with theoretical predictions. Highest peak brightness is obtained in the case of counter propagating laser pulse and electron beam bunch, in the minimum focusing before nonlinear threshold. The new short wavelength light source is now well matured to demonstrate single-shot phase contrast bio imaging in

The major challenge of the laser Compton source in the EUV/SXR region is the lower electron beam voltage, which in turn results in a larger interaction cross section. Figure 11 describes the schematic of the laser-Compton interaction between electron beam and laser.

sustain the amplified pulse width for the requirement by dispersion compensation.

Δν = 424 MHz (6)

P = 100 Torr (7)

Δν·Δt = 0.44 (8)

the gas temperature in K. Δν is given as

hard X-ray region (Oliva, et.al, 2010).

Fig. 11. Schematic of laser-Compton scattering process

for typical gas parameters as

as

Laser-Compton scattering photon spectrum has a peak in the forward direction at a wavelength;

$$\lambda\_p = \frac{\lambda\_\perp (1 + \frac{K^2}{2})}{2\gamma^2 (1 + \beta \cos \phi)} \tag{9}$$

where γ and β are Lorentz factors, λL the laser undulation period (laser wavelength), K the K parameter of the undulator which is equivalent to the laser intensity parameter, and Φ the colliding angle. The spectrum depends on the angular distribution; the wavelength λ is emitted at

$$\Theta = \frac{1}{\gamma} \sqrt{\frac{\lambda - \lambda\_p}{\lambda\_p}} \tag{10}$$

It is seen that higher γ electron beam produces less divergent light. Figure 12 shows the relationship between electron beam energy and maximum (forward) photon energy for both laser wavelengths by Nd:YAG laser (1.06µm) and CO2 laser (10.6µm). As a result of Fig. 12, the required electron beam energy is 3.2MeV (1.06µm) and 10.2MeV (10.6µm) in order to produce 6.7nm SXR. It makes large difference to treat such a low energy electron beam. The Lorentz factor γ is 6.3 and 20.0, respectively, which means 3 times better directivity with 10.6µm laser than that of 1.06µm.

The general formula of obtainable photon flux N0 is calculated in the normal collision by the following expression.

$$N\_0 \approx \frac{\sigma\_\epsilon N\_\epsilon N\_p}{4\pi r^2} \tag{11}$$

where σc is the Compton cross section (6.7 x 10-25 cm2), Ne the total electron number, Np the total photon number, and r the interaction area radius.

Fig. 12. Laser-Compton photon energy vs electron beam energy. Comparison 1064nm (Nd:YAG) with 10600nm (CO2) wavelength as the photon target.

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 175

1

where Reff is �R�R�. As described above, higher reflectivity provides a higher enhancement super-cavity. Particularly, the loss, which includes both absorption and scattering, on the reflection coating is critical issue for storing a high power laser beam as described above. Such a high quality optical mirror was difficult for far infrared wavelength, however, there are now some products usable for super-cavity mirrors (Ophir Optics, 2009). Super-cavity for 10.6μm laser pulse can be achieved with the enhancement of about 600 by using best mirrors available. Figure 14 shows the calculated transmission, reflection and stored power of the super-cavity as a function of the phase advance in one cavity circulation i.e. supercavity length. The dotted line shows the reflection/transmission from the cavity and the solid line is stored power inside the super-cavity, assuming as input power is 1. There is no transmission light because Mirror 2 transmission is 0%. The enhancement of 600 is achieved by this super-cavity. The precision of cavity length adjustment is one issue for stable operation. The requirement is one-order relaxed due to the wavelength in case of CO2 laser, thus the stable operation with enhancement of 600 and more can be easily achieved from our experiences in 1μm laser storage. Critical issue for higher enhancement is to obtain the extremely low loss and high reflectivity mirrors, which is the key R&D of multi-layer

Fig. 14. Calculated results of CO2 laser super-cavity as a function of phase advance in one revolution of cavity. 2 π phase advance corresponds to λ/2 cavity length mismatch with the

Concerning a small waist achievement, our source requires 40μm waist (2σ). The waist of

*L L cav cav <sup>w</sup>*

where λ is wavelength of laser, Lcav cavity length, ρ curvature of cavity mirror. While high enhancement is easier, small waist cavity is difficult for 10.6μm laser as described in Eq. (15). However the two-mirror, Fabry-Perot cavity would be difficult to achieve small waist due to the cavity structure is confocal, we are developing a concentric, four-mirror super-cavity (Y.Honda, et.al. 2009). This technique can reduce the mirror alignment requirements as two order magnitude. We estimate that 40μm waist can be achieved using concentric super-cavity.

(2 ) 2

<sup>λ</sup> ρ − <sup>=</sup> π (15)

2 0 π

*eff eff*

<sup>=</sup> − (14)

*R R*

F

coatings with high resistance substrates.

laser frequency.

super-cavity is described as;

It is useful to calculate standard SXR photon numbers obtainable in ideal parameters in both cases. As described in Eq. (11), the SXR number is proportional to the laser photon number. The approach to increase the photon average flux is to increase Ne, Np and decrease r, but there are instrumental limitations to realize these simultaneously. The practical limitation of laser average power is determined by a damage on optical components, which is determined by average and peak intensity (W/cm2). It is suggested that the usage of 10.6µm CO2 laser has an advantage to produce one order larger number of SXR photons by the same intensity compared with 1µm solid state lasers. Another limitation is the onset of the nonlinear threshold of the higher harmonics generation, which is evident over 1017W/cm2 laser irradiation intensity (Kumita, 2008).

Usual approach is to increase the repetition rate of the event, and the obtainable photon average flux is expressed as;

$$\mathbf{N} = \mathbf{f} \times \mathbf{N}\_0 \tag{12}$$

where f is the repetition frequency. Characterization of the laser-Compton X-ray source has been undertaken with f as 1-10 Hz typically. High flux mode requires f in the range from kHz to MHz region.

It is under development of pulsed solid state laser storage in an optical super-cavity for laser-Compton X-ray sources (Sakaue, 2010, 2011). The enhancement inside the optical cavity was 600, in which the finess was more than 2000, and the waist of 60μm (2σ) was stably achieved using a 1μm wavelength Nd:Vanadium mode-locked laser with repetition rate 357MHz, pulse width 7ps, and average power 7W. Schematic of super-cavity is shown in Figure 13.

Fig. 13. Schematic of laser storage super-cavity.

Design and optimization is described here on a super-cavity for storing 10.6μm CO2 laser pulses. Super-cavity requires high reflectivity and high transmittance mirror i.e. ultra-low loss mirror as an input and high reflectivity mirror as an output for high enhancement. The enhancement is presented by using cavity finesse (F) as (Hodgson, et.al, 2005);

$$\mathbf{S}\_{\text{cav}} = \frac{\mathbf{F}}{\pi} \tag{13}$$

It is noted that the assumed cavity length is perfectly matched with input laser light. Finesse (F) is given by;

It is useful to calculate standard SXR photon numbers obtainable in ideal parameters in both cases. As described in Eq. (11), the SXR number is proportional to the laser photon number. The approach to increase the photon average flux is to increase Ne, Np and decrease r, but there are instrumental limitations to realize these simultaneously. The practical limitation of laser average power is determined by a damage on optical components, which is determined by average and peak intensity (W/cm2). It is suggested that the usage of 10.6µm CO2 laser has an advantage to produce one order larger number of SXR photons by the same intensity compared with 1µm solid state lasers. Another limitation is the onset of the nonlinear threshold of the higher harmonics generation, which is evident over 1017W/cm2

Usual approach is to increase the repetition rate of the event, and the obtainable photon

where f is the repetition frequency. Characterization of the laser-Compton X-ray source has been undertaken with f as 1-10 Hz typically. High flux mode requires f in the range from

It is under development of pulsed solid state laser storage in an optical super-cavity for laser-Compton X-ray sources (Sakaue, 2010, 2011). The enhancement inside the optical cavity was 600, in which the finess was more than 2000, and the waist of 60μm (2σ) was stably achieved using a 1μm wavelength Nd:Vanadium mode-locked laser with repetition rate 357MHz, pulse width 7ps, and average power 7W. Schematic of super-cavity is shown

Design and optimization is described here on a super-cavity for storing 10.6μm CO2 laser pulses. Super-cavity requires high reflectivity and high transmittance mirror i.e. ultra-low loss mirror as an input and high reflectivity mirror as an output for high enhancement. The

> cav <sup>F</sup> <sup>S</sup> <sup>=</sup> <sup>π</sup>

It is noted that the assumed cavity length is perfectly matched with input laser light. Finesse

enhancement is presented by using cavity finesse (F) as (Hodgson, et.al, 2005);

N f = × *N*0 (12)

(13)

laser irradiation intensity (Kumita, 2008).

Fig. 13. Schematic of laser storage super-cavity.

average flux is expressed as;

kHz to MHz region.

in Figure 13.

(F) is given by;

$$\mathbf{F} = \frac{\pi \sqrt{R\_{\text{eff}}}}{1 - R\_{\text{eff}}} \tag{14}$$

where Reff is �R�R�. As described above, higher reflectivity provides a higher enhancement super-cavity. Particularly, the loss, which includes both absorption and scattering, on the reflection coating is critical issue for storing a high power laser beam as described above. Such a high quality optical mirror was difficult for far infrared wavelength, however, there are now some products usable for super-cavity mirrors (Ophir Optics, 2009). Super-cavity for 10.6μm laser pulse can be achieved with the enhancement of about 600 by using best mirrors available. Figure 14 shows the calculated transmission, reflection and stored power of the super-cavity as a function of the phase advance in one cavity circulation i.e. supercavity length. The dotted line shows the reflection/transmission from the cavity and the solid line is stored power inside the super-cavity, assuming as input power is 1. There is no transmission light because Mirror 2 transmission is 0%. The enhancement of 600 is achieved by this super-cavity. The precision of cavity length adjustment is one issue for stable operation. The requirement is one-order relaxed due to the wavelength in case of CO2 laser, thus the stable operation with enhancement of 600 and more can be easily achieved from our experiences in 1μm laser storage. Critical issue for higher enhancement is to obtain the extremely low loss and high reflectivity mirrors, which is the key R&D of multi-layer coatings with high resistance substrates.

Fig. 14. Calculated results of CO2 laser super-cavity as a function of phase advance in one revolution of cavity. 2 π phase advance corresponds to λ/2 cavity length mismatch with the laser frequency.

Concerning a small waist achievement, our source requires 40μm waist (2σ). The waist of super-cavity is described as;

$$\left|w\_0^2 = \frac{\lambda}{\pi} \frac{\sqrt{L\_{\rm cav}(2\mathfrak{p} - L\_{\rm cav})}}{2}\right.\tag{15}$$

where λ is wavelength of laser, Lcav cavity length, ρ curvature of cavity mirror. While high enhancement is easier, small waist cavity is difficult for 10.6μm laser as described in Eq. (15). However the two-mirror, Fabry-Perot cavity would be difficult to achieve small waist due to the cavity structure is confocal, we are developing a concentric, four-mirror super-cavity (Y.Honda, et.al. 2009). This technique can reduce the mirror alignment requirements as two order magnitude. We estimate that 40μm waist can be achieved using concentric super-cavity.

High Average Power Pulsed CO2 Laser for Short Wavelength Light Sources 177

Ariga,T 2007 Development of a short pulse and high average power CO2 laser for EUV

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Decker,J.E. Lagace,S. Berube,J. Beaudoin,Y. Lin,S.L. (1991); Stable operation of a powerful 3-

Endo,A. (2010); CO2 laser produced Tin plasma light source as the solution for EUV

Endo,A.; Hoshino, H.; Ariga, T. & Miura, T. (2006). High power pulsed CO2 laser for EUV

Haglund,R.F. Nowak,A.V. Czuchlewski,S.J. (1981); Gaseous saturable absorbers for the helios CO2 laser system, IEEE Quantum Electron. QE17, pp1799-1808 Harrach, R.J. (1975); Effect of rotational and intramode vibrational coupling on short pulse

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CA, February, 2008, SPIE

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Higashiguchi,T Yugami,N Dunne,P O'Sullivan,G (2011) Scaling of laser produced

The first preliminary experimental results were obtained by using a single transverse mode, CW 10W CO2 laser in a two mirror super cavity (Sakaue, et.al. 2011). The reflectivity of the input mirror was 99.5% with 15m curvature, and the CW CO2 laser was operated with 10W maximum power of single longitudinal mode. The obtained transmitted light is shown on the oscilloscope with a sweeping voltage signal to the Piezo driver. The highest peak signal corresponds to the fundamental transverse mode, followed by higher spatial modes. The measured Finesse was around 300, which is almost half of the calculated value 624. Measured beam waist was 2.1mm, compared to the calculated value 1.8mm. The experiment showed a relatively stable result of the optical storage cavity in the CO2 laser wavelength. Next step is planned as a demonstration of the optical storage with picosecond pulses.

Fig. 15. Experimental setup and first result of CO2 laser storage. Signal train corresponds to the transmission light with cavity length interval of 5 μm.

#### **5. Conclusion**

High average power, short pulse width CO2 laser is originated in the EUV light source research in the beginning, but expanding its application to universal short wavelength plasma and non plasma sources. Reliable gas laser amplifiers with various geometrical structures are now employed with advanced solid state, semiconductor seeders to control its wavelength more precisely, and with advanced optics to enhance its pulsed average power to unprecedented level.

The author deeply expresses his thanks to his colleagues in the trials of research and development in EUV program. Early study on the CO2 laser technology was successfully driven by Dr. T. Miura. He contributed also in the application of OPA technology as the broadband seeder for CO2 laser oscillators. QCL was successfully studied as a seeder for precision control of the lasing lines by Dr. K. M. Nowak. Dr. H. Mizoguchi of Gigaphoton Inc. kindly gave me a chance to write this overview. The author deeply appreciates coworkers in Waseda University, especially Dr. K. Sakaue and Professor M. Washio in the CO2 laser super-cavity program.

#### **6. References**

Abrams, R.L 1974 Broadening coefficients for the P(20) laser transition; Appl.Phys.Lett. 25, pp609-611

The first preliminary experimental results were obtained by using a single transverse mode, CW 10W CO2 laser in a two mirror super cavity (Sakaue, et.al. 2011). The reflectivity of the input mirror was 99.5% with 15m curvature, and the CW CO2 laser was operated with 10W maximum power of single longitudinal mode. The obtained transmitted light is shown on the oscilloscope with a sweeping voltage signal to the Piezo driver. The highest peak signal corresponds to the fundamental transverse mode, followed by higher spatial modes. The measured Finesse was around 300, which is almost half of the calculated value 624. Measured beam waist was 2.1mm, compared to the calculated value 1.8mm. The experiment showed a relatively stable result of the optical storage cavity in the CO2 laser wavelength. Next step is planned as a demonstration of the optical storage with picosecond pulses.

Fig. 15. Experimental setup and first result of CO2 laser storage. Signal train corresponds to

High average power, short pulse width CO2 laser is originated in the EUV light source research in the beginning, but expanding its application to universal short wavelength plasma and non plasma sources. Reliable gas laser amplifiers with various geometrical structures are now employed with advanced solid state, semiconductor seeders to control its wavelength more precisely, and with advanced optics to enhance its pulsed average power

The author deeply expresses his thanks to his colleagues in the trials of research and development in EUV program. Early study on the CO2 laser technology was successfully driven by Dr. T. Miura. He contributed also in the application of OPA technology as the broadband seeder for CO2 laser oscillators. QCL was successfully studied as a seeder for precision control of the lasing lines by Dr. K. M. Nowak. Dr. H. Mizoguchi of Gigaphoton Inc. kindly gave me a chance to write this overview. The author deeply appreciates coworkers in Waseda University, especially Dr. K. Sakaue and Professor M. Washio in the CO2

Abrams, R.L 1974 Broadening coefficients for the P(20) laser transition; Appl.Phys.Lett. 25,

the transmission light with cavity length interval of 5 μm.

**5. Conclusion** 

to unprecedented level.

laser super-cavity program.

pp609-611

**6. References** 


**6** 

*India* 

Rakesh Kumar Soni

**Diffusion Cooled V-Fold CO2 Laser** 

*Raja Ramanna Centre for Advanced Technology, Indore (M.P.)* 

A laser is light amplifier. The acronym LASER stands for Light Amplification by Stimulated Emission of Radiation. It is an electromagnetic radiation with wavelength ranging from ultraviolet to infrared. The fundamental concept of laser operation was first introduced by Einstein in 1917 in one of his three papers on the quantum theory of radiation (Einstein 1917). Almost half a century later, in 1960, T.H. Maiman was the first person to demonstrate the laser by using a ruby crystal. It is a coherent, convergent and monochromatic beam of light. Lasers have various applications in various fields and to appreciate the competency of a laser radiation it is essential to comprehend the basic operation mechanism and properties of laser radiation. The fundamental concept of laser operation is stimulated emission. The three processes required to produce the high energy laser beam are: (a) population inversion, (b) stimulated emission and (c) amplification. Population inversion is a necessary condition for stimulated emission and corresponds to a non-equilibrium distribution of electrons such that the higher energy states have a larger number of electrons than the lower energy states. The process of achieving the population inversion by exciting the electrons to the higher energy states is referred to as pumping (Svelto and Hanna 1989). In general, population inversion is achieved by optical pumping and electrical pumping. In optical pumping, gas-filled flash lamps are most popular. Flash lamps are essentially glass or quartz tubes filled with gases such as xenon and krypton. Some wavelength of the flash (emission spectrum of flash lamp) matches with the absorption characteristics of the active laser medium facilitating population inversion. This is used in solid-state lasers like ruby and Nd:YAG (yttrium–aluminum–garnet). The basic differences between lasers and other light sources are the characteristics often used to describe a laser: (i) the output beam is narrow (ii) the light is monochromatic and (iii) the emission is coherent. The laser light is categorized by different properties and many applications of lasers use these properties. These properties are: (a) mono-chromaticity (b) collimation (c) coherence (d) brightness or radiance (e) focal spot size (f) low divergence (g) transverse modes and (g) temporal modes.

After the demonstration of the first ruby laser, the laser action has been demonstrated in many materials. Lasers are generally classified depending on the physical nature of the active medium used: (I) solid-state lasers (II) gas lasers (III) semiconductor lasers and (IV) dye lasers. It is beyond the purview of this chapter to describe the principles of operation of all these lasers. Here only gas laser systems and typically V-fold CO2 laser is explained.

**1. Introduction** 

**2. Gas lasers** 

plasma UTA emission down to 3 nm for next generation lithography and short wavelength imaging, *Proceeding of SPIE Optics+Photonics* vol.8139, San Diego,CA,August 2011


### **6**

### **Diffusion Cooled V-Fold CO2 Laser**

#### Rakesh Kumar Soni

*Raja Ramanna Centre for Advanced Technology, Indore (M.P.) India* 

#### **1. Introduction**

178 CO2 Laser – Optimisation and Application

Lowenthal, D.D. Egglestone,J.M. (1986); ASE effects in small aspect ratio laser oscillators and

Nowak, K.M.; Suganuma, T.; Endo, A.; Sumitani, A.; Goryachkin, D.A.; Romanov, N.A.;

Oliva,P. Carpinelli,M. Golosio,B. Delogu,P. Endrizzi,M. Park,J. Pogorelsky,I. Yakimenko,V.

Ramis,R (1983) Electron temperature versus laser intensity times wavelength squared: a

Rheault,F. Lachambre,J.L. Gilbert,J. Fortin,R. Blanchard,M (1973); Saturation properties of TEA-CO2 amplifiers in the nanosecond pulse regime, Opt.Commun. 8, pp132-135 Sakai,T. & Hamada,N. (1994). Q-switched CO2 laser using intense pulsed RF discharge and

Sakaue, K Araki, S Fukuda, M Higashi, Y Honda, Y Sasao, N Shimizu, H Taniguchi, T

Sakaue, K Endo,A and Washio,M (2011) Development of a 10μm optical storage cavity, *2011* 

Sakaue, K Washio, M Araki, S K Fukuda, M Higashi, Y Honda, Y Omori, T Taniguchi, T

Slattery, J.E. Thompson,J.S. Schroeder,J.B. (1975); Thermal pulse damage thresholds in

Suckewer, S.; Skinner, C.; Voorhees, D.; Milchberg, D.; Keane, C. & Semet, A. (1983).

Yorozu, M Yang, J Okada, Y Yanagida, T Sakai, F Ito, S and Endo, A (2003) Spatial beam

magnetically confined plasma column, *IEEE-QE* 19 pp1855-1860

comparison of theory and experiments, Nucl.Fusion 23739

Germany, September 1994, SPIE

scattering, Nucl.Instrum.Meth. A637 S107-S111

Scattering of Electron and Laser Beams, Laser Phys. 16 pp267-271

cadmium telluride, Appl.Opt. 14, pp2234-2237

Appl.Phys. B76 pp293-297

Diego,CA,August 2011

1173

9, 2011

134104

9, 2011

plasma UTA emission down to 3 nm for next generation lithography and short wavelength imaging, *Proceeding of SPIE Optics+Photonics* vol.8139, San

amplifiers with nonsaturable absorption, IEEE J.Quantum Electron. QE-22, pp1165-

Sherstobitov, V.E.; Kovalchuk, L.V.; Rodionov, A.Y. (2008). Efficient and compact short pulse MOPA system for laser-produced-plasma extreme-UV sources employing RF-discharge slab-waveguide CO2 amplifiers, *Proceedings of SPIE High-Power Laser Ablation,* vol.7005, ISBN: 9780819472069, Taos, NM, April 2008, SPIE Nowak,K.M. (2011). Towards 20kW CO2 laser system for Sn-LPP EUV source, *2011* 

*International Workshop on EUV and Soft X-Ray Sources*, Dublin, Ireland November 7-

Williams,O. Rosenzweig,J (2010), Quantitative evaluation of single-shot inline phase contrast imaging using an inverse Compton x-ray source, Appl.Phys.Lett. 97,

high speed rotating chopper, *Proceedings of SPIE Gas Flow and Chemical Lasers: Tenth International Symposium*, vol.2502, pp. 25-30, ISBN: 9780819418609, Friedrichshafen,

Urakawa, J and Washio, M (2011) Development of a laser pulse storage technique in an optical super-cavity for a compact X-ray source based on laser-Compton

*International Workshop on EUV and Soft X-Ray Sources*, Dublin, Ireland November 7-

Terunuma, N Urakawa, J and Sasao, N (2009) Observation of pulsed x-ray trains produced by laser-electron Compton scatterings, Rev.Sci.Instrum. 80 123304 1-7

Population inversion and gain measurements for soft X-ray laser development in a

profile of the femtosecond X-ray pulses generated by a laser-Compton scheme,

A laser is light amplifier. The acronym LASER stands for Light Amplification by Stimulated Emission of Radiation. It is an electromagnetic radiation with wavelength ranging from ultraviolet to infrared. The fundamental concept of laser operation was first introduced by Einstein in 1917 in one of his three papers on the quantum theory of radiation (Einstein 1917). Almost half a century later, in 1960, T.H. Maiman was the first person to demonstrate the laser by using a ruby crystal. It is a coherent, convergent and monochromatic beam of light. Lasers have various applications in various fields and to appreciate the competency of a laser radiation it is essential to comprehend the basic operation mechanism and properties of laser radiation. The fundamental concept of laser operation is stimulated emission. The three processes required to produce the high energy laser beam are: (a) population inversion, (b) stimulated emission and (c) amplification. Population inversion is a necessary condition for stimulated emission and corresponds to a non-equilibrium distribution of electrons such that the higher energy states have a larger number of electrons than the lower energy states. The process of achieving the population inversion by exciting the electrons to the higher energy states is referred to as pumping (Svelto and Hanna 1989). In general, population inversion is achieved by optical pumping and electrical pumping. In optical pumping, gas-filled flash lamps are most popular. Flash lamps are essentially glass or quartz tubes filled with gases such as xenon and krypton. Some wavelength of the flash (emission spectrum of flash lamp) matches with the absorption characteristics of the active laser medium facilitating population inversion. This is used in solid-state lasers like ruby and Nd:YAG (yttrium–aluminum–garnet). The basic differences between lasers and other light sources are the characteristics often used to describe a laser: (i) the output beam is narrow (ii) the light is monochromatic and (iii) the emission is coherent. The laser light is categorized by different properties and many applications of lasers use these properties. These properties are: (a) mono-chromaticity (b) collimation (c) coherence (d) brightness or radiance (e) focal spot size (f) low divergence (g) transverse modes and (g) temporal modes.

#### **2. Gas lasers**

After the demonstration of the first ruby laser, the laser action has been demonstrated in many materials. Lasers are generally classified depending on the physical nature of the active medium used: (I) solid-state lasers (II) gas lasers (III) semiconductor lasers and (IV) dye lasers. It is beyond the purview of this chapter to describe the principles of operation of all these lasers. Here only gas laser systems and typically V-fold CO2 laser is explained.

Diffusion Cooled V-Fold CO2 Laser 181

Laser Type Linear Power Density (W/m) Max. Power (W) Efficiency (%) HeNe 0.1 1 0.1 Argon 1-10 50 0.1 CO2 60-80 1200 15-20

The CO2 laser is a gas discharge device which operates by electric excitation. The active medium in a CO2 laser is a mixture of carbon dioxide, nitrogen, and helium. Each gas plays a distinct role. Carbon dioxide is the light emitter. The CO2 molecules are excited so they vibrate in three different types such as symmetric stretching, bending, and asymmetric stretching (Fig. 1). The molecules then lose part of the excitation energy by dropping to one of two other, lower energy vibrational states as shown in Fig.2. Once the molecules have emitted their laser photons, they continue to drop down the energy-level ladder until they reach the ground state. The nitrogen molecules help to excite CO2 to the upper laser level. Nitrogen molecules are excited first. This is most often done with high voltage direct current, but may also be accomplished by radio frequency excitation. Energy level of the nitrogen molecule is nearly resembles to the (001) vibrational levels of CO2 molecule. Laser transition takes place between initial level (001) and final levels (100) and (020), resulting in 10.6 and 9.6 μm laser radiations, respectively. The nitrogen molecules mechanically transfer energy to CO2 molecules via collisions. In practice, the presence of N2 significantly enhances laser operation, and that gas is almost always present in CO2 lasers. Helium plays a dual role. It serves as a buffer gas to aid in heat transfer and helps the CO2 molecules drop from the lower laser levels to the ground state, thus maintaining the population inversion needed for laser operation. However, the laser radiation at 10.6 μm is the strongest and forms the most usual mode of operation. This process is efficient only if the carbon dioxide is cold, so that its energy levels match that of the nitrogen. High-power systems use elaborate heat exchangers to keep the gas cool. The type of CO2 lasers as slow flow, transverse or cross flow and fast axial flow determines the properties of a CO2 laser. CO2 lasers are capable of both continuous wave (CW) and pulsed operation (Wilson and Hawkes 1987) and in most

Table 2. Comparison of Gas Lasers

**2.2 Excitation mechanism of CO2 lasers** 

systems; the electric excitation is controlled to do this.

Fig. 1. Vibrational Modes of CO2 Molecule

The first gas laser, a helium-neon type, conceived and developed by Ali Javan. It was demonstrated for the first time on December 12, 1960, at Bell Telephone Laboratories in Murray Hill, New Jersey. Gas lasers have certain advantages such as homogeneous medium, easy transportation for replenishment, cooling and relatively inexpensive. However, due to physical nature of the gases (low densities), a large volume of gas is required to achieve the significant population inversion for laser action. Hence, gas lasers are usually relatively larger than the solid-state lasers. Gas lasers can be classified into atomic, ionic, and molecular lasers depending on whether the laser transitions are taking place between the energy levels of atoms, ions, and molecules respectively. There are several laser systems in each class. Only some of the typical gas lasers and their wavelengths are shown below in Table-1.


Table 1. Gas lasers and Their Wavelengths

#### **2.1 Carbon dioxide lasers**

C.K.N. Patel in 1964 working at Bell laboratories made the most efficient gas laser, known as carbon dioxide (CO2) laser. The carbon dioxide laser is one of the most versatile type laser on the market today and most widely used materials processing laser. Also, they are efficient and inexpensive in terms of cost per unit power. It emits infrared radiation between 9 and 11 micro-meters (μm), either at a single line selected by the user or on the strongest lines in un-tuned cavities. It can produce continuous output powers ranging from well under 1 watt (W) for scientific applications to many kilowatts (kW) for material processing. It can generate pulses from the nanosecond to millisecond regimes. Custom-made CO2 lasers have produced continuous beams of hundreds of kilowatts for military laser weapon research (Hecht, 1984) or nanosecond-long pulses of 40 kilojoules (kJ) for research in laserinduced nuclear fusion (Los Alamos National Laboratory, 1982). This versatility comes from the fact that there are several distinct types of carbon dioxide lasers. Thus users see several distinct types, such as waveguide, low-power sealed-tube, high-power flowing-gas, and pulsed transversely excited CO2 lasers. The great interest in carbon dioxide lasers stems from their continuous power capability, high efficiency and ease of construction. Table-2 illustrates their advantages over other gas lasers.

The first gas laser, a helium-neon type, conceived and developed by Ali Javan. It was demonstrated for the first time on December 12, 1960, at Bell Telephone Laboratories in Murray Hill, New Jersey. Gas lasers have certain advantages such as homogeneous medium, easy transportation for replenishment, cooling and relatively inexpensive. However, due to physical nature of the gases (low densities), a large volume of gas is required to achieve the significant population inversion for laser action. Hence, gas lasers are usually relatively larger than the solid-state lasers. Gas lasers can be classified into atomic, ionic, and molecular lasers depending on whether the laser transitions are taking place between the energy levels of atoms, ions, and molecules respectively. There are several laser systems in each class. Only some of the typical gas lasers and their wavelengths are

> Laser Type Wavelength (nm) ArF 191 KrF 249 XeCl 308 HeCd 325, 441.5 XeF 351 Argon 488, 514.5 Copper vapor 510.6, 578.2 Krypton 520–676 Gold vapor 628 HeNe 632.8 CO2 10,600

C.K.N. Patel in 1964 working at Bell laboratories made the most efficient gas laser, known as carbon dioxide (CO2) laser. The carbon dioxide laser is one of the most versatile type laser on the market today and most widely used materials processing laser. Also, they are efficient and inexpensive in terms of cost per unit power. It emits infrared radiation between 9 and 11 micro-meters (μm), either at a single line selected by the user or on the strongest lines in un-tuned cavities. It can produce continuous output powers ranging from well under 1 watt (W) for scientific applications to many kilowatts (kW) for material processing. It can generate pulses from the nanosecond to millisecond regimes. Custom-made CO2 lasers have produced continuous beams of hundreds of kilowatts for military laser weapon research (Hecht, 1984) or nanosecond-long pulses of 40 kilojoules (kJ) for research in laserinduced nuclear fusion (Los Alamos National Laboratory, 1982). This versatility comes from the fact that there are several distinct types of carbon dioxide lasers. Thus users see several distinct types, such as waveguide, low-power sealed-tube, high-power flowing-gas, and pulsed transversely excited CO2 lasers. The great interest in carbon dioxide lasers stems from their continuous power capability, high efficiency and ease of construction. Table-2

shown below in Table-1.

Table 1. Gas lasers and Their Wavelengths

illustrates their advantages over other gas lasers.

**2.1 Carbon dioxide lasers** 


Table 2. Comparison of Gas Lasers

#### **2.2 Excitation mechanism of CO2 lasers**

The CO2 laser is a gas discharge device which operates by electric excitation. The active medium in a CO2 laser is a mixture of carbon dioxide, nitrogen, and helium. Each gas plays a distinct role. Carbon dioxide is the light emitter. The CO2 molecules are excited so they vibrate in three different types such as symmetric stretching, bending, and asymmetric stretching (Fig. 1). The molecules then lose part of the excitation energy by dropping to one of two other, lower energy vibrational states as shown in Fig.2. Once the molecules have emitted their laser photons, they continue to drop down the energy-level ladder until they reach the ground state. The nitrogen molecules help to excite CO2 to the upper laser level. Nitrogen molecules are excited first. This is most often done with high voltage direct current, but may also be accomplished by radio frequency excitation. Energy level of the nitrogen molecule is nearly resembles to the (001) vibrational levels of CO2 molecule. Laser transition takes place between initial level (001) and final levels (100) and (020), resulting in 10.6 and 9.6 μm laser radiations, respectively. The nitrogen molecules mechanically transfer energy to CO2 molecules via collisions. In practice, the presence of N2 significantly enhances laser operation, and that gas is almost always present in CO2 lasers. Helium plays a dual role. It serves as a buffer gas to aid in heat transfer and helps the CO2 molecules drop from the lower laser levels to the ground state, thus maintaining the population inversion needed for laser operation. However, the laser radiation at 10.6 μm is the strongest and forms the most usual mode of operation. This process is efficient only if the carbon dioxide is cold, so that its energy levels match that of the nitrogen. High-power systems use elaborate heat exchangers to keep the gas cool. The type of CO2 lasers as slow flow, transverse or cross flow and fast axial flow determines the properties of a CO2 laser. CO2 lasers are capable of both continuous wave (CW) and pulsed operation (Wilson and Hawkes 1987) and in most systems; the electric excitation is controlled to do this.

Fig. 1. Vibrational Modes of CO2 Molecule

Diffusion Cooled V-Fold CO2 Laser 183

recombination reaction. Such measures can be used to produce sealed CO2 lasers which can operate for up to several thousand hours before their output seriously degrades. Sometimes hydrogen or water to the gas mixture is added so that it can regenerate CO2 by the carbon monoxide produced by the discharge. In traditional sealed CO2 lasers, the maximum output power possible with this longitudinal discharge is about 50 W per meter of cavity length, and maximum continuous-wave output is about 100 W. A new methodology is radiofrequency (RF) discharge transverse to the tube axis. This design does not require high-voltage electrodes and offers some other advantages, including the ability to electronically control output at rates to 10 kilohertz (kHz), lower operating voltage and potentially lower tube cost. On the other hand, RF power supplies are more complex and less efficient than DC supplies. RF excitation has been growing in popularity for sealed-tube CO2 lasers. It can generate more power because it can excite a broader area than a DC discharge, but it also works well at low powers. All sealed-tube CO2 lasers are limited in output by the difficulty in removing heat.

This type of laser structure is efficient way to produce a compact CW CO2 laser. It consists of two transverse radio-frequency (RF) electrodes separated by insulating sections. An RF power supply is connected to the electrodes to provide a high-frequency alternating field across the electrodes within the bore region. The waveguide modes access the entire gain volume since the modes reflect off the discharge walls in a zigzag fashion. The waveguide itself traverses the laser length in a zigzag. Waveguide lasers are a type of sealed CO2 laser in which the inner diameter of a sealed CO2 laser is shrunk to a few millimeters and the tube

> Minimize Voltage Variation Permitting uniform pumping

The waveguide design limits diffraction losses that would otherwise impair operation of a narrow-tube laser. The tube normally is sealed with a gas reservoir separate from the waveguide itself. Waveguide lasers may be excited by DC discharges or intense RF fields. Waveguides may be made of metal, dielectric or combinations of the two. The waveguide laser is very attractive for low powers, particularly under about 50 W. It provides a good beam quality. It can operate continuously or pulsed and can be readily tuned to many discrete lines in the CO2 spectrum. Its size is comparable to the size of a helium-neon laser

is constructed in the form of a waveguide, as shown in Fig. 4.

**2.3.2 Waveguide lasers**

Fig. 4. Waveguide Laser

but able to generate power in watts.

The energy level diagram for the operation of CO2 laser is shown in Fig.2.

Fig. 2. Energy Level Diagram of CO2 Laser

#### **2.3 Types of CO2 lasers**

#### **2.3.1 Sealed-tube lasers**

The sealed-tube CO2 laser is a glass tube filled with CO2, He, and N2, with mirrors forming a resonant cavity, as shown in Fig.3.

Fig. 3. Sealed Tube Laser

Electrodes are placed near the two ends of the tube. Proper gas mixtures are filled in the tube and seal it. A high voltage is applied to the electrodes to pass a discharge through the gas. A sealed CO2 laser with an ordinary gas mixture would stop operating within a few minutes. The electric discharge in the tube breaks down the CO2 in CO and O2. Catalyst is added in the path to regenerate CO2. Nickel cathode (at 300°C) can catalyze the

The sealed-tube CO2 laser is a glass tube filled with CO2, He, and N2, with mirrors forming a

Electrodes are placed near the two ends of the tube. Proper gas mixtures are filled in the tube and seal it. A high voltage is applied to the electrodes to pass a discharge through the gas. A sealed CO2 laser with an ordinary gas mixture would stop operating within a few minutes. The electric discharge in the tube breaks down the CO2 in CO and O2. Catalyst is added in the path to regenerate CO2. Nickel cathode (at 300°C) can catalyze the

The energy level diagram for the operation of CO2 laser is shown in Fig.2.

Fig. 2. Energy Level Diagram of CO2 Laser

**2.3 Types of CO2 lasers 2.3.1 Sealed-tube lasers**

Fig. 3. Sealed Tube Laser

resonant cavity, as shown in Fig.3.

recombination reaction. Such measures can be used to produce sealed CO2 lasers which can operate for up to several thousand hours before their output seriously degrades. Sometimes hydrogen or water to the gas mixture is added so that it can regenerate CO2 by the carbon monoxide produced by the discharge. In traditional sealed CO2 lasers, the maximum output power possible with this longitudinal discharge is about 50 W per meter of cavity length, and maximum continuous-wave output is about 100 W. A new methodology is radiofrequency (RF) discharge transverse to the tube axis. This design does not require high-voltage electrodes and offers some other advantages, including the ability to electronically control output at rates to 10 kilohertz (kHz), lower operating voltage and potentially lower tube cost. On the other hand, RF power supplies are more complex and less efficient than DC supplies. RF excitation has been growing in popularity for sealed-tube CO2 lasers. It can generate more power because it can excite a broader area than a DC discharge, but it also works well at low powers. All sealed-tube CO2 lasers are limited in output by the difficulty in removing heat.

#### **2.3.2 Waveguide lasers**

This type of laser structure is efficient way to produce a compact CW CO2 laser. It consists of two transverse radio-frequency (RF) electrodes separated by insulating sections. An RF power supply is connected to the electrodes to provide a high-frequency alternating field across the electrodes within the bore region. The waveguide modes access the entire gain volume since the modes reflect off the discharge walls in a zigzag fashion. The waveguide itself traverses the laser length in a zigzag. Waveguide lasers are a type of sealed CO2 laser in which the inner diameter of a sealed CO2 laser is shrunk to a few millimeters and the tube is constructed in the form of a waveguide, as shown in Fig. 4.

Fig. 4. Waveguide Laser

The waveguide design limits diffraction losses that would otherwise impair operation of a narrow-tube laser. The tube normally is sealed with a gas reservoir separate from the waveguide itself. Waveguide lasers may be excited by DC discharges or intense RF fields. Waveguides may be made of metal, dielectric or combinations of the two. The waveguide laser is very attractive for low powers, particularly under about 50 W. It provides a good beam quality. It can operate continuously or pulsed and can be readily tuned to many discrete lines in the CO2 spectrum. Its size is comparable to the size of a helium-neon laser but able to generate power in watts.

Diffusion Cooled V-Fold CO2 Laser 185

flow lasers because the gas moves very quickly through the discharge zone. After leaving the discharge zone, the gas is cooled by heat exchanger. The fast axial-flow laser has become the most common industrial CO2 laser in the power range of 500 W to 5 kW, because of short resonator and small floor space required. Besides the advantages, these lasers have

In transverse flow lasers, gas flow direction, electric discharge and direction of laser cavity axis are in three mutually perpendicular directions as shown in Fig.7. It can produce very

The gas flows across a much wider region and recycled by passing it through a system which regenerates CO2 and adds some fresh gas to the mixture. In this laser, beam mode structure and beam symmetry are considerably poorer than in fast or slow axial-flow lasers.

At the end of the 1960s, the gas-dynamic laser was an important breakthrough that made it possible for the first time to reach power levels of 100 kW or more. Basic structure of gas dynamic laser is shown in Fig.8. In gas dynamic lasers the gas is flowed in the transverse direction to the laser axis. Laser gas which is initially at a pressure of several atmospheres is heated electrically or thermally to excite the molecules and population inversion takes place. The high speed pumps are used to rapidly flow the gas. It is then allowed to expand supersonically through an expansion nozzle into a low-pressure region. This expansion causes the gas to supercool and thereby provide rapid relaxation of the lower laser level from the highest rotational states to the lowest rotational states, leaving a population inversion of those empty higher lying rotational states with respect to the upper laser level. A laser beam is extracted from the gas by placing a pair of mirrors on opposite sides of the expansion chamber. Lasers of this design have produced CW output powers greater than 100 kW. This type of excitation was developed primarily for military applications, but

lower-power versions have found applications in materials processing.

some limitations of complex system design and poor mode quality.

**2.3.5 Transverse flow laser**

Fig. 7. Transverse Flow Laser

**2.3.6 Gas dynamic laser**

high power of the order of 10 kW per meter.

#### **2.3.3 Longitudinal (axial) slow flow laser**

These lasers are operated as conventional gas discharge lasers in the form of long, narrow, cylindrically shaped glass enclosures with electrodes at opposite ends from which the discharge excitation current is introduced as shown in Fig.5. These lasers can be either pulsed or continuous wave and can have lengths of up to several meters. In some versions the discharge enclosure is sealed off and in other versions the gas flows through the tube longitudinally and can be re-circulated to conserve the gases. A water coolant jacket usually surrounds the discharge region. Electric discharge is applied along the tube's axis.

Fig. 5. Longitudinal (Axial) Slow Flow Laser

Low gas pressure and low consumption of gas by recycling methods are some of the salient features of this laser. Slow axial-flow CO2 lasers produce continuous-wave output proportional to the tube length. Average or continuous power of about 500 W can be produced by folding the laser beam with mirrors through multiple tube segments. This also makes the system compact and the design is simple enough. Heat is removed by conduction mode of heat transfer. Laser gases transfer its heat to the walls of the tube and ultimately that heat can be removed by water circulation or other coolant around the tube.

#### **2.3.4 Fast axial flow laser**

The efficiency of axial flow lasers can be increased dramatically by using a pump or turbine to move the gas rapidly through the discharge area as shown in Fig.6.

Fig. 6. Fast Axial Flow Laser

This design allows short resonators to produce relatively high powers; 800 W/m is a typical value of power per unit length. Excitation usually is with a longitudinal discharge, as in slow axial-flow lasers, but some fast axial-flow lasers are powered by radio-frequency discharges. The main advantage of the fast flow is that it cools the laser gas better than slow-

These lasers are operated as conventional gas discharge lasers in the form of long, narrow, cylindrically shaped glass enclosures with electrodes at opposite ends from which the discharge excitation current is introduced as shown in Fig.5. These lasers can be either pulsed or continuous wave and can have lengths of up to several meters. In some versions the discharge enclosure is sealed off and in other versions the gas flows through the tube longitudinally and can be re-circulated to conserve the gases. A water coolant jacket usually

Low gas pressure and low consumption of gas by recycling methods are some of the salient features of this laser. Slow axial-flow CO2 lasers produce continuous-wave output proportional to the tube length. Average or continuous power of about 500 W can be produced by folding the laser beam with mirrors through multiple tube segments. This also makes the system compact and the design is simple enough. Heat is removed by conduction mode of heat transfer. Laser gases transfer its heat to the walls of the tube and ultimately

The efficiency of axial flow lasers can be increased dramatically by using a pump or turbine

This design allows short resonators to produce relatively high powers; 800 W/m is a typical value of power per unit length. Excitation usually is with a longitudinal discharge, as in slow axial-flow lasers, but some fast axial-flow lasers are powered by radio-frequency discharges. The main advantage of the fast flow is that it cools the laser gas better than slow-

that heat can be removed by water circulation or other coolant around the tube.

to move the gas rapidly through the discharge area as shown in Fig.6.

surrounds the discharge region. Electric discharge is applied along the tube's axis.

**2.3.3 Longitudinal (axial) slow flow laser**

Fig. 5. Longitudinal (Axial) Slow Flow Laser

**2.3.4 Fast axial flow laser**

Fig. 6. Fast Axial Flow Laser

flow lasers because the gas moves very quickly through the discharge zone. After leaving the discharge zone, the gas is cooled by heat exchanger. The fast axial-flow laser has become the most common industrial CO2 laser in the power range of 500 W to 5 kW, because of short resonator and small floor space required. Besides the advantages, these lasers have some limitations of complex system design and poor mode quality.

#### **2.3.5 Transverse flow laser**

In transverse flow lasers, gas flow direction, electric discharge and direction of laser cavity axis are in three mutually perpendicular directions as shown in Fig.7. It can produce very high power of the order of 10 kW per meter.

Fig. 7. Transverse Flow Laser

The gas flows across a much wider region and recycled by passing it through a system which regenerates CO2 and adds some fresh gas to the mixture. In this laser, beam mode structure and beam symmetry are considerably poorer than in fast or slow axial-flow lasers.

#### **2.3.6 Gas dynamic laser**

At the end of the 1960s, the gas-dynamic laser was an important breakthrough that made it possible for the first time to reach power levels of 100 kW or more. Basic structure of gas dynamic laser is shown in Fig.8. In gas dynamic lasers the gas is flowed in the transverse direction to the laser axis. Laser gas which is initially at a pressure of several atmospheres is heated electrically or thermally to excite the molecules and population inversion takes place. The high speed pumps are used to rapidly flow the gas. It is then allowed to expand supersonically through an expansion nozzle into a low-pressure region. This expansion causes the gas to supercool and thereby provide rapid relaxation of the lower laser level from the highest rotational states to the lowest rotational states, leaving a population inversion of those empty higher lying rotational states with respect to the upper laser level. A laser beam is extracted from the gas by placing a pair of mirrors on opposite sides of the expansion chamber. Lasers of this design have produced CW output powers greater than 100 kW. This type of excitation was developed primarily for military applications, but lower-power versions have found applications in materials processing.

Diffusion Cooled V-Fold CO2 Laser 187

transverse gas flow, depending on power levels. The prime attractions of TEA lasers are their generation of short, intense pulses and the extraction of high power per unit volume of laser gas. High-pressure operation also broadens emission lines, permitting the use of mode locking techniques to generate pulses lasting about 1 nanosecond. It allows tuning over

Table-3 illustrate a comparison among details of attainable laser power per cubic cm of

CO2 Laser System Power Scaling (W/m)

In the previous paragraphs, we studied about a brief history of lasers and some details about the CO2 lasers. Here we are going to study about the topic of this chapter i.e. "V-fold diffusion cooled laser" in detail. Fig. 10 is a real photograph of 500 W diffusion cooled CO2 laser indigenously developed at Department of Atomic Energy, Raja Ramanna Centre for

V-fold laser is also a type of CO2 laser with some salient features. The name V-fold is given to this laser because of its resonator geometry which is V-folded resonator. Basically this laser is slow flow diffusion cooled CO2 laser. Convection accompanied by conduction is the mode of heat transfer of this laser. Compare to convective cooled lasers, diffusion cooled laser devoid of bulky heat exchangers and blowers. It makes laser head more attractive, compact & simple in the power range of 300-500 W. In the diffusion cooled laser the laser power can be scaled up by increasing the discharge length at the rate of 50 W/m. We

Sealed-off systems 70 Slow flow systems 100 Fast flow systems 800 Pulsed system (TEA Laser) 1.2 TW pulse

Table 3. Comparison of Power Scaling of Different Types of CO2 Lasers

most of the CO2 wavelength range.

active volume in the different types of CO2 lasers.

**3. V-fold diffusion cooled CO2 laser** 

Advanced Technology, Indore, MP, India.

Fig. 10. Photograph of Diffusion Cooled V-fold CO2 Laser

Fig. 8. Gas Dynamic Laser

#### **2.3.7 Transversely Excited Atmospheric (TEA) flow laser**

These lasers operate at high total gas pressures of 1 atmosphere or more in order to benefit from obtaining a much higher energy output per unit volume of gas. A schematic of TEA CO2 laser is shown in Fig.9.

Fig. 9. Transversely Excited Atmospheric (TEA) Flow Laser

Extremely high voltages are required initially to ionize the gas and thereby initiate the discharge process to operate the laser at high pressure. Due to the high gas pressure, arcing tends to form within the discharge. In a transverse discharge, the two electrodes are placed parallel to each other over the length of the discharge and a high voltage is applied across the electrodes. Pre-ionization is used to ionize the space between the electrodes uniformly before applying the high voltage. With this pre-ionization, the discharge can then proceed in a uniform fashion over the entire electrode assembly rather than forming a narrow highcurrent arc at just one location. The pre-ionization is produced by flashes of ultraviolet light from a row of pre-ionizing UV spark discharges. Such lasers can produce many joules of energy for unit discharge volume. Tens of nanoseconds to microseconds pulse can be produced by passing electric pulses through the gas in a direction transverse to the laser cavity axis. TEA lasers are available in versions with sealed tubes, slow or fast axial flow, or

These lasers operate at high total gas pressures of 1 atmosphere or more in order to benefit from obtaining a much higher energy output per unit volume of gas. A schematic of TEA

Extremely high voltages are required initially to ionize the gas and thereby initiate the discharge process to operate the laser at high pressure. Due to the high gas pressure, arcing tends to form within the discharge. In a transverse discharge, the two electrodes are placed parallel to each other over the length of the discharge and a high voltage is applied across the electrodes. Pre-ionization is used to ionize the space between the electrodes uniformly before applying the high voltage. With this pre-ionization, the discharge can then proceed in a uniform fashion over the entire electrode assembly rather than forming a narrow highcurrent arc at just one location. The pre-ionization is produced by flashes of ultraviolet light from a row of pre-ionizing UV spark discharges. Such lasers can produce many joules of energy for unit discharge volume. Tens of nanoseconds to microseconds pulse can be produced by passing electric pulses through the gas in a direction transverse to the laser cavity axis. TEA lasers are available in versions with sealed tubes, slow or fast axial flow, or

Fig. 8. Gas Dynamic Laser

CO2 laser is shown in Fig.9.

**2.3.7 Transversely Excited Atmospheric (TEA) flow laser**

Fig. 9. Transversely Excited Atmospheric (TEA) Flow Laser

transverse gas flow, depending on power levels. The prime attractions of TEA lasers are their generation of short, intense pulses and the extraction of high power per unit volume of laser gas. High-pressure operation also broadens emission lines, permitting the use of mode locking techniques to generate pulses lasting about 1 nanosecond. It allows tuning over most of the CO2 wavelength range.

Table-3 illustrate a comparison among details of attainable laser power per cubic cm of active volume in the different types of CO2 lasers.


Table 3. Comparison of Power Scaling of Different Types of CO2 Lasers

### **3. V-fold diffusion cooled CO2 laser**

In the previous paragraphs, we studied about a brief history of lasers and some details about the CO2 lasers. Here we are going to study about the topic of this chapter i.e. "V-fold diffusion cooled laser" in detail. Fig. 10 is a real photograph of 500 W diffusion cooled CO2 laser indigenously developed at Department of Atomic Energy, Raja Ramanna Centre for Advanced Technology, Indore, MP, India.

Fig. 10. Photograph of Diffusion Cooled V-fold CO2 Laser

V-fold laser is also a type of CO2 laser with some salient features. The name V-fold is given to this laser because of its resonator geometry which is V-folded resonator. Basically this laser is slow flow diffusion cooled CO2 laser. Convection accompanied by conduction is the mode of heat transfer of this laser. Compare to convective cooled lasers, diffusion cooled laser devoid of bulky heat exchangers and blowers. It makes laser head more attractive, compact & simple in the power range of 300-500 W. In the diffusion cooled laser the laser power can be scaled up by increasing the discharge length at the rate of 50 W/m. We

Diffusion Cooled V-Fold CO2 Laser 189

The above relation is valid only when the rise in laser gas temperature ΔT ~250°C, without bottlenecking at the lower laser level and maintaining a stable and uniform discharge. The temperature above 250°C populates the lower laser level and destroys population inversion. From Eq.(5), a larger mass flow rate is required for higher laser power. Mass flow rate depends upon area of discharge zone, gas flow velocity or gas mixture density. Since the density for a gas mixture is constant at a particular pressure. So increasing either area of discharge zone or gas flow velocity can only increase power. Discharge Area (A) is the function of electrode separation or discharge height (d) and discharge length (L). So the laser power would increase with the increase of d or L. But it is observed that the maximum discharge current, discharge voltage and the laser power remained almost constant for different electrode separations (d). This is because of the electric field would remain constant to maintain the same discharge current. Laser power may also increase with the discharge length (L) but we found that on increasing the length after a certain optimum value, power decreases due to saturation and due to predominance of cavity losses. Also there are limitations of space and alignment on increasing the discharge length. Therefore length cannot be increased after a certain optimum value to increase the power. Thus, after certain value, increasing either discharge length (L) or electrode separation (d) cannot increase laser power i.e. the discharge area cannot be increased too much. Thus to increase the power gas flow velocity may be increased. So to achieve more gas flow velocity, higher capacity pumps/blowers with high discharge and high pressure are required. An effective heat exchanger is needed to dissipate the heat and to keep the gas temperature below 250°C

CO2 Laser Systems Power (kW/m3)

Transverse Flow 1500 Fast Axial Flow 3000 Slab Laser 3300

Diffusion Cooled (length scaling) 500

<sup>η</sup> − 1� . �. C�. ΔT. V�. �. � � 1�� �� (5)

In a convective cooled laser, the laser power can be scaled up with the following equation:

P� = � <sup>η</sup>

Where

� = electro-optic efficiency, ρ = laser gas density,

in discharge zone.

Table 4. Power per Unit Volume of Laser Gas

C� = specific heat of laser gas, ΔT = rise in laser gas temperature, �� = flow velocity of laser gas, L = discharge length and

d = discharge height or electrode separation, �� = mass flow rate of gas through discharge zone

adopted symmetric concave resonator geometry to reduce diffraction loss. V-folding over a cylindrical surface minimizes the astigmatism effect. We obtained more than 380 W laser power in a 7.5 meter discharge length.

#### **3.1 Design considerations**

In order to design a V-fold CO2 laser, the physical dimensions of the active volume, gas flow velocity, output coupling of optical resonator are to be decided. The desired output power *Po* can be calculated for the required volume of the active medium, if we know the typical input power density *Pin* that can be dissipated in the homogeneous and stable discharge. *Pin* depends on several factors such as electrode design, gas mixture, its pressure, excitation method, gas flow velocity and its uniformity. Following considerations are taken into account in determining the design parameters such as the discharge length, discharge aperture, optimum reflectivity and gas pressure.


$$T\_{opt} = 1 - \exp\left[-2L\left\{\left(\mathbf{g}\_0 \times a\right)^{1/2} - a\right\}\right] \tag{1}$$

iii. The small signal gain is usually experimentally measured and it is in the range of 0.5 to 1% per cm. In optimum laser design it can be seen that the transmissivity (*T*) is almost constant, independent of small signal gain and the laser power. We can write for the intra-cavity intensity *Ic* incident on the output coupler as:

$$\mathbf{l\_c = l\_s \times g\_0 \times L} \tag{2}$$

$$\frac{\mathbf{I\_c}}{\mathbf{I\_s}} = \mathbf{g\_0} \times \mathbf{L} \tag{3}$$

iv. The damage threshold of the output coupler limits the maximum value of *Ic* and thus the maximum value of g� × L is also limited. In the optimum laser design the intracavity losses a×L is kept minimum and this is also independent of laser power. Usually the total intra-cavity loss should not be more than 5% of total gain. Thus, g� × L and a × L being constant, the optimum transmittivity T��� is also constant. For the typical values of I�and I� are about 300-500 W/cm2 and 1 kW/cm2 respectively. g� × L is in the range of 2-3 in high power lasers. For these conditions:

$$\text{T}\_{\text{opt}} \approx 50 - 60\% \tag{4}$$

v. Minimum diffraction loss in the resonator criterion should also be considered in designing the V-fold resonator.

In a convective cooled laser, the laser power can be scaled up with the following equation:

$$\text{P}\_{\text{L}} = \left[\frac{\eta}{\eta - 1}\right], \rho. \text{C}\_{\text{p}}.\Delta \text{T. V}. \text{L}. \text{d} \approx \ 120 \ \dot{M} \tag{5}$$

Where

188 CO2 Laser – Optimisation and Application

adopted symmetric concave resonator geometry to reduce diffraction loss. V-folding over a cylindrical surface minimizes the astigmatism effect. We obtained more than 380 W laser

In order to design a V-fold CO2 laser, the physical dimensions of the active volume, gas flow velocity, output coupling of optical resonator are to be decided. The desired output power *Po* can be calculated for the required volume of the active medium, if we know the typical input power density *Pin* that can be dissipated in the homogeneous and stable discharge. *Pin* depends on several factors such as electrode design, gas mixture, its pressure, excitation method, gas flow velocity and its uniformity. Following considerations are taken into account in determining the design parameters such as the discharge length, discharge

i. The maximum laser power density should be less than the damage threshold of optical elements, however, it should be more than the saturation intensity Is which is proportional to ��, where p is gas pressure in mbar and n = 2 in slow flow laser. The damage threshold intensity of the ZnSe mirror, usually used as output coupler in CO2 lasers is about 2 kW/cm2. Considering this the incident intensity *Ic* on the output

ii. The optimum output coupling or transmissivity (*T*) of the resonator can be estimated with the knowledge of the discharge length '*L*' small signal gain '*go*' and the intra-cavity

iii. The small signal gain is usually experimentally measured and it is in the range of 0.5 to 1% per cm. In optimum laser design it can be seen that the transmissivity (*T*) is almost constant, independent of small signal gain and the laser power. We can write for the

> I� I�

iv. The damage threshold of the output coupler limits the maximum value of *Ic* and thus the maximum value of g� × L is also limited. In the optimum laser design the intracavity losses a×L is kept minimum and this is also independent of laser power. Usually the total intra-cavity loss should not be more than 5% of total gain. Thus, g� × L and a × L being constant, the optimum transmittivity T��� is also constant. For the typical values of I�and I� are about 300-500 W/cm2 and 1 kW/cm2 respectively. g� × L

v. Minimum diffraction loss in the resonator criterion should also be considered in

���� = � − ��� �−�� ��g� × ��� �� − ��� (1)

I� = I� × g� × L (2)

T��� ≈ 50 − 60% (4)

= g� × L (3)

power in a 7.5 meter discharge length.

aperture, optimum reflectivity and gas pressure.

losses (*a*) by the following relation:

designing the V-fold resonator.

coupler should be maintained at around 1.0 kW/cm2.

intra-cavity intensity *Ic* incident on the output coupler as:

is in the range of 2-3 in high power lasers. For these conditions:

**3.1 Design considerations** 

� = electro-optic efficiency, ρ = laser gas density, C� = specific heat of laser gas, ΔT = rise in laser gas temperature, �� = flow velocity of laser gas, L = discharge length and d = discharge height or electrode separation, �� = mass flow rate of gas through discharge zone

The above relation is valid only when the rise in laser gas temperature ΔT ~250°C, without bottlenecking at the lower laser level and maintaining a stable and uniform discharge. The temperature above 250°C populates the lower laser level and destroys population inversion. From Eq.(5), a larger mass flow rate is required for higher laser power. Mass flow rate depends upon area of discharge zone, gas flow velocity or gas mixture density. Since the density for a gas mixture is constant at a particular pressure. So increasing either area of discharge zone or gas flow velocity can only increase power. Discharge Area (A) is the function of electrode separation or discharge height (d) and discharge length (L). So the laser power would increase with the increase of d or L. But it is observed that the maximum discharge current, discharge voltage and the laser power remained almost constant for different electrode separations (d). This is because of the electric field would remain constant to maintain the same discharge current. Laser power may also increase with the discharge length (L) but we found that on increasing the length after a certain optimum value, power decreases due to saturation and due to predominance of cavity losses. Also there are limitations of space and alignment on increasing the discharge length. Therefore length cannot be increased after a certain optimum value to increase the power. Thus, after certain value, increasing either discharge length (L) or electrode separation (d) cannot increase laser power i.e. the discharge area cannot be increased too much. Thus to increase the power gas flow velocity may be increased. So to achieve more gas flow velocity, higher capacity pumps/blowers with high discharge and high pressure are required. An effective heat exchanger is needed to dissipate the heat and to keep the gas temperature below 250°C in discharge zone.


Table 4. Power per Unit Volume of Laser Gas

Diffusion Cooled V-Fold CO2 Laser 191

jacketed construction. Inner tubes have outer diameter 12 mm, inner diameter 9 mm and length 750 mm. Outer (jacket) tubes are having 22 mm OD (Fig.13). Outer tubes also have ports for water inlet and outlet. Water flows through the annular space between inner and outer tube. A chiller unit supplies water at a total flow rate 12 lit/min and 15°C in water

ANODE BLOCK

WATER OUTLET

jackets for cooling of gases.

Fig. 11. Components of V-fold CO2 Laser

Fig. 12. Photograph of Anode Block

WATER INLET

Fig. 13. Schematic of Water Jacket


Table 5. Discharge Volume to Total Volume Ratio of Different Types of CO2 Lasers

As we go from diffusion-cooled lasers to convective cooled lasers, the power-scaling move from length to volume. From calculation, slab lasers give more power per cubic meter of laser gas compared to various types of CO2 lasers. Following tables shows the laser power output for unit volume of laser gas (Table-4) and typical volume of discharge region to total volume in percentage (Table-5) for various types of CO2 laser.

From above two tables, it is concluded that the maximum power could be achieved in slab laser and power is moderate in transverse flow laser. In all other laser, except transverse flow lasers, the power scaling up to multi-kilowatt is not easy. The laser power depends on length of active medium (diffusion cooled) or area of discharge electrode (in slab laser) but in transverse flow lasers, power is scaled-up by volume so it is relatively easy. From the above data, it is clear that the power per unit laser gas and discharge volume to total volume ratio is maximum for slab laser. So, if we somehow move from transverse configuration to Slab (area) or diffusion cooled configuration then we can definitely enhance the power of our laser.

#### **3.2 Construction of V-fold laser**

The complete laser assembly is mounted on a 3 meter long aluminum pipe (Fig.11). Outer diameter of aluminum pipe is 200 mm. Since the whole laser assembly is mounted on this pipe only therefore best possible straightness of pipe was required. It is very difficult to get single pipe of 3 meter length and straightness 1 mm therefore the whole pipe is casted in 3 segments, each of 1 meter. All the three segments are welded with straightness in 1 mm. To maintain the straightness and rigidity, both the ends are joined with a flange and tie rod. The aluminum pipe is supported at the ends by a support system made of stainless steel plate of 10 mm thick. Bottom of support system is bolted with the support table. There is no middle support for the pipe due to assembly constraints of glass tube. Since the straightness of tube is very important we calculated the deflection at the mid-point of pipe and it is found that the deflection is insignificant. Five rings of stainless steel 304 (SS304) are inserted in the pipe.

Anode support ring is supporting the anode part of this laser at the center. Additional rings of nylon are also placed near to this central ring to give extra support to the joint of glass tube and anode block. Anode block is made of metalon-6 which acts as insulator (Fig.12). Anode pins made of SS304 are placed at the center separated/isolated by metalon-6 tube. The anode block contains two anodes at each end. Anodes are made of stainless steel. Viton® O-rings are used in between glass tube and anode for sealing. Gas inlet ports are also provided on the anode block. Gas flows from the anode block to cathode through the glass tube. Low thermal expansion borosilicate glass tubes are used. These tubes have

Fast Axial Flow 10 Transverse Flow 14 Diffusion Cooled 20 Slab Laser 27

Table 5. Discharge Volume to Total Volume Ratio of Different Types of CO2 Lasers

volume in percentage (Table-5) for various types of CO2 laser.

our laser.

in the pipe.

**3.2 Construction of V-fold laser** 

As we go from diffusion-cooled lasers to convective cooled lasers, the power-scaling move from length to volume. From calculation, slab lasers give more power per cubic meter of laser gas compared to various types of CO2 lasers. Following tables shows the laser power output for unit volume of laser gas (Table-4) and typical volume of discharge region to total

From above two tables, it is concluded that the maximum power could be achieved in slab laser and power is moderate in transverse flow laser. In all other laser, except transverse flow lasers, the power scaling up to multi-kilowatt is not easy. The laser power depends on length of active medium (diffusion cooled) or area of discharge electrode (in slab laser) but in transverse flow lasers, power is scaled-up by volume so it is relatively easy. From the above data, it is clear that the power per unit laser gas and discharge volume to total volume ratio is maximum for slab laser. So, if we somehow move from transverse configuration to Slab (area) or diffusion cooled configuration then we can definitely enhance the power of

The complete laser assembly is mounted on a 3 meter long aluminum pipe (Fig.11). Outer diameter of aluminum pipe is 200 mm. Since the whole laser assembly is mounted on this pipe only therefore best possible straightness of pipe was required. It is very difficult to get single pipe of 3 meter length and straightness 1 mm therefore the whole pipe is casted in 3 segments, each of 1 meter. All the three segments are welded with straightness in 1 mm. To maintain the straightness and rigidity, both the ends are joined with a flange and tie rod. The aluminum pipe is supported at the ends by a support system made of stainless steel plate of 10 mm thick. Bottom of support system is bolted with the support table. There is no middle support for the pipe due to assembly constraints of glass tube. Since the straightness of tube is very important we calculated the deflection at the mid-point of pipe and it is found that the deflection is insignificant. Five rings of stainless steel 304 (SS304) are inserted

Anode support ring is supporting the anode part of this laser at the center. Additional rings of nylon are also placed near to this central ring to give extra support to the joint of glass tube and anode block. Anode block is made of metalon-6 which acts as insulator (Fig.12). Anode pins made of SS304 are placed at the center separated/isolated by metalon-6 tube. The anode block contains two anodes at each end. Anodes are made of stainless steel. Viton® O-rings are used in between glass tube and anode for sealing. Gas inlet ports are also provided on the anode block. Gas flows from the anode block to cathode through the glass tube. Low thermal expansion borosilicate glass tubes are used. These tubes have

CO2 Laser Systems Typical volume of discharge region

compared to total volume (%)

jacketed construction. Inner tubes have outer diameter 12 mm, inner diameter 9 mm and length 750 mm. Outer (jacket) tubes are having 22 mm OD (Fig.13). Outer tubes also have ports for water inlet and outlet. Water flows through the annular space between inner and outer tube. A chiller unit supplies water at a total flow rate 12 lit/min and 15°C in water jackets for cooling of gases.

Fig. 11. Components of V-fold CO2 Laser

Fig. 12. Photograph of Anode Block

Fig. 13. Schematic of Water Jacket

Diffusion Cooled V-Fold CO2 Laser 193

cathode blocks, which are connected to a rotary vane vacuum pump of pumping speed of 500 lit/min. Pressure, temperature and gas mixture have been optimized for the maximum output power. Optimum gas pressure is 30 mbar. In the diffusion cooled laser the laser power can be scaled up by increasing the discharge length at the rate of 50 W/m. With the increase of discharge length and therefore optical resonator length, the Fresnel number NF = r2 / λ.l where r, l and λ are the radius of mirror clear aperture, resonator length and laser wavelength respectively. NF reduces and with this the diffraction loss increases. Due to this the input power in a laser with plano-concave resonator did not scale up with discharge length beyond 3-4 meters. We adopted the symmetric concave resonator geometry to reduce diffraction loss and V-folding over a cylindrical surface instead of a flat surface for laying the discharge tubes to minimize the astigmatism effect. Each section of V-fold laser has about 1.5 meter discharge length, distance between two mirrors is 2.5 meter. All resonator mirrors i.e. rear reflector, ZnSe output coupler and all folding mirrors are having concave surface of 5 meter ROC. Since, the laser mode formed in any section are sustained in all the other sections therefore the length of one section determines the Fresnel number. Corresponding to the resultant Fresnel number the diffraction loss is low. Introduction of curved folding mirrors through a small folding angle of 5° could introduce considerable aberration due to astigmatism after large number of folding. In order to minimize the overall effect of astigmatism, the tubes were mounted on a cylindrical surface instead of a flat surface to have ~2π folding. The central supporting aluminum pipe due to high moment of inertia have minimum deflection thus minimizes the misalignment. With a fully reflecting mirror on the left and a partially transmitting mirror on the right, the device becomes a Vfold laser which radiates in the far infrared at 10.6 microns. Till date, 420 W power in 10.5

All gas discharges operated in the glow discharge region have electrical characteristics similar to those indicated in Fig.16. The voltage and current values and the exact shape of the curve depend on the type of gases, gas pressure and the length & diameter of the

meter discharge length is obtained from this laser system.

Fig. 16. Voltage-Current Curve of a Gaseous Discharge

**VOLTAGE**

**CURRENT**

**3.4 Electrical characteristics of V-fold laser** 

discharge tube.

The jacketed glass tube is supported by cathode block which is ultimately supported by a plate and ring over the aluminum pipe (Fig.14.). Two glass tubes in V-shape are supported by a cathode block on one side. Cathode block is made of SS304 have the advantage of low scaling problem caused by electrical discharge. A mirror holder is connected on the other side of the cathode block through a glass tube of 45 mm OD (Fig.14 & 15). Each mirror holder consists of one mirror and they are placed at the extreme ends on both sides. Mirror holder assembly is also supported on pipe through a ring and plate. Rear mirrors and folding mirrors are made of OFHC Copper substrate of 25 mm diameter and radius of curvature (ROC) 5 meter. Mirrors are gold coated with ∼99% reflectivity. Two micrometer screws are fitted on the back side of the each mirror holder to align the laser beam. Alignment is the most critical part of this laser. The alignment accuracy of 0.5 mrad mirror tilt was targeted and achieved by the micrometer screw. Output power is obtained through a ZnSe output coupler having concave geometry of ROC 5 meter and 17% reflectivity.

Fig. 14. Cathode Block

Fig. 15. Mirror Holder

#### **3.3 Working of V-fold laser**

The working principle of the laser is similar to other CO2 lasers. The gas mixture of CO2, N2, and He enters in each discharge tube at its center and flows symmetrically towards the

The jacketed glass tube is supported by cathode block which is ultimately supported by a plate and ring over the aluminum pipe (Fig.14.). Two glass tubes in V-shape are supported by a cathode block on one side. Cathode block is made of SS304 have the advantage of low scaling problem caused by electrical discharge. A mirror holder is connected on the other side of the cathode block through a glass tube of 45 mm OD (Fig.14 & 15). Each mirror holder consists of one mirror and they are placed at the extreme ends on both sides. Mirror holder assembly is also supported on pipe through a ring and plate. Rear mirrors and folding mirrors are made of OFHC Copper substrate of 25 mm diameter and radius of curvature (ROC) 5 meter. Mirrors are gold coated with ∼99% reflectivity. Two micrometer screws are fitted on the back side of the each mirror holder to align the laser beam. Alignment is the most critical part of this laser. The alignment accuracy of 0.5 mrad mirror tilt was targeted and achieved by the micrometer screw. Output power is obtained through a ZnSe output coupler having concave geometry of ROC 5 meter and 17% reflectivity.

CATHODE BLOCK

The working principle of the laser is similar to other CO2 lasers. The gas mixture of CO2, N2, and He enters in each discharge tube at its center and flows symmetrically towards the

Fig. 14. Cathode Block

MICROMETER

MIRROR HOLDER

SCREW

Fig. 15. Mirror Holder

**3.3 Working of V-fold laser** 

cathode blocks, which are connected to a rotary vane vacuum pump of pumping speed of 500 lit/min. Pressure, temperature and gas mixture have been optimized for the maximum output power. Optimum gas pressure is 30 mbar. In the diffusion cooled laser the laser power can be scaled up by increasing the discharge length at the rate of 50 W/m. With the increase of discharge length and therefore optical resonator length, the Fresnel number NF = r2 / λ.l where r, l and λ are the radius of mirror clear aperture, resonator length and laser wavelength respectively. NF reduces and with this the diffraction loss increases. Due to this the input power in a laser with plano-concave resonator did not scale up with discharge length beyond 3-4 meters. We adopted the symmetric concave resonator geometry to reduce diffraction loss and V-folding over a cylindrical surface instead of a flat surface for laying the discharge tubes to minimize the astigmatism effect. Each section of V-fold laser has about 1.5 meter discharge length, distance between two mirrors is 2.5 meter. All resonator mirrors i.e. rear reflector, ZnSe output coupler and all folding mirrors are having concave surface of 5 meter ROC. Since, the laser mode formed in any section are sustained in all the other sections therefore the length of one section determines the Fresnel number. Corresponding to the resultant Fresnel number the diffraction loss is low. Introduction of curved folding mirrors through a small folding angle of 5° could introduce considerable aberration due to astigmatism after large number of folding. In order to minimize the overall effect of astigmatism, the tubes were mounted on a cylindrical surface instead of a flat surface to have ~2π folding. The central supporting aluminum pipe due to high moment of inertia have minimum deflection thus minimizes the misalignment. With a fully reflecting mirror on the left and a partially transmitting mirror on the right, the device becomes a Vfold laser which radiates in the far infrared at 10.6 microns. Till date, 420 W power in 10.5 meter discharge length is obtained from this laser system.

#### **3.4 Electrical characteristics of V-fold laser**

All gas discharges operated in the glow discharge region have electrical characteristics similar to those indicated in Fig.16. The voltage and current values and the exact shape of the curve depend on the type of gases, gas pressure and the length & diameter of the discharge tube.

Fig. 16. Voltage-Current Curve of a Gaseous Discharge

Diffusion Cooled V-Fold CO2 Laser 195

resistance. Pre-ionization initiates discharge in all the tubes simultaneously and maintain it stable at even low currents. Ballast resistor is required to control the current flowing in the circuit, as discharge has a negative dynamic resistance; hence ballast resistance is an important parameter in getting a uniform stable discharge. If ballast resistance is not proper, it may result in large flow of current, which may result in formation of arcs and no laser action take place. Moreover we require discharge intensity equal in all zones, if instability creeps into one zone, it will affect the other zone and we will not get uniformity in the discharge. If the ballast resistance is of high value, there will be much of power losses in the ballast resistors. We experimented with four different values of ballast resistors. They are 140, 249, 300 and 191 kΩ. With 140 kΩ we could not get the required current density for maximum output optical power. The other three gave us stable discharge and the optimum current in each discharge zone is found to be 26 mA. We finally used the 191 kΩ resistor in

Design of a suitable optical resonator is needed to extract the laser power from the annular discharge region and also to provide the feedback to the laser. Resonators are classified

The simplest optical resonator (The Fabry-Perot resonator or confocal) consists of a pair of plane or spherical mirrors located opposite one another. They are cantered to a common optical axis and are aligned perpendicular to this axis. For lasers in the low to medium power range (1 mW - 200 W), the hemispherical resonator is mainly used and for high

depending on beam stability inside the resonator and named as follows:

our circuit considering the maximum overall efficiency of 10.6%.

Fig. 17. Schematic of Power Supply of V-fold Laser

**3.6 Laser resonator of V-fold laser** 

I. Stable II. Unstable

Before ionization, the current through the gas is essentially zero. Increasing the voltage on the gas results in a small pre-breakdown current due to a very small amount of easily ionized matter, which is always present in a gas near room temperature (point A). Increasing the applied voltage further will increase this current slightly until the breakdown voltage is reached (point B). At this voltage level, a significant number of atoms become ionized because of the high electric field present in the gas. The free negative electrons are attracted toward the anode and the heavier positive ions toward the cathode. This increases conductivity of the gas and lowers the electrical resistance of the discharge. The electrons are sufficiently accelerated by the electric field to free other electrons through collisions with gas atoms or molecules. Thus, as current increases (from point C to point D), ionization increases and voltage across the discharge tube decreases. This means that an increase in current results in a decrease in resistance. This property of gas discharges is called negative dynamic resistance. This does not mean that the resistance of the tube is a negative value, but that the slope of the voltage-current curve has a negative value. Current through the gas will increase until it is limited by some other electrical component in the circuit or until the power supply can no longer sustain the current. In the case of low-current CW devices such as He-Ne laser tubes, the current is limited at a lower level (point C). In the flashlamps of pulsed solid-state lasers, current is allowed to increase to a value of many kilo-amps (point E) before energy stored in the capacitors is exhausted.

#### **3.5 Power supply of V-fold laser**

The Pulser/Sustainer technique is utilized for the production of uniform electrical discharge in the glow discharge regime. The Pulser/Sustainer concept produces pressure and volume scalable plasmas by essentially applying two successive discharges to the gas. The first fast high-voltage pulse creates the electron density uniformly between its electrodes using only a small amount of energy. However a second discharge applies the proper voltage to this plasma to tune the electrons to a temperature sufficiently high for efficient laser pumping but not high enough to generate any appreciable further increase in electron density. Thus, the dominant amount of energy is put into the gas (by the sustainer) exactly where it is desired (vibration excitation of N2 and CO2) without triggering. Such plasma instabilities as arcs and sparking are usually associated with substantial ionization rates. The plasma is then with two "knobs"- one controlling electron density, the other electron temperature. The result is a stable uniform tuned high-power-density plasma that is not wall controlled and, hence a high power efficient N2/CO2 laser. To realize this concept we have used a 25 kV DC Power supply, 500 mA of current and a pulser with 9 kV of peak voltage, 2 µsec pulse and 5 kHz frequency. The schematic circuit diagram of laser power supply is shown in the Fig.17. An experiment was also performed to know the minimum pulse energy required per pulse to create the uniform discharge. This was studied by the use of another pulser which was available to us with peak voltage of 6 kV, 5 kHz frequency and with variable pulse width. By changing the pulse width we got the situation where we got the uniform smooth discharge. To initiate the discharge in all tubes simultaneously, pre-ionization technique has been adopted. For pre-ionization, a high frequency pulser of peak voltage 6 kV and repetition rate 2-5 kHz has been developed. Pulse width can be varied from 2 to 8 μsec. Pulser is connected to the anode pins by a DC power supply of 30 kV / 750 mA rating through a capacitor of 1.7 nF to block the high voltage DC excitation current. Thick film noninductive resistors of 191 kΩ are used between DC Supply and anode pins as ballast

Before ionization, the current through the gas is essentially zero. Increasing the voltage on the gas results in a small pre-breakdown current due to a very small amount of easily ionized matter, which is always present in a gas near room temperature (point A). Increasing the applied voltage further will increase this current slightly until the breakdown voltage is reached (point B). At this voltage level, a significant number of atoms become ionized because of the high electric field present in the gas. The free negative electrons are attracted toward the anode and the heavier positive ions toward the cathode. This increases conductivity of the gas and lowers the electrical resistance of the discharge. The electrons are sufficiently accelerated by the electric field to free other electrons through collisions with gas atoms or molecules. Thus, as current increases (from point C to point D), ionization increases and voltage across the discharge tube decreases. This means that an increase in current results in a decrease in resistance. This property of gas discharges is called negative dynamic resistance. This does not mean that the resistance of the tube is a negative value, but that the slope of the voltage-current curve has a negative value. Current through the gas will increase until it is limited by some other electrical component in the circuit or until the power supply can no longer sustain the current. In the case of low-current CW devices such as He-Ne laser tubes, the current is limited at a lower level (point C). In the flashlamps of pulsed solid-state lasers, current is allowed to increase to a value of many kilo-amps (point

The Pulser/Sustainer technique is utilized for the production of uniform electrical discharge in the glow discharge regime. The Pulser/Sustainer concept produces pressure and volume scalable plasmas by essentially applying two successive discharges to the gas. The first fast high-voltage pulse creates the electron density uniformly between its electrodes using only a small amount of energy. However a second discharge applies the proper voltage to this plasma to tune the electrons to a temperature sufficiently high for efficient laser pumping but not high enough to generate any appreciable further increase in electron density. Thus, the dominant amount of energy is put into the gas (by the sustainer) exactly where it is desired (vibration excitation of N2 and CO2) without triggering. Such plasma instabilities as arcs and sparking are usually associated with substantial ionization rates. The plasma is then with two "knobs"- one controlling electron density, the other electron temperature. The result is a stable uniform tuned high-power-density plasma that is not wall controlled and, hence a high power efficient N2/CO2 laser. To realize this concept we have used a 25 kV DC Power supply, 500 mA of current and a pulser with 9 kV of peak voltage, 2 µsec pulse and 5 kHz frequency. The schematic circuit diagram of laser power supply is shown in the Fig.17. An experiment was also performed to know the minimum pulse energy required per pulse to create the uniform discharge. This was studied by the use of another pulser which was available to us with peak voltage of 6 kV, 5 kHz frequency and with variable pulse width. By changing the pulse width we got the situation where we got the uniform smooth discharge. To initiate the discharge in all tubes simultaneously, pre-ionization technique has been adopted. For pre-ionization, a high frequency pulser of peak voltage 6 kV and repetition rate 2-5 kHz has been developed. Pulse width can be varied from 2 to 8 μsec. Pulser is connected to the anode pins by a DC power supply of 30 kV / 750 mA rating through a capacitor of 1.7 nF to block the high voltage DC excitation current. Thick film noninductive resistors of 191 kΩ are used between DC Supply and anode pins as ballast

E) before energy stored in the capacitors is exhausted.

**3.5 Power supply of V-fold laser** 

resistance. Pre-ionization initiates discharge in all the tubes simultaneously and maintain it stable at even low currents. Ballast resistor is required to control the current flowing in the circuit, as discharge has a negative dynamic resistance; hence ballast resistance is an important parameter in getting a uniform stable discharge. If ballast resistance is not proper, it may result in large flow of current, which may result in formation of arcs and no laser action take place. Moreover we require discharge intensity equal in all zones, if instability creeps into one zone, it will affect the other zone and we will not get uniformity in the discharge. If the ballast resistance is of high value, there will be much of power losses in the ballast resistors. We experimented with four different values of ballast resistors. They are 140, 249, 300 and 191 kΩ. With 140 kΩ we could not get the required current density for maximum output optical power. The other three gave us stable discharge and the optimum current in each discharge zone is found to be 26 mA. We finally used the 191 kΩ resistor in our circuit considering the maximum overall efficiency of 10.6%.

Fig. 17. Schematic of Power Supply of V-fold Laser

#### **3.6 Laser resonator of V-fold laser**

Design of a suitable optical resonator is needed to extract the laser power from the annular discharge region and also to provide the feedback to the laser. Resonators are classified depending on beam stability inside the resonator and named as follows:


The simplest optical resonator (The Fabry-Perot resonator or confocal) consists of a pair of plane or spherical mirrors located opposite one another. They are cantered to a common optical axis and are aligned perpendicular to this axis. For lasers in the low to medium power range (1 mW - 200 W), the hemispherical resonator is mainly used and for high

Diffusion Cooled V-Fold CO2 Laser 197

0

0 <sup>1</sup> <sup>2</sup> <sup>2</sup> <sup>2</sup> πω R z1

λ z = +

<sup>1</sup> <sup>2</sup> <sup>2</sup>

(8)

(9)

0

Equation 1 and 2 gives the value of ω0 and ω is 2.72 mm and 3.153 mm respectively.

The parameters that affect such optimization for flowing gas systems are:

should be prepared to perform experimental exploration of his own system.

few tricks in aligning this particular laser. Step by step, they are as follows:

• Optical mode control, wavelength control, and output coupling

Performance of CO2 lasers may be optimized in several ways: maximize multimode power; maximize single- mode power; maximize efficiency; and/or minimize size and complexity.

Optimization is by no means simple, because the various parameters are strongly interrelated. All results, therefore, should be viewed only as indicative of performance trends. The engineer

Aligning this laser was very challenging job for us. Since the inner diameter of the discharge tube is 9 mm, we require alignment accuracy in microns. Since small amount of misalignment can lead to appreciable loss in output power, a great deal of work was done in making the system rigid. Height or position of the glass CO2 laser tube should never change because any small movement throws it out of alignment and this could take days to realign. Instead, change the laser system by varying the mirror orientations, grating orientation and He-Ne laser orientation. The idea is to make the two mirrors at the ends of the laser cavity reflect a beam back-and forth many times without striking the walls of the tube. There are a

i. Make sure that there is no high voltage at the electrodes of the laser tube by checking

0

where

= = = = =

2

• Tube length, diameter and wall temperature • Gas mixture, pressure, and flow speed

• Electrical discharge control and current density

**3.7.1 Alignment procedure of V-fold laser** 

that the power supply is turned off.

R radius of curvature of the mirror

**3.7 Optimization of V-fold laser** 

ω beam radius at the mirrors ω minimum spot size z distance from the waist λ wavelength of CO laser

<sup>λ</sup> <sup>z</sup> ω ω <sup>1</sup> <sup>2</sup> πω = +

power laser both stable and unstable types of resonator are used. There are many combinations depending on their stability criteria given below:

$$0 \le \mathbf{g}\_1 \mathbf{g}\_2 \le 1 \quad \text{stability condition} \tag{6}$$

$$\mathbf{g}\_l = \mathbf{1} - \frac{L}{R\_l} \qquad \text{g-parameter} \tag{7}$$

Where

L = Length of resonator,

R*i* = Radius of curvature of resonator

We use the resonator mostly which satisfy this condition. The stability curve shown below represents that which resonator is preferred in stability criteria.

Fig. 18. Resonator Stability Curve

In our present laser we are using a concave–concave type resonator (where 2L=R) in a Vfold manner. Resonator mirrors for visible laser are generally made of glass but in CO2 laser the radiation is of 10.6 µm which comes in infrared region and this wavelength is absorbed by glass. So a special type of output coupler made up of ZnSe is generally used. The V-Fold laser resonator is a stable resonator comprising of concave mirrors of radius of curvature of 5 meter. The distance between the mirrors is 2.5 meter. Concave mirrors keep the beam bound inside the cavity and tends to reduce the diffraction losses. For a Gaussian beam to exist in a resonator, its wave fronts must fit exactly into the curvature of the mirrors. Thus beam radius at the waist and at the mirrors can be found out using the following equation:

$$\mathbf{u} = \mathbf{u}\_0 \left[ 1 + \left( \frac{\lambda \mathbf{z}}{\mathbf{n} \, \mathbf{a}\_0^2} \right)^2 \right]^{\frac{1}{2}} \tag{8}$$

$$\mathbf{R} = \mathbf{z} \left[ \mathbf{1} + \left( \frac{\mathbf{n} \, \alpha\_0^2}{\lambda \, \mathbf{z}} \right)^2 \right]^{\frac{1}{2}} \tag{9}$$

where

196 CO2 Laser – Optimisation and Application

power laser both stable and unstable types of resonator are used. There are many

� ��

We use the resonator mostly which satisfy this condition. The stability curve shown below

�� <sup>g</sup>�g� = 1

In our present laser we are using a concave–concave type resonator (where 2L=R) in a Vfold manner. Resonator mirrors for visible laser are generally made of glass but in CO2 laser the radiation is of 10.6 µm which comes in infrared region and this wavelength is absorbed by glass. So a special type of output coupler made up of ZnSe is generally used. The V-Fold laser resonator is a stable resonator comprising of concave mirrors of radius of curvature of 5 meter. The distance between the mirrors is 2.5 meter. Concave mirrors keep the beam bound inside the cavity and tends to reduce the diffraction losses. For a Gaussian beam to exist in a resonator, its wave fronts must fit exactly into the curvature of the mirrors. Thus beam radius at the waist and at the mirrors can be found out using the following

<sup>g</sup>� =1−

0 ≤ <sup>g</sup>�g� ≤ 1 stability condition (6)

g-parameter (7)

<sup>g</sup>� =1−

� ��

combinations depending on their stability criteria given below:

represents that which resonator is preferred in stability criteria.

<sup>g</sup>� =1−

�

<sup>g</sup>�g� = 1

Where

L = Length of resonator,

R*i* = Radius of curvature of resonator

Fig. 18. Resonator Stability Curve

equation:

ω beam radius at the mirrors =

0 ω minimum spot size =

z distance from the waist =

2 λ wavelength of CO laser =

R radius of curvature of the mirror =

Equation 1 and 2 gives the value of ω0 and ω is 2.72 mm and 3.153 mm respectively.

#### **3.7 Optimization of V-fold laser**

Performance of CO2 lasers may be optimized in several ways: maximize multimode power; maximize single- mode power; maximize efficiency; and/or minimize size and complexity. The parameters that affect such optimization for flowing gas systems are:


Optimization is by no means simple, because the various parameters are strongly interrelated. All results, therefore, should be viewed only as indicative of performance trends. The engineer should be prepared to perform experimental exploration of his own system.

#### **3.7.1 Alignment procedure of V-fold laser**

Aligning this laser was very challenging job for us. Since the inner diameter of the discharge tube is 9 mm, we require alignment accuracy in microns. Since small amount of misalignment can lead to appreciable loss in output power, a great deal of work was done in making the system rigid. Height or position of the glass CO2 laser tube should never change because any small movement throws it out of alignment and this could take days to realign. Instead, change the laser system by varying the mirror orientations, grating orientation and He-Ne laser orientation. The idea is to make the two mirrors at the ends of the laser cavity reflect a beam back-and forth many times without striking the walls of the tube. There are a few tricks in aligning this particular laser. Step by step, they are as follows:

i. Make sure that there is no high voltage at the electrodes of the laser tube by checking that the power supply is turned off.

Diffusion Cooled V-Fold CO2 Laser 199

c. Reflection losses - Whenever light is incident on a transparent surface, some portion of it always is reflected. Brewster windows and antireflection coatings greatly reduce this

d. Diffraction loss - Part of the laser light may pass over the edges of the mirror or strike the edges of the aperture and be removed from the beam. This is the largest loss factor in many lasers. When a light beam passes through a limiting aperture, the waves at the edge of the beam bend outward slightly, causing the beam to diverge. This phenomenon is termed "diffraction". When laser light moves, diffraction occurs at the aperture and the beam diverges. When the beam returns to the aperture after reflection from the mirror, its diameter is larger than the diameter of the aperture and the edges of the beam are blocked. The portion of the beam that does pass through the aperture is

e. Absorption Loss – This loss occurs due to the mirrors either fully or partially reflecting. No mirror is considered to be the 100% reflecting mirror and some part of incident laser get absorbed in the mirror. So as the number of mirrors will increase, the loss will also

In order to ensure the high-power and stable CO2 laser operation, misalignment sensitivity has to be known. The power and stability of the laser greatly depends on the misalignment of the optical resonator. In such type of resonator in which a V-fold resonator is used, misalignment is the main cause of reduction in power. So the effect of mirror misalignment of folded resonators is investigated experimentally and compared to first-order perturbation theory. An expression *D* is derived, which characterizes the misalignment sensitivity of any folded resonator. It is proved experimentally that this misalignment sensitivity depends on

The misalignment sensitivity of a resonator is defined as the sensitivity with which the diffraction losses or the output power are changed due to mirror tilt. By adapting the diameter of the TEM00 mode to the diameter of the active medium, the efficiency of a laser oscillator can be increased considerably. This requires either a large mirror distance *L* or an optical resonator operating near the limit of stability. In either case the resonator becomes

diffracted again and experiences additional loss on the next pass.

loss of light but cannot eliminate it entirely.

**3.9 Misalignment sensitivity of V-fold laser** 

Fig. 19. Misaligned Spherical Resonator

the effective resonator length *L\** and the *gi* parameters only.

increase.


#### **3.7.2 Power scaling of V-fold laser**

The output power of the laser scales up with the input power and input electrical power is limited by two factors. First is the rise in laser gas temperature and second is discharge instability. The most common being the ionization thermal instability. For efficient and reliable laser operation the input power density should be smaller and determined by the cooling and the discharge stabilization processes. In V-fold laser, the maximum input power density is limited by the heating effect and not by the discharge instability. Also, laser power in a V-fold diffusion cooled laser is directly proportional to the discharge length and is independent of the tube diameter and gas pressure. Thus, the laser power in V-fold diffusion cooled CO2 laser can be scaled up by increasing the active length only and it has been incorporated by introducing several discharge tubes arranged optically in series.

#### **3.8 Losses in optical cavities of V-fold laser**

The following factors contribute to losses within the optical cavities of the lasers:


ii. Set up a He-Ne laser alongside the cavity with a pin hole exiting the He-Ne Laser. Use two mirrors and direct the beam down the center bore of the CO2 laser tube. The He-Ne laser beam should be positioned on the center of the mirrors for adjustment purposes. In the beginning, blank off the back mirror with a piece of paper so that reflections don't

iii. Direct the He-Ne beam through the middle of the output mirror (the first mirror it

iv. Adjust the mirrors until the He-Ne laser beam goes through the middle of the bore without reflecting off the walls of the tube. It may not look as if it goes through the middle of the Brewster windows, and it may not go exactly through the middle of the

v. Remove the paper blocking the back mirror and adjust the mirror so that the reflection is centered on the output port of the He-Ne laser (it is easier to align if you place a card

vii. Blank off the output port of the He-Ne laser with a fire brick to protect it from the CO2 beam. Place the power detector in front of the CO2 output port and place a fire brick behind the detector. Whenever you change scales on the power meter, you should reset

The output power of the laser scales up with the input power and input electrical power is limited by two factors. First is the rise in laser gas temperature and second is discharge instability. The most common being the ionization thermal instability. For efficient and reliable laser operation the input power density should be smaller and determined by the cooling and the discharge stabilization processes. In V-fold laser, the maximum input power density is limited by the heating effect and not by the discharge instability. Also, laser power in a V-fold diffusion cooled laser is directly proportional to the discharge length and is independent of the tube diameter and gas pressure. Thus, the laser power in V-fold diffusion cooled CO2 laser can be scaled up by increasing the active length only and it has been incorporated by introducing several discharge tubes arranged optically in

The following factors contribute to losses within the optical cavities of the lasers:

a. Misalignment of the mirrors - If the mirrors of the cavity are not aligned properly with the optical axis, the beam will not be contained within the cavity, but will move farther

b. Dirty optics - Dust, dirt, fingerprints and scratches on optical surfaces scatter the laser

with a small hole punched in it at the output port of the Helium- Neon laser). vi. Now adjust the output mirror so that the inner surface reflection of that mirror (the bigger, dimmer one of the two) is centered on the back mirror reflection spot at the Helium- Neon laser. Fringes can usually be seen on the reflections when the two are aligned (Fabry-Perot interferometer). Alignment is pretty much complete. It may take

passes through). You will see more than one dot reflecting back.

output mirror. Going down the center of the bore is the most important.

confuse matters the set-up.

you a day or two to get to this point.

**3.8 Losses in optical cavities of V-fold laser** 

toward one edge of the cavity after each reflection.

light and cause permanent damage to the optical surfaces.

**3.7.2 Power scaling of V-fold laser** 

it to zero.

series.


#### **3.9 Misalignment sensitivity of V-fold laser**

In order to ensure the high-power and stable CO2 laser operation, misalignment sensitivity has to be known. The power and stability of the laser greatly depends on the misalignment of the optical resonator. In such type of resonator in which a V-fold resonator is used, misalignment is the main cause of reduction in power. So the effect of mirror misalignment of folded resonators is investigated experimentally and compared to first-order perturbation theory. An expression *D* is derived, which characterizes the misalignment sensitivity of any folded resonator. It is proved experimentally that this misalignment sensitivity depends on the effective resonator length *L\** and the *gi* parameters only.

Fig. 19. Misaligned Spherical Resonator

The misalignment sensitivity of a resonator is defined as the sensitivity with which the diffraction losses or the output power are changed due to mirror tilt. By adapting the diameter of the TEM00 mode to the diameter of the active medium, the efficiency of a laser oscillator can be increased considerably. This requires either a large mirror distance *L* or an optical resonator operating near the limit of stability. In either case the resonator becomes

Diffusion Cooled V-Fold CO2 Laser 201

*V* ( ) *w aw aw* ( ) ( ) 2 2 <sup>2</sup>

Generally a resonator has limiting apertures on both mirrors. Then the loss factor by tilting

*V VV i j i ii ji* ( )1 2

1 12 .exp 2

For small losses (1-*Vji*, 1-*Vii* << 1), Eq. (16) combined with Eq. (17) can be approximated by

*a a a a V V*

<sup>1</sup> 1 exp 2 exp 2 <sup>2</sup> =− − + −

For minimizing diffraction losses on the one hand and preventing multimode oscillation on the other hand, it is reasonable to use pinhole radii a bit larger than the beam radii.

> *io i i <sup>S</sup> V V <sup>D</sup>*

α

*j*

1 2 \* 2 1 2

*i <sup>L</sup> <sup>g</sup> g g <sup>D</sup>*

Equation (20) represents the diffraction loss factor *Vi* per resonator bounce, if mirror *Si* is

additional losses of 10% are caused. This gives a clear idea of the meaning of the misalignment sensitivity *Di*. However, the low-gain lasers are affected much more by an

*i*

π

λ

resonator length *L*\* and the *gi* parameters. If a mirror is tilted by an angle

<sup>2</sup> 1

= − <sup>−</sup>

*S* 2 2 2

( )

*i.* Misalignment sensitivity *Di*, which according to Eq. (22) depends on the

3 2 1 2

*g g g*

1 1

exp2 1

*ji j j*

*a a*

2 2 2 2 exp 2 exp 2 <sup>Δ</sup> <sup>Δ</sup> ≅ − − + <sup>−</sup>

2 2 2

*j j j*

*ww w*

*ji j j ii i i*

*j j j ii i*

*j i*

2 2

*i j a a*

*w w*

*ww w ww w*

 Δ =− + <sup>−</sup>

*w* = beam diameter of the TEM00 field pattern at the pinhole, and

*ji*

*V*

*Vo* is the loss factor of the aligned system with

*o*

*V*

Combining the above equations, we finally get

Where

*a* = pinhole radius,

mirror *Si* is given by:

*i o*

tilted by

α

*V* = loss factor per resonator bounce.

=− + Δ 1 12 exp 2<sup>−</sup> (15)

= ≠ . (16)

(17)

(19)

(20)

α

 *= 1*/*Di*,

*V S <sup>o</sup>* ( ) <sup>2</sup> =− − 1 exp 2 (21)

<sup>+</sup> <sup>=</sup> <sup>−</sup> (22)

(18)

very sensitive to a misalignment of the mirrors. From symmetry we may deduce that the increase of diffraction loss due to misalignment is proportional to the square of the mirrortilting angle αoi. Therefore, a suitable expression for the loss factor *Vi* per resonator bounce is:

$$V\_l = V\_o[1 - (a\_l/a\_{ol})^2] \tag{10}$$

Where *i* indicates mirror Si, which is tilted by an angle αi with respect to the resonator axis (see Fig.19). The misalignment sensitivity of the resonator is characterized by αoi. In the following sections the relation between αoi and the resonator parameters is investigated experimentally and theoretically.

#### **3.9.1 Background**

There are few papers dealing with the influence of misalignment on diffraction losses. Numerical calculations were carried out for special systems such as symmetric or confocal resonators and plane-plane resonators using first-order perturbation theory. But they assume that the aperture of the system does not disturb the field distribution of the infinite mirror. The laser oscillator consists of two spherical mirrors, radii of curvature *R1* and *R2* in a distance (*L)* and refractive index. It is assumed to be homogeneous. The mode properties of the resonator are characterized by the effective length *L\** and the *gi* parameters. For infinite mirrors, the spot size of the TEM00 mode is given by:

$$\mathcal{W}\_{i}^{2} = \frac{\mathcal{\lambda}L^{\*}}{\pi} \left(\frac{\mathcal{g}\_{i}}{\mathcal{g}\_{i} \left(1 - \mathcal{g}\_{1}\mathcal{g}\_{2}\right)}\right)^{\mathcal{W}^{2}} \tag{11}$$

The resonator axis is defined by the two centers of mirror curvature *M1* and *M2*. If mirror *Si* is tilted by an angle α*i*, the resonator axis is rotated by an angle θ*<sup>i</sup>*, and the centers of the field intensity patterns are shifted. A simple geometric consideration delivers the relations:

$$\theta\_i = \alpha\_i \frac{1 - g\_i}{1 - g\_1 g\_2} \tag{12}$$

$$
\Delta\_{il} = \alpha\_i \mathbf{g}\_i \mathbf{L}^" \;/\left(1 - \mathbf{g}\_1 \mathbf{g}\_2\right) \tag{13}
$$

$$
\Delta\_{\psi} = \alpha\_{\rangle} \mathbf{L}^\* \;/\left(\mathbf{1} - \mathbf{g}\_1 \mathbf{g}\_2\right) \qquad i \neq j \tag{14}
$$

Δ*ij* means the displacement of the intensity pattern at mirror *Si*, if mirror *Sj* is tilted by α*j*. Near the limit of stability ( ) *g g*1 2 → 1 , the beam steering angle *<sup>i</sup>* θ and the displacement Δ*ij* may become considerably large. Nevertheless, as long as infinite mirrors are considered, the resonator remains aligned, and there are no diffraction losses. But if a limiting aperture is inserted into the resonator, e.g., the active medium or a mode selecting pinhole, diffraction losses occur and increase rapidly with increasing mirror tilt angle. Tilting a mirror is equivalent to a displacement of the pinhole. For a system with only one pinhole, Berger et al calculated the dependence of diffraction loss factor *V* on the pinhole displacement (Δ). A first-order perturbation theory for the TEM00 mode delivers:

$$V = 1 - \left[1 + 2\left(\Delta / w\right)^2 \left(a / w\right)^2\right] \exp\left[-2\left(a / w\right)^2\right] \tag{15}$$

Where

200 CO2 Laser – Optimisation and Application

very sensitive to a misalignment of the mirrors. From symmetry we may deduce that the increase of diffraction loss due to misalignment is proportional to the square of the mirrortilting angle αoi. Therefore, a suitable expression for the loss factor *Vi* per resonator bounce is:

�� � ���1 − ���� � ���

Where *i* indicates mirror Si, which is tilted by an angle αi with respect to the resonator axis (see Fig.19). The misalignment sensitivity of the resonator is characterized by αoi. In the following sections the relation between αoi and the resonator parameters is investigated

There are few papers dealing with the influence of misalignment on diffraction losses. Numerical calculations were carried out for special systems such as symmetric or confocal resonators and plane-plane resonators using first-order perturbation theory. But they assume that the aperture of the system does not disturb the field distribution of the infinite mirror. The laser oscillator consists of two spherical mirrors, radii of curvature *R1* and *R2* in a distance (*L)* and refractive index. It is assumed to be homogeneous. The mode properties of the resonator are characterized by the effective length *L\** and the *gi* parameters. For infinite

> ( ) *j*

> > *i*

*g g g*1 2

1 1

( ) *ii i i g L g g* \* Δ= −

( ) *ij jL g g i j* \* Δ= − ≠

Δ*ij* means the displacement of the intensity pattern at mirror *Si*, if mirror *Sj* is tilted by α*j*.

may become considerably large. Nevertheless, as long as infinite mirrors are considered, the resonator remains aligned, and there are no diffraction losses. But if a limiting aperture is inserted into the resonator, e.g., the active medium or a mode selecting pinhole, diffraction losses occur and increase rapidly with increasing mirror tilt angle. Tilting a mirror is equivalent to a displacement of the pinhole. For a system with only one pinhole, Berger et al calculated the dependence of diffraction loss factor *V* on the pinhole displacement (Δ). A

1 2 1

*g gg* 1 2 \*

*i*

The resonator axis is defined by the two centers of mirror curvature *M1* and *M2*. If mirror *Si*

<sup>=</sup> <sup>−</sup>

*<sup>L</sup> <sup>g</sup> <sup>W</sup>*

intensity patterns are shifted. A simple geometric consideration delivers the relations:

*i i*

θ α

α

α

Near the limit of stability ( ) *g g*1 2 → 1 , the beam steering angle *<sup>i</sup>*

first-order perturbation theory for the TEM00 mode delivers:

λ

π

experimentally and theoretically.

mirrors, the spot size of the TEM00 mode is given by:

*i*

is tilted by an angle α*i*, the resonator axis is rotated by an angle

2

**3.9.1 Background** 

�� (10)

(11)

*<sup>i</sup>*, and the centers of the field

and the displacement Δ*ij*

θ

<sup>−</sup> <sup>=</sup> − (12)

/ 1 1 2 (13)

/ 1 1 2 (14)

θ

*a* = pinhole radius,

*w* = beam diameter of the TEM00 field pattern at the pinhole, and

*V* = loss factor per resonator bounce.

Generally a resonator has limiting apertures on both mirrors. Then the loss factor by tilting mirror *Si* is given by:

$$V\_i = \left(V\_{ii} \cdot V\_{ji}\right)^{\sharp 2} \qquad \qquad i \neq j \tag{16}$$

$$V\_{ji} = 1 - \left[ 1 + 2\left(\frac{\Delta\_{ji}}{w\_j}\right)^2 \left(\frac{a\_j}{w\_j}\right)^2 \right] \cdot \exp\left[-2\left(\frac{a\_j}{w\_j}\right)^2\right] \tag{17}$$

For small losses (1-*Vji*, 1-*Vii* << 1), Eq. (16) combined with Eq. (17) can be approximated by

$$V\_i \equiv V\_o - \left\{ \left[ \left( \frac{\Delta\_{\vec{\mu}}}{w\_j} \right) \left( \frac{a\_j}{w\_j} \right) \right]^2 \exp \left[ -2 \left( \frac{a\_j}{w\_j} \right)^2 \right] + \left[ \left( \frac{\Delta\_{\vec{\mu}}}{w\_i} \right) \left( \frac{a\_i}{w\_i} \right) \right]^2 \exp \left[ -2 \left( \frac{a\_i}{w\_i} \right)^2 \right] \right\} \tag{18}$$

*Vo* is the loss factor of the aligned system with

$$V\_o = 1 - \frac{1}{2} \left\{ \exp \left[ -2 \left( \frac{a\_i}{w\_i} \right)^2 \right] + \exp \left[ -2 \left( \frac{a\_j}{w\_j} \right)^2 \right] \right\} \tag{19}$$

For minimizing diffraction losses on the one hand and preventing multimode oscillation on the other hand, it is reasonable to use pinhole radii a bit larger than the beam radii. Combining the above equations, we finally get

$$V\_i = V\_o \left(1 - \alpha\_i^2 \frac{S^2}{\exp 2S^2 - 1} D\_i^2\right) \tag{20}$$

$$V\_o = 1 - \exp\left(-\mathfrak{D}S^2\right) \tag{21}$$

$$D\_i^2 = \frac{\pi L^\*}{\lambda} \left(\frac{\mathcal{g}\_j}{\mathcal{g}\_i}\right)^{\mathcal{Y}^2} \frac{1 + \mathcal{g}\_1 \mathcal{g}\_2}{\left(1 - \mathcal{g}\_1 \mathcal{g}\_2\right)^{\mathcal{Y}^2}}\tag{22}$$

Equation (20) represents the diffraction loss factor *Vi* per resonator bounce, if mirror *Si* is tilted by α*i.* Misalignment sensitivity *Di*, which according to Eq. (22) depends on the resonator length *L*\* and the *gi* parameters. If a mirror is tilted by an angle α *= 1*/*Di*, additional losses of 10% are caused. This gives a clear idea of the meaning of the misalignment sensitivity *Di*. However, the low-gain lasers are affected much more by an

Diffusion Cooled V-Fold CO2 Laser 203

coupling loss of resonator & long gain length. The radiation, which begins from the output coupler-end, sees the round trip gain while the radiation which begins from the rear mirror; sees only single trip, and the starting intensity of radiation in the first case is relatively smaller than that in the second case. Therefore the misalignment in first case (output coupler) has relatively less effect on the laser power build up compared to the misalignment of the second case (rear reflector). Furthermore, the experimental results indicate that sensitivity

SL – Single limb, DL – Double limb, CC – Concave-Concave resonator, PC – Plano-Concave

parameter '*D'* is a suitable parameter to describe the alignment stability of a resonator.

S.No. Type of Resonator Active Medium Length (cm) D (mrad) 1 Concave-Concave 150 1.687 2 Concave-Concave 300 2.378 3 Plano-Concave 150 2.286 4 Plano-Concave 300 3.223

Table 6. Theoretical Value of Misalignment Sensitivity Parameter '*D'*

Note: Micro-meters are numbered 1 & 2 in anticlockwise direction.

resonator, M1 – Micrometer1, M2 – Micrometer2

Fig. 20. Misalignment in Single Limb for Reflector

Fig. 21. Misalignment in Single Limb for Output Coupler

additional loss of 10% than the high-gain lasers. Thus, misalignment sensitivities of different resonator configurations may be compared if their gains are the same. If both mirrors are misaligned, the losses proportional to *Di* 2 are summed up. Therefore, the misalignment of the complete system is defined as *DDD* ( )1 2 2 2 = +1 2 and is given by:

$$D = \left[ \left( \frac{\pi L \, ^\star}{\lambda} \right) \frac{1 + g\_1 g\_2}{\left( 1 - g\_1 g\_2 \right)^{3/2}} \frac{\left| g\_1 + g\_2 \right|}{\left( g\_1 g\_2 \right)^{3/2}} \right]^{3/2} \tag{23}$$

Where, 'D' is a number characterizing any spherical resonator with respect to its sensitivity against mirror tilting. High value of *D* means high misalignment sensitivity. The most insensitive resonator is the symmetric con-focal one with *g1=g2=0.*

$$D\_0 = \left(\frac{2\pi L}{\mathcal{A}}\right)^{\text{y2}} \tag{24}$$

But, from the stability diagram, we learn that *g1=g2=0* represents a discontinuity. Small deviations from symmetry may cause high losses and high misalignment sensitivity.

#### **3.9.2 Experimental investigation**

The power and stability of a laser system is mainly governed by the misalignment sensitivity of optical resonator. To ensure stable and high power from laser system misalignment sensitivity has to be known. The effect of reflector and output coupler misalignment for concave -concave & Plano-concave resonators in single and double limbs of V-fold laser are investigated experimentally and compared to first-order perturbation theory. Eq.23 is used to quantify the misalignment sensitivity of the V-fold laser resonator. It is proved experimentally that this misalignment sensitivity depends on the effective resonator length *L\** and the *gi* parameters only. High value of *D* means high misalignment sensitivity. The influence of mirror misalignment on laser output and field distribution was investigated by various authors. Experiment was carried out for four different arrangements.


Laser was operated with all these arrangements and then misaligned with the help of micrometer screw fitted on the backside of the optics. These four arrangements gave the misalignment characteristics for the single and double limb as well as Plano-concave and concave-concave resonator. Power was measured in the best-aligned condition then graphs were plotted for laser power v/s misalignment (Fig.20). The experimental results are verified by theoretical calculation of the misalignment sensitivity parameter '*D'* (Table-6).

Misalignment sensitivity increases with L\* i.e. no. of limbs. It is also observed that the planoconcave resonator is more sensitive to misalignment then the concave-concave resonator (Fig.20 & 22). It is also interesting to observe that the output coupler is less sensitive to misalignment compare to the rear concave reflector (Fig.21 & 23). This is due to very high

additional loss of 10% than the high-gain lasers. Thus, misalignment sensitivities of different resonator configurations may be compared if their gains are the same. If both mirrors are

*<sup>L</sup> g g g g <sup>D</sup>*

*<sup>L</sup> <sup>D</sup>*

0

deviations from symmetry may cause high losses and high misalignment sensitivity.

 <sup>+</sup> <sup>+</sup> <sup>=</sup> −

Where, 'D' is a number characterizing any spherical resonator with respect to its sensitivity against mirror tilting. High value of *D* means high misalignment sensitivity. The most

> 2 \* π

<sup>=</sup>

But, from the stability diagram, we learn that *g1=g2=0* represents a discontinuity. Small

The power and stability of a laser system is mainly governed by the misalignment sensitivity of optical resonator. To ensure stable and high power from laser system misalignment sensitivity has to be known. The effect of reflector and output coupler misalignment for concave -concave & Plano-concave resonators in single and double limbs of V-fold laser are investigated experimentally and compared to first-order perturbation theory. Eq.23 is used to quantify the misalignment sensitivity of the V-fold laser resonator. It is proved experimentally that this misalignment sensitivity depends on the effective resonator length *L\** and the *gi* parameters only. High value of *D* means high misalignment sensitivity. The influence of mirror misalignment on laser output and field distribution was investigated by various authors. Experiment was carried out for four different arrangements.

Laser was operated with all these arrangements and then misaligned with the help of micrometer screw fitted on the backside of the optics. These four arrangements gave the misalignment characteristics for the single and double limb as well as Plano-concave and concave-concave resonator. Power was measured in the best-aligned condition then graphs were plotted for laser power v/s misalignment (Fig.20). The experimental results are verified by theoretical calculation of the misalignment sensitivity parameter '*D'* (Table-6). Misalignment sensitivity increases with L\* i.e. no. of limbs. It is also observed that the planoconcave resonator is more sensitive to misalignment then the concave-concave resonator (Fig.20 & 22). It is also interesting to observe that the output coupler is less sensitive to misalignment compare to the rear concave reflector (Fig.21 & 23). This is due to very high

λ

\* 1 1

( ) ( )

*gg gg*

1 2 1 2 32 12 12 12

1 2

2 are summed up. Therefore, the misalignment of

(24)

(23)

1 2

misaligned, the losses proportional to *Di*

**3.9.2 Experimental investigation** 

a. Single limb with concave-concave resonator b. Single limb with Plano-concave resonator

c. Double limbs with concave-concave resonator and d. Double limbs with Plano-concave resonator.

the complete system is defined as *DDD* ( )1 2 2 2 = +1 2 and is given by:

insensitive resonator is the symmetric con-focal one with *g1=g2=0.*

π

λ


Table 6. Theoretical Value of Misalignment Sensitivity Parameter '*D'*

coupling loss of resonator & long gain length. The radiation, which begins from the output coupler-end, sees the round trip gain while the radiation which begins from the rear mirror; sees only single trip, and the starting intensity of radiation in the first case is relatively smaller than that in the second case. Therefore the misalignment in first case (output coupler) has relatively less effect on the laser power build up compared to the misalignment of the second case (rear reflector). Furthermore, the experimental results indicate that sensitivity parameter '*D'* is a suitable parameter to describe the alignment stability of a resonator.

SL – Single limb, DL – Double limb, CC – Concave-Concave resonator, PC – Plano-Concave resonator, M1 – Micrometer1, M2 – Micrometer2

Note: Micro-meters are numbered 1 & 2 in anticlockwise direction.

Fig. 20. Misalignment in Single Limb for Reflector

Fig. 21. Misalignment in Single Limb for Output Coupler

Diffusion Cooled V-Fold CO2 Laser 205

Decreasing reflectivity to extract more power increases the overall loss of the system, requiring greater pumping power to reach threshold. Increasing the output coupler reflectivity increases the cavity photon life time, thereby increasing the photon loss and

There must be an optimum reflectivity of an output coupler at which the radiant output power will be a maximum. This part reports the variation of output power as a function of output coupler reflectivity and active medium length for a V-fold diffusion cooled CO2 gas laser. A relationship (Eq.26) is used for optimum transmission coefficient of the output

( ) *opt*

0

*<sup>a</sup> T g La g L*

1 2

1 = −

In the development of a high-power CW CO2 laser; it is a design challenge to reach high output power simultaneously with good beam quality. The problem becomes stringent in multi-fold diffusion cooled CO2 lasers that uses a stable resonator configuration, where many meters of resonator length are required to generate a few kilowatts of energy, owing to the low aspect ratio between the discharge diameter and the discharge length necessary to obtain a mono mode beam. A laser will operate satisfactorily with many possible combinations of output coupler reflectivity, provided that the gain in a single pass through the amplifier is sufficiently large to equal or exceed the mirror transmission losses (or other

Experiment is carried out to test the performance of the laser for different reflectivity of output couplers and different active medium length. We used a concave-concave resonator; consist of gold coated copper mirror and a concave ZnSe output coupler of 5 meter radius of curvature each. In our experimental set-up, we have taken five different output couplers of reflectivity 5, 10, 17, 50 and 60% and corresponding output power was measured for 1.5, 3.0, 4.5 and 6.0 meter active medium length. These results are plotted for active medium length v/s output power for different output couplers (Fig.25) & reflectivity v/s output power for above stated active medium lengths (Fig.26). Output power of diffusion cooled laser is proportional to active medium length but we can see (Fig.25) that as the length increases

1 2

(26)

0

resulting in decrease of laser output power (Fig.24).

Fig. 24. Theoretical Curve for Output Coupling Reflectance

couplers to verify experimental measurements.

losses).

Fig. 22. Misalignment in Double Limb for Reflector

Fig. 23. Misalignment in Double Limb for Output Coupler

#### **3.10 Optimum reflectivity of output coupler of V-fold laser**

In V-fold type of resonator since there are more number of limbs and each limb has different output coupling reflectivity. So the output power of a laser that can be extracted depends on the reflectivity/transmission of the output coupler (Eq.25).

$$P\_{out} = A\_b I\_s \frac{1 - R}{1 - R + \sqrt{R} \left(1/a - a\right)} \left[g\_0 l - \ln \sqrt{R \times a^2}\right] \tag{25}$$

Where

Ab = Cross section area of medium, R = Reflectivity, a = cavity losses, Is = Saturation Intensity and *g l*<sup>0</sup> = Small signal gain.

Fig. 22. Misalignment in Double Limb for Reflector

Fig. 23. Misalignment in Double Limb for Output Coupler

the reflectivity/transmission of the output coupler (Eq.25).

Where

R = Reflectivity, a = cavity losses,

Ab = Cross section area of medium,

Is = Saturation Intensity and *g l*<sup>0</sup> = Small signal gain.

( ) *out b s*

1 1

**3.10 Optimum reflectivity of output coupler of V-fold laser** 

In V-fold type of resonator since there are more number of limbs and each limb has different output coupling reflectivity. So the output power of a laser that can be extracted depends on

*<sup>R</sup> P AI gl R a R R aa*

0

<sup>1</sup> ln

<sup>−</sup> <sup>=</sup> − × −+ −

2

(25)

Decreasing reflectivity to extract more power increases the overall loss of the system, requiring greater pumping power to reach threshold. Increasing the output coupler reflectivity increases the cavity photon life time, thereby increasing the photon loss and resulting in decrease of laser output power (Fig.24).

Fig. 24. Theoretical Curve for Output Coupling Reflectance

There must be an optimum reflectivity of an output coupler at which the radiant output power will be a maximum. This part reports the variation of output power as a function of output coupler reflectivity and active medium length for a V-fold diffusion cooled CO2 gas laser. A relationship (Eq.26) is used for optimum transmission coefficient of the output couplers to verify experimental measurements.

$$T\_{opt} = \left(g\_o L a\right)^{\mathcal{V}2} \left[1 - \left(\frac{a}{g\_o L}\right)^{\mathcal{V}2}\right] \tag{26}$$

In the development of a high-power CW CO2 laser; it is a design challenge to reach high output power simultaneously with good beam quality. The problem becomes stringent in multi-fold diffusion cooled CO2 lasers that uses a stable resonator configuration, where many meters of resonator length are required to generate a few kilowatts of energy, owing to the low aspect ratio between the discharge diameter and the discharge length necessary to obtain a mono mode beam. A laser will operate satisfactorily with many possible combinations of output coupler reflectivity, provided that the gain in a single pass through the amplifier is sufficiently large to equal or exceed the mirror transmission losses (or other losses).

Experiment is carried out to test the performance of the laser for different reflectivity of output couplers and different active medium length. We used a concave-concave resonator; consist of gold coated copper mirror and a concave ZnSe output coupler of 5 meter radius of curvature each. In our experimental set-up, we have taken five different output couplers of reflectivity 5, 10, 17, 50 and 60% and corresponding output power was measured for 1.5, 3.0, 4.5 and 6.0 meter active medium length. These results are plotted for active medium length v/s output power for different output couplers (Fig.25) & reflectivity v/s output power for above stated active medium lengths (Fig.26). Output power of diffusion cooled laser is proportional to active medium length but we can see (Fig.25) that as the length increases

Diffusion Cooled V-Fold CO2 Laser 207

• Make sure that everyone in the vicinity of the laser or anywhere the beam (or its reflection) may be is fully aware of the safety issues and has proper eyewear. • Provide visible and unambiguous indications that the laser is powered and the beam is on. • A kill switch is essential and should be located far enough from the laser tube so that it

• For flowing gas lasers, provide adequate ventilation. While the lasing gasses (helium, nitrogen, and carbon dioxide) are not toxic, and not very much is involved for laser operation, a leak in the gas delivery system could go undetected. CO2 in particular is heavier than air so it will displace air in an enclosed space which may result in various

• Where maintenance or repair is involved, be aware of the properties of the specific materials used for the optics and elsewhere. For example, the biohazards of zinc

In the present laser, power of 380 Watts from 7.5 m discharge length and maximum 420 W from seven limbs (10.5 meter discharge length) has been achieved. The maximum average power of 50 W/m is obtained from this laser, which is comparable to other diffusion-cooled laser developed till now. Studies have shown that dissociation of CO2 molecules increases with the increase of no of tube or discharge length. Care has been taken to have a low gas residence time to reduce the deleterious effect of CO2 dissociation. The electro-optic

The power and stability of a laser system is mainly governed by the misalignment sensitivity of the optical resonator. To ensure stable and high power from a laser system misalignment sensitivity has to be known. The experimental results indicate that sensitivity parameter D is a suitable parameter to describe the alignment stability of a resonator.

The output power of a laser that can be extracted depends on the reflectivity/transmission of the output coupler. There must be an optimum reflectivity of an output coupler at which

According to Rigrod's formula if length increases power reduces, as there are many other parameters, which are not optimized. So power goes on decreases when length increases.

Author is thankful to Sh. Mukesh Jewariya, Sh. Firoz Koser, Sh. D.D. Saha, Sh. M.B. Pote, Sh. S.V. Deshmukh, Sh. A.K. Nath, Sh. Dinesh Nagpure, Sh. Abrat Verma and all other colleagues of Laser and Material Processing Division, RRCAT, who directly or indirectly involve in design and development of this laser. Author is also thankful to Sh. Abhay

Dahotre, Narendra B. & Harimkar, Sandip P. (2008). *Laser Fabrication and Machining of Materials,* Springer Science + Business Media, ISBN 978-0-387-72343-3, USA

Kumar (IMA Section) and Sh. Arup Ratan Jana (Accelerator and Beam Physics Lab.).

is accessible in an emergency even if a total meltdown is in progress.

symptoms from nausea to asphyxiation.

selenide and beryllia.

efficiency of the laser is about 13%.

the radiant output power will be a maximum.

Beam size also affects the output power.

**6. Acknowledgement** 

**7. References** 

**5. Conclusion** 

power increases but the rate of increase of output power decreases. This is because of diffraction losses increases with increase of length. For theoretical calculation, in order to estimate *g*<sup>0</sup> and *a* in our laser, we have used the Eq.25 of laser power in a V-fold CO2 laser. Substituting the value of laser power for three different reflectivity of the output coupler, the three unknowns i.e. *<sup>s</sup> g a I* <sup>0</sup> , & are calculated theoretically. Thus using these values in expression (Eq.26), the *Topt* is estimated to be 66% for 6 meter active medium length theoretically. Experimentally also we have observed that laser output power is 209 watts for 83% transmissivity and 150 watts for 50% transmissivity. From the above data we can predict that the optimum value of transmissivity lies somewhere between 50 & 83%.

Fig. 25. Experimental Curve: Output Power v/s Active Medium Length

Fig. 26. Experimental Curve: Output Power v/s Reflectivity

#### **4. Safety precautions**

Some general considerations when working with V-fold CO2 lasers are as follows:


power increases but the rate of increase of output power decreases. This is because of diffraction losses increases with increase of length. For theoretical calculation, in order to estimate *g*<sup>0</sup> and *a* in our laser, we have used the Eq.25 of laser power in a V-fold CO2 laser. Substituting the value of laser power for three different reflectivity of the output coupler, the three unknowns i.e. *<sup>s</sup> g a I* <sup>0</sup> , & are calculated theoretically. Thus using these values in expression (Eq.26), the *Topt* is estimated to be 66% for 6 meter active medium length theoretically. Experimentally also we have observed that laser output power is 209 watts for 83% transmissivity and 150 watts for 50% transmissivity. From the above data we can

predict that the optimum value of transmissivity lies somewhere between 50 & 83%.

Fig. 25. Experimental Curve: Output Power v/s Active Medium Length

Fig. 26. Experimental Curve: Output Power v/s Reflectivity

Some general considerations when working with V-fold CO2 lasers are as follows:

• Clearly mark and if possible, block off access to the path of the beam.

• Provide a beam stop capable of safely absorbing this power on a continuous basis.

• Reflected beams may have nearly as much power as the original and are just as dangerous. Although many common materials will block 10.6 µm, specular surfaces

**4. Safety precautions** 

will reflect it quite well.


### **5. Conclusion**

In the present laser, power of 380 Watts from 7.5 m discharge length and maximum 420 W from seven limbs (10.5 meter discharge length) has been achieved. The maximum average power of 50 W/m is obtained from this laser, which is comparable to other diffusion-cooled laser developed till now. Studies have shown that dissociation of CO2 molecules increases with the increase of no of tube or discharge length. Care has been taken to have a low gas residence time to reduce the deleterious effect of CO2 dissociation. The electro-optic efficiency of the laser is about 13%.

The power and stability of a laser system is mainly governed by the misalignment sensitivity of the optical resonator. To ensure stable and high power from a laser system misalignment sensitivity has to be known. The experimental results indicate that sensitivity parameter D is a suitable parameter to describe the alignment stability of a resonator.

The output power of a laser that can be extracted depends on the reflectivity/transmission of the output coupler. There must be an optimum reflectivity of an output coupler at which the radiant output power will be a maximum.

According to Rigrod's formula if length increases power reduces, as there are many other parameters, which are not optimized. So power goes on decreases when length increases. Beam size also affects the output power.

#### **6. Acknowledgement**

Author is thankful to Sh. Mukesh Jewariya, Sh. Firoz Koser, Sh. D.D. Saha, Sh. M.B. Pote, Sh. S.V. Deshmukh, Sh. A.K. Nath, Sh. Dinesh Nagpure, Sh. Abrat Verma and all other colleagues of Laser and Material Processing Division, RRCAT, who directly or indirectly involve in design and development of this laser. Author is also thankful to Sh. Abhay Kumar (IMA Section) and Sh. Arup Ratan Jana (Accelerator and Beam Physics Lab.).

#### **7. References**

Dahotre, Narendra B. & Harimkar, Sandip P. (2008). *Laser Fabrication and Machining of Materials,* Springer Science + Business Media, ISBN 978-0-387-72343-3, USA

**7** 

*Kyoto University* 

*Japan* 

**Heterodyne Interferometer for Measurement** 

Keiichiro Urabe and Kunihide Tachibana

**of Electron Density in High-Pressure Plasmas** 

Conventional material processes using plasmas generated in low pressure gaseous media are recently being transposed to high-pressure plasma processes, because of the potential of high-pressure plasmas to reduce costs for vacuum systems in industrial applications. In many kinds of high-pressure plasma sources, small-scale atmospheric-pressure plasmas (APPs) having a property of thermal non-equilibrium, have been especially attracting much interest of researchers over the last 20 years (Becker, 2005). In such a high pressure gaseous medium, generating the small-scale plasmas in mm or μm order is effective to keep its ignition voltage low and discharge behavior stable, following a famous rule on discharge ignition called a "Paschen's law" (Paschen, 1889; von Engel, 1994). Using these small-scale high-pressure plasmas, localized maskless processes, for example etching (Ichiki et al., 2004) and deposition (Babayan et al., 1998), have been reported. Also, nanomaterial synthesis was realized by the APP utilizing their property of short residence time of source particles inside the plasma (Nozaki et al., 2007). In addition to the inorganic solid material processes, process objects of the APPs are spreading toward liquids (Bruggeman & Leys, 2009) and

In characterization and comparison of plasma properties, electron density is one of the most important parameters. This is because that electrons play a major role for carrying external energy to heavy particles inside the plasma, and all other excited species can be calculated theoretically from the plasma parameters of electron density, electron energy distribution, and gas composition. Diagnostics of electron density have in the APPs have been reported by many researchers using Langmuir probe methods (Chang, 1973; Chang & Laframboise, 1976), Stark broadening measurement (Laux et al., 2003), and laser Thomson scattering measurement (Kono & Iwamoto, 2004). However, these methods have limitations for the APP measurements due to their finite sensitivities, expected perturbations or interferences, spatiotemporal resolutions, etc. For instance, the Langmuir probe is difficult be applied to the small-scale APPs since its theory in a collision dominant condition is not well developed and there are discharge perturbations by the metallic probe. The Stark broadening spectroscopic method enables us to derive electron density only for over 5×1013 cm-3 due to the large pressure broadening superposed over the Lorentzian shape (Laux et al., 2003). The laser Thomson scattering method is not applicable to molecular gases although its spatial resolution is high enough, because large Raman scattering components overlap with the

biocells (Kong et al., 2009) which cannot present in low-pressure conditions.

**1. Introduction** 

Thomson scattering signal.

Endo, Masamori & Walter, Robert F. (2007). *Gas Lasers*, CRC Press, ISBN 0-8493-3553-1, USA


### **Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas**

Keiichiro Urabe and Kunihide Tachibana *Kyoto University Japan* 

#### **1. Introduction**

208 CO2 Laser – Optimisation and Application

Endo, Masamori & Walter, Robert F. (2007). *Gas Lasers*, CRC Press, ISBN 0-8493-3553-1, USA Freiberg, R.J. and Halsted, A. S. (1969). Properties of Low Order Transverse Modes in Argon Ion Lasers. *Applied Optics*, Vol. 8, No. 2, (1969), pp. (355-362), ISSN 1559-128X Hitz, B.; Ewing, J.J. and Hetch, J. (2005). *Introduction to laser technology* (Third Edition), John

Hoag, Ethan; Pease, Henry; Staal, John and Zar, Jacob. (1974). Performance Characteristics of

Hodgson, N. (1997). Optical resonators: fundamentals, advanced concepts and applications,

Koechner, W. (1988). Solid State Laser Engineering, Springer-Verlag, ISBN 3-540-18747-2,

Migliore, Leonard. (1996). *Laser Materials Processing*, Marcel Dekker Inc., ISBN 0-8247-9714-0,

Nath, A.K. and Golubev, V.S. (1998). Design considerations and scaling laws for high power

Scott, Marion W. and Myers, Gary D. (1984). Steady-state CO2 laser model. *Applied Optics*,

Seigman, A.E. (1986). *Lasers*, University Science Books, Mill Valley, California, USA, ISBN 0-

Soni, R.K. et al. (2005). Diffusion Cooled V-Fold CO2 Laser, *Proceedings of Fourth DAE-BRNS* 

Soni, R.K. et al. (2005). Misalignment Sensitivity of a V-Fold Optical Resonator, *Proceedings of* 

Soni, R.K. et al. (2005). Optimum Reflectivity for a Diffusion Cooled CO2 Laser, *Proceedings* 

Svelto, Orazio. (2010). *Principles of Lasers* (Fifth Edition), Springer Science+Business Media,

Thyagarajan, K. & Ghatak, Ajoy. (2010). *Lasers: Fundamentals and Applications* (Second

Weber, H., Herziger, G. & Poprawe, R. (2006). *Laser Physics and Applications Sub volume A: Laser Fundamentals Part 2*, Springer, ISBN 978-3-540-28824-4, Germany Xinju, Lan. (2010). *Laser Technology* (Second Edition), CRC Press, ISBN 978-1-4200-9171-7,

Editiion), Springer Science+Business Media, New York, USA

Vol. 23, No. 17, (September 1984), pp. (2874-2878), ISSN 1559-128X

convective cooled CW CO2 lasers. *Pramana*, Vol. 51, No. 3-4, (September-October

*National Laser Symposium, 185 January 10-13, 2005*, ISBN 8177647342, 9788177647341,

*Fifth DAE-BRNS National Laser Symposium (NLS-5), December 7-10, 2005, page 96*,

*of Fifth DAE-BRNS National Laser Symposium (NLS-5), December 7-10, 2005, page 98*,

a 10-kW Industrial CO2 Laser System. *Applied Optics*, Vol. 13, No. 8, (August 1974),

Wiley & Sons Inc., USA

Berlin

New York, USA

935702-11-5, USA

www.springer.com

USA

pp. (1959-1964), ISSN 1559-128X

1998), pp. (463-479), 0304-4289

Mumbai (India), January 2005

ISBN , Tamil Nadu (India), December 7-10, 2005

ISBN , Tamil Nadu (India), December 2005

Springer, ISBN 3-540-76137-3, Berlin

Conventional material processes using plasmas generated in low pressure gaseous media are recently being transposed to high-pressure plasma processes, because of the potential of high-pressure plasmas to reduce costs for vacuum systems in industrial applications. In many kinds of high-pressure plasma sources, small-scale atmospheric-pressure plasmas (APPs) having a property of thermal non-equilibrium, have been especially attracting much interest of researchers over the last 20 years (Becker, 2005). In such a high pressure gaseous medium, generating the small-scale plasmas in mm or μm order is effective to keep its ignition voltage low and discharge behavior stable, following a famous rule on discharge ignition called a "Paschen's law" (Paschen, 1889; von Engel, 1994). Using these small-scale high-pressure plasmas, localized maskless processes, for example etching (Ichiki et al., 2004) and deposition (Babayan et al., 1998), have been reported. Also, nanomaterial synthesis was realized by the APP utilizing their property of short residence time of source particles inside the plasma (Nozaki et al., 2007). In addition to the inorganic solid material processes, process objects of the APPs are spreading toward liquids (Bruggeman & Leys, 2009) and biocells (Kong et al., 2009) which cannot present in low-pressure conditions.

In characterization and comparison of plasma properties, electron density is one of the most important parameters. This is because that electrons play a major role for carrying external energy to heavy particles inside the plasma, and all other excited species can be calculated theoretically from the plasma parameters of electron density, electron energy distribution, and gas composition. Diagnostics of electron density have in the APPs have been reported by many researchers using Langmuir probe methods (Chang, 1973; Chang & Laframboise, 1976), Stark broadening measurement (Laux et al., 2003), and laser Thomson scattering measurement (Kono & Iwamoto, 2004). However, these methods have limitations for the APP measurements due to their finite sensitivities, expected perturbations or interferences, spatiotemporal resolutions, etc. For instance, the Langmuir probe is difficult be applied to the small-scale APPs since its theory in a collision dominant condition is not well developed and there are discharge perturbations by the metallic probe. The Stark broadening spectroscopic method enables us to derive electron density only for over 5×1013 cm-3 due to the large pressure broadening superposed over the Lorentzian shape (Laux et al., 2003). The laser Thomson scattering method is not applicable to molecular gases although its spatial resolution is high enough, because large Raman scattering components overlap with the Thomson scattering signal.

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 211

separated by a beam splitter, and the beam's phase change is caused by variations of the refractive index of the tested material placed only in one path. Difference of the refractive indexes between the two paths is derived from the merged beam by a second beam splitter. A heterodyne technique is a reducing method of observing frequency from light frequency to external oscillator frequency in a instrumentally manageable range. When this method is applied to the Mach-Zehnder interferometer, the light frequency in one of two paths is modulated, and in the other path the frequency is not modulated but its phase is shifted by the tested material. After merging the two laser beams, a beat signal at the modulation frequency in the merged beam can be isolated from the original output signal of a solid-state

> 2 2 2 1 2 1 2 12 <sup>0</sup> *It U t U t E E EE* () () () cos( ) *Δ t ΔΦ*

where *U*1(*t*) = *E*1cos(*ωt*+*Δωt*) is the electric field of the laser beam passing through the frequency modulating device with a modulation frequency at *Δω*, *U*2(*t*) = *E*2cos(*ωt*+*ΔΦ*) is the electric field of the beam passing through the tested material, and *ΔΦ* is the phase shift of the beam by the tested material. Components in a light frequency range are automatically eliminated from the signal because of the response-speed limitation of detectors. From the output signal, *I*(*t*), we can derive the phase shift by the tested material *ΔΦ* using a phase detecting device and a reference signal which is separated from the frequency-modulation

ω

**Detector**

**Lock-in Amp.**

**Oscilloscope**

<sup>=</sup> = + =++ − , (1)

**AOM**

ω

Fig. 1. Experimental setup of CO2-laser heterodyne interferometer in Mach-Zhender principle for measurement of electron density inside high-pressure plasma source. AOM is acousto optical modulator shifting CO2-laser frequency at frequency of RF driver's signal. DC is directional coupler taking small amplitude of RF signal driving AOM to input

**Plasma source**

**ZnSe lens**

**RF driver DC**

**Mirror**

A practical experimental setup of the CO2-laser heterodyne interferometer used in our studies is shown in Fig. 1. The original CO2 laser beam was split by a ZnSe half mirror. The beam frequency in one path was shifted an acousto-optical modulator (AOM) whose modulation frequency *Δω* = 40 MHz. In the other path, the beam was focused on a tested plasma source by a pair of ZnSe lens, and the beam phase was shifted by the tested plasma. These two beams were superposed again at another ZnSe half mirror, and their beat signal

detecting device, *I*(*t*), which is expressed in a following equation.

signal.

reference signal to lock-in amplifier.

**Half mirror**

For the purpose of diagnostics in the small-scale high-pressure plasmas, refractive-index measurement using electromagnetic (EM) waves is appropriate since they can provide plasma property's information with negligible perturbation to the plasma. Also, in the refractive-index measurement, we can ignore excitation and scattering processes that are largely dependent on gas compositions and densities, which are indispensable for the above listed other measurement methods. For typical APPs whose electron densities range from 1012 to 1015 cm-3, microwaves and millimeter-waves are suitable to detect absorption of the probing EM waves and derive the electron density from the absorption ratio (Tachibana et al., 2005(a), 2005(b); Sakai et al., 2005; Ito et al., 2010). However, diagnostics using those EM waves cannot have good spatial resolutions for the small-scale plasmas because of their diffraction limits. Meanwhile, a heterodyne interferometer of CO2 laser beam, which is a theme in this chapter, can be in a category of the refractive-index measurement methods and have a good spatial resolution at the same time. This interferometer detects the laser beam's phase shift caused by the presence of tested plasma and provides line-integrated information of electron density with a spatial resolution in sub mm order (Leipold et al., 2000; Choi et al., 2009).

This chapter is focused on descriptions of the CO2-laser heterodyne interferometer for the measurement in small-scale high-pressure plasma sources, because detailed descriptions of the interferometer for the low-pressure plasmas have been written in other chapters and textbooks (*for example* Hutchinson, 2002). In high-pressure plasmas, large contribution of gas-particle density (atoms and/or molecules in ground states) to the change of the refractive index is expected due to Joule heating in the discharge region, and this must be accurately separated from the signal in order to derive the absolute value of electron density. Therefore, we firstly explain how to divide the two components in the CO2-laser beam's phase shift, which are the phase shifts due to electron generation and gas heating. Then, the fundamental properties of our CO2-laser heterodyne interferometer, for example spatial resolution and lower limit of electron-density detection, are verified reviewing experimental measurements of the small-scale APPs driven by DC applied voltages (Choi et al., 2009). Finally, a combination measurement method composed of the CO2-laser heterodyne interferometer and a millimeter-wave transmission method is introduced as a solution of spatiotemporally resolved electron-density measurement in small-scale APPs with high-speed temporal evolution of electron density (Urabe et al., 2011).

#### **2. Fundamentals of heterodyne interferometer**

This section includes brief introduction of a Mach-Zehnder principle and a heterodyne technique used in our interferometer and theoretical descriptions of the phase shift in the CO2 laser beam induced by electrons in a tested plasma source, and explanations how to derive electron density in small-scale high-pressure plasmas eliminating influence of gas heating from total phase shift signals.

#### **2.1 Mach-Zehnder heterodyne interferometer**

Measurements of refractive index in tested materials are often done by some forms of interferometer. Most of interferometers are in Michelson, Fabry-Perot, and Mach-Zehnder configurations. Mach-Zehnder interferometer is a two-beam interferometer having two paths in which the laser beams travel in only one direction. The original laser beam is 210 CO2 Laser – Optimisation and Application

For the purpose of diagnostics in the small-scale high-pressure plasmas, refractive-index measurement using electromagnetic (EM) waves is appropriate since they can provide plasma property's information with negligible perturbation to the plasma. Also, in the refractive-index measurement, we can ignore excitation and scattering processes that are largely dependent on gas compositions and densities, which are indispensable for the above listed other measurement methods. For typical APPs whose electron densities range from 1012 to 1015 cm-3, microwaves and millimeter-waves are suitable to detect absorption of the probing EM waves and derive the electron density from the absorption ratio (Tachibana et al., 2005(a), 2005(b); Sakai et al., 2005; Ito et al., 2010). However, diagnostics using those EM waves cannot have good spatial resolutions for the small-scale plasmas because of their diffraction limits. Meanwhile, a heterodyne interferometer of CO2 laser beam, which is a theme in this chapter, can be in a category of the refractive-index measurement methods and have a good spatial resolution at the same time. This interferometer detects the laser beam's phase shift caused by the presence of tested plasma and provides line-integrated information of electron density with a spatial resolution in sub mm order (Leipold et al.,

This chapter is focused on descriptions of the CO2-laser heterodyne interferometer for the measurement in small-scale high-pressure plasma sources, because detailed descriptions of the interferometer for the low-pressure plasmas have been written in other chapters and textbooks (*for example* Hutchinson, 2002). In high-pressure plasmas, large contribution of gas-particle density (atoms and/or molecules in ground states) to the change of the refractive index is expected due to Joule heating in the discharge region, and this must be accurately separated from the signal in order to derive the absolute value of electron density. Therefore, we firstly explain how to divide the two components in the CO2-laser beam's phase shift, which are the phase shifts due to electron generation and gas heating. Then, the fundamental properties of our CO2-laser heterodyne interferometer, for example spatial resolution and lower limit of electron-density detection, are verified reviewing experimental measurements of the small-scale APPs driven by DC applied voltages (Choi et al., 2009). Finally, a combination measurement method composed of the CO2-laser heterodyne interferometer and a millimeter-wave transmission method is introduced as a solution of spatiotemporally resolved electron-density measurement in small-scale APPs

This section includes brief introduction of a Mach-Zehnder principle and a heterodyne technique used in our interferometer and theoretical descriptions of the phase shift in the CO2 laser beam induced by electrons in a tested plasma source, and explanations how to derive electron density in small-scale high-pressure plasmas eliminating influence of gas

Measurements of refractive index in tested materials are often done by some forms of interferometer. Most of interferometers are in Michelson, Fabry-Perot, and Mach-Zehnder configurations. Mach-Zehnder interferometer is a two-beam interferometer having two paths in which the laser beams travel in only one direction. The original laser beam is

with high-speed temporal evolution of electron density (Urabe et al., 2011).

**2. Fundamentals of heterodyne interferometer** 

heating from total phase shift signals.

**2.1 Mach-Zehnder heterodyne interferometer** 

2000; Choi et al., 2009).

separated by a beam splitter, and the beam's phase change is caused by variations of the refractive index of the tested material placed only in one path. Difference of the refractive indexes between the two paths is derived from the merged beam by a second beam splitter.

A heterodyne technique is a reducing method of observing frequency from light frequency to external oscillator frequency in a instrumentally manageable range. When this method is applied to the Mach-Zehnder interferometer, the light frequency in one of two paths is modulated, and in the other path the frequency is not modulated but its phase is shifted by the tested material. After merging the two laser beams, a beat signal at the modulation frequency in the merged beam can be isolated from the original output signal of a solid-state detecting device, *I*(*t*), which is expressed in a following equation.

$$I(t) = \left| \left. U\_1(t) + \left. U\_2(t) \right| \right|\_{\alpha=0}^2 = E\_1^2 + E\_2^2 + E\_1 E\_2 \cos(\Delta a t - \Delta \Phi) \right. \tag{1}$$

where *U*1(*t*) = *E*1cos(*ωt*+*Δωt*) is the electric field of the laser beam passing through the frequency modulating device with a modulation frequency at *Δω*, *U*2(*t*) = *E*2cos(*ωt*+*ΔΦ*) is the electric field of the beam passing through the tested material, and *ΔΦ* is the phase shift of the beam by the tested material. Components in a light frequency range are automatically eliminated from the signal because of the response-speed limitation of detectors. From the output signal, *I*(*t*), we can derive the phase shift by the tested material *ΔΦ* using a phase detecting device and a reference signal which is separated from the frequency-modulation signal.

Fig. 1. Experimental setup of CO2-laser heterodyne interferometer in Mach-Zhender principle for measurement of electron density inside high-pressure plasma source. AOM is acousto optical modulator shifting CO2-laser frequency at frequency of RF driver's signal. DC is directional coupler taking small amplitude of RF signal driving AOM to input reference signal to lock-in amplifier.

A practical experimental setup of the CO2-laser heterodyne interferometer used in our studies is shown in Fig. 1. The original CO2 laser beam was split by a ZnSe half mirror. The beam frequency in one path was shifted an acousto-optical modulator (AOM) whose modulation frequency *Δω* = 40 MHz. In the other path, the beam was focused on a tested plasma source by a pair of ZnSe lens, and the beam phase was shifted by the tested plasma. These two beams were superposed again at another ZnSe half mirror, and their beat signal

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 213

where *A* and *B* are the specific values for gas species, *n*g0 is the gas particle density under the standard temperature and pressure (STP) conditions, and *n*g is the gas-particle density inside the tested plasma source (Allen, 1973). Considering the influence of gas-particle density on the refractive index, the phase shift of the CO2 laser beam in the high-pressure plasmas is described by two components of the electron density, *ΔΦ*e, and the gas-particle

2

ε π

*e AB ΔΦ ΔΦ ΔΦ n d n d m c n*

Table 1 lists change directions of the phase shift in the CO2-laser heterodyne interferometer. Whereas we used the gas-particle density *n*g for the calculation in Eq. (6), *ΔΦ*g can be also expressed using gas temperature in the plasma. Each component of the phase shift in the high-pressure plasma, *ΔΦ*e and *ΔΦ*g, changes to negative direction due to the electron production and the decrease of gas-particle density by the Joule heating. The separation of these two components becomes a crucial problem for accurate derivation of the electron density in practical measurements of the high-pressure plasmas, because these two components are only measured together in the heterodyne interferometer and start

Increase Decrease

Electron density Negative Positive

Gas temperature Negative Positive

Table 1. Change directions of CO2-laser beam's phase shift by changes of electron density,

For the separation of two components in the phase shift of the CO2 laser beam, difference of time constants of the two phenomena is utilized, because the change of electron density is much faster than that of gas temperature in the high-pressure discharge (Leipold et al., 2000; Choi et al., 2009). Applicability of this technique can be confirmed by experimental evidence as explained below. Also, in general, the two terms of electron density, *n*e, and gas-particle density, *n*g, can be derived directly by solving a system of two equations using a twowavelength heterodyne interferometer, because the phase-shift components due to the electron and gas-particle densities depend differently on the laser wavelength. Some groups have tried to measure both electron and gas-particle densities inside the plasma by an additional heterodyne interferometer using a He-Ne laser beam at 633 nm (Adler & Kindel,

Figure 2 shows an example waveform of the output phase-shift signal of the lock-in amplifier obtained in a small-scale high-pressure plasma source operated at 70 Torr driven by a pulsed DC voltage at 300 V with a 300-μs pulse duration. The phase-shift signal recorded in the oscilloscope is proportional to the phase shift in a specification ratio of the

gas-particle density, and gas temperature, when they increase or decrease.

density Positive Negative

λ

4

e g 2 2 e g e 0 g0

<sup>2</sup> <sup>1</sup>

= + =− + + . (6)

λ

 π

λ

density, *ΔΦ*g, as a following equation.

decreasing at the same timing.

2003; Acedo et al., 2004).

Gas-particle

was detected by a HgCdTe IR detector operated at room temperature. The output signal of the IR detector, *I*(*t*), was put into a lock-in amplifier with the reference signal, cos(*Δωt*), which was divided from a RF signal driving the AOM by a directional coupler (DC). The lock-in amplifier outputs a signal proportional to the phase shift, *ΔΦ*, and its temporal evolution was recorded in an oscilloscope.

#### **2.2 Phase shift of CO2 laser beam by electrons inside plasmas**

In refractive-index measurement inside a tested plasma source having no gas temperature fluctuation, for example plasmas generated in gaseous media at very lower pressure than atmosphere, the phase shift by tested plasma, *ΔΦ*, measured using the Mach-Zehnder heterodyne interferometer becomes

$$
\Delta \Phi = \int (k\_{\text{plasma}} - k\_0) \, dl = \int (N\_{\text{plasma}} - 1) \frac{2\pi}{\mathcal{N}} \, dl \, \, \, \tag{2}
$$

where *k*plasma and *k*0 are the wavenumbers of the plasma and vacuum, *N*plasma is the refractive index of the plasma, and *λ* is the wavelength of the CO2 laser beam. Absolute electron density inside the plasma, *n*e (m), can be derived using a following relationship.

$$N\_{\rm plasma} = \sqrt{1 - \frac{\alpha\_{\rm plasma}^2}{\alpha^2}} \sqrt{\frac{\alpha}{\alpha^2} - 1} - \frac{1}{2} \left(\frac{\alpha\_{\rm plasma}^2}{\alpha^2}\right) = 1 - \frac{1}{2} \frac{n\_\circ e^2}{m\_\circ e\_0} \frac{\lambda^2}{4\pi^2 c^2} \,\,\,\tag{3}$$

where *ω*plasma and *ω* are the electron plasma frequency and the angular frequency of laser beam, *m*e is the mass of electron, *ε*0 is the permittivity of vacuum, *c* is the velocity of light (Hutchinson, 2002). We used an approximate expansion in this calculation because electron density is sufficiently smaller than gas-particle density in weakly ionized plasmas generated in laboratories. When we assume that electron density inside the tested plasma is spacially homogeneous and its length along the laser path is *d* (m), the relationship between the phase shift and the electron density becomes

$$
\Delta\Phi = (N\_{\text{plasma}} - 1)\frac{2\pi}{\lambda}d = -\frac{e^2\lambda}{4m\_e\varepsilon\_0\pi c^2}n\_ed = -\left(3.0 \times 10^{-20}\right)n\_ed \text{ (rad)},\tag{4}
$$

in the CO2-laser heterodyne interferometer at *λ* = 10.6 μm.

#### **2.3 Electron-density measurement in high-pressure plasmas**

In this subsection, influence of dense gas particles in high-pressure plasmas on the calculation of electron density from the phase shift of the CO2 laser beam, which can be ignored in the measurement of low-pressure plasmas, is introduced. It should be noted that increase of gas temperature corresponding to decrease of gas-particle density is promoted in the high-pressure plasmas because of high collision frequencies between electrons and gas particles. This change of gas-particle density results in the change of the refractive index in gaseous medium. The refractive index of the gaseous medium, *N*gas, is

$$N\_{g\text{as}} = 1 + A \left(1 + \frac{B}{\lambda^2} \right) \frac{n\_{\text{g}}}{n\_{\text{g0}}} \, , \tag{5}$$

was detected by a HgCdTe IR detector operated at room temperature. The output signal of the IR detector, *I*(*t*), was put into a lock-in amplifier with the reference signal, cos(*Δωt*), which was divided from a RF signal driving the AOM by a directional coupler (DC). The lock-in amplifier outputs a signal proportional to the phase shift, *ΔΦ*, and its temporal

In refractive-index measurement inside a tested plasma source having no gas temperature fluctuation, for example plasmas generated in gaseous media at very lower pressure than atmosphere, the phase shift by tested plasma, *ΔΦ*, measured using the Mach-Zehnder

> plasma 0 plasma <sup>2</sup> *ΔΦ* ( ) ( 1) *k k dl N dl*

where *k*plasma and *k*0 are the wavenumbers of the plasma and vacuum, *N*plasma is the refractive index of the plasma, and *λ* is the wavelength of the CO2 laser beam. Absolute electron

1 1 11 1

 ω

where *ω*plasma and *ω* are the electron plasma frequency and the angular frequency of laser beam, *m*e is the mass of electron, *ε*0 is the permittivity of vacuum, *c* is the velocity of light (Hutchinson, 2002). We used an approximate expansion in this calculation because electron density is sufficiently smaller than gas-particle density in weakly ionized plasmas generated in laboratories. When we assume that electron density inside the tested plasma is spacially homogeneous and its length along the laser path is *d* (m), the relationship between the phase

> plasma 2 e e e 0 <sup>2</sup> ( 1) 3.0 10 4 *<sup>e</sup> ΔΦ N d n d n d m c*

In this subsection, influence of dense gas particles in high-pressure plasmas on the calculation of electron density from the phase shift of the CO2 laser beam, which can be ignored in the measurement of low-pressure plasmas, is introduced. It should be noted that increase of gas temperature corresponding to decrease of gas-particle density is promoted in the high-pressure plasmas because of high collision frequencies between electrons and gas particles. This change of gas-particle density results in the change of the refractive index in

gas 2

*N A*

1 1 *<sup>B</sup> <sup>n</sup>*

=+ +

λ*n*

 λ

ε π

*n e <sup>N</sup>*

= − ≈− = −

2 2 2 2 plasma plasma e plasma 2 2 2 2

 ω

2 2 4

( ) <sup>2</sup>

<sup>−</sup> = − =− ≈− × (rad), (4)

g

g0

density inside the plasma, *n*e (m), can be derived using a following relationship.

ω

π

λ

**2.3 Electron-density measurement in high-pressure plasmas** 

gaseous medium. The refractive index of the gaseous medium, *N*gas, is

in the CO2-laser heterodyne interferometer at *λ* = 10.6 μm.

π

λ= −= − , (2)

e 0

20

, (5)

ε π

*m c*

λ

, (3)

evolution was recorded in an oscilloscope.

heterodyne interferometer becomes

shift and the electron density becomes

**2.2 Phase shift of CO2 laser beam by electrons inside plasmas** 

ω

where *A* and *B* are the specific values for gas species, *n*g0 is the gas particle density under the standard temperature and pressure (STP) conditions, and *n*g is the gas-particle density inside the tested plasma source (Allen, 1973). Considering the influence of gas-particle density on the refractive index, the phase shift of the CO2 laser beam in the high-pressure plasmas is described by two components of the electron density, *ΔΦ*e, and the gas-particle density, *ΔΦ*g, as a following equation.

$$
\Delta\Phi = \Delta\Phi\_{\text{e}} + \Delta\Phi\_{\text{g}} = -\frac{e^2 \mathcal{X}}{4m\_{\text{e}}\varepsilon\_0 \pi c^2} n\_{\text{e}} d + \frac{2\pi A}{\lambda n\_{\text{g}0}} \left(1 + \frac{B}{\lambda^2}\right) n\_{\text{g}} d \tag{6}
$$

Table 1 lists change directions of the phase shift in the CO2-laser heterodyne interferometer. Whereas we used the gas-particle density *n*g for the calculation in Eq. (6), *ΔΦ*g can be also expressed using gas temperature in the plasma. Each component of the phase shift in the high-pressure plasma, *ΔΦ*e and *ΔΦ*g, changes to negative direction due to the electron production and the decrease of gas-particle density by the Joule heating. The separation of these two components becomes a crucial problem for accurate derivation of the electron density in practical measurements of the high-pressure plasmas, because these two components are only measured together in the heterodyne interferometer and start decreasing at the same timing.


Table 1. Change directions of CO2-laser beam's phase shift by changes of electron density, gas-particle density, and gas temperature, when they increase or decrease.

For the separation of two components in the phase shift of the CO2 laser beam, difference of time constants of the two phenomena is utilized, because the change of electron density is much faster than that of gas temperature in the high-pressure discharge (Leipold et al., 2000; Choi et al., 2009). Applicability of this technique can be confirmed by experimental evidence as explained below. Also, in general, the two terms of electron density, *n*e, and gas-particle density, *n*g, can be derived directly by solving a system of two equations using a twowavelength heterodyne interferometer, because the phase-shift components due to the electron and gas-particle densities depend differently on the laser wavelength. Some groups have tried to measure both electron and gas-particle densities inside the plasma by an additional heterodyne interferometer using a He-Ne laser beam at 633 nm (Adler & Kindel, 2003; Acedo et al., 2004).

Figure 2 shows an example waveform of the output phase-shift signal of the lock-in amplifier obtained in a small-scale high-pressure plasma source operated at 70 Torr driven by a pulsed DC voltage at 300 V with a 300-μs pulse duration. The phase-shift signal recorded in the oscilloscope is proportional to the phase shift in a specification ratio of the

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 215

As explained in the previous paragraph, because the temporal changes of electron and gasparticle density can be observed only in the discharge ignition or termination timings, there is a need to pulse modulation of continuous discharge for the separation of phase-shift components measured in the CO2-laser heterodyne interferometer. In order to understand appropriate range of duration times for the pulse modulation, especially minimum duration time, it is important to measure the phase-shift signal decreasing the modulating pulse duration. Figure 3 shows waveforms of the phase-shift signal measured in our heterodyne interferometer using five pulse duration times ranging from 60 to 700 µs. From the measured waveforms, it could be confirmed that the pulse modulation with the duration time shorter than 200 µs does not give us accurate information of electron density in our setup, and we used the modulation pulse with duration times larger than 500 µs in our studies. This temporal behavior of the output signal of the heterodyne interferometer is of

Fig. 4. Calculated beam spot radii of CO2 laser beam at 10.6 µm as a function of distance from lens (Yariv, 1997). Initial spot radius at 1.0 mm and focal lengths of lens at 5 and 20 cm

*f* = 5 cm

should be determined by reference to these kinds of beam-profile evaluations.

**3. Spatial distribution of electron density in high-pressure plasmas** 

Some of the specific measurement results of our CO2-laser heterodyne interferometer are introduced in this section. Influence of gas heating on detected phase-shift signals, spatial

For measuring the spatial distributions of electron density, evaluation of the spot radius of the CO2 laser beam inside the tested plasma source is required. In order to measure the spatial distribution of electron density inside the high-pressure plasmas whose scale are usually below cm order, the CO2-laser beam has to be focused in μm order using a pair of ZnSe lens as shown in Fig. 1. Assuming that the laser beam is a Gaussian beam, we can calculate a profile of the beam spot radius along the laser path from the beam parameter and focal length of the ZnSe lens using an ABCD matrix analysis (Yariv, 1997). Figrue 4 shows the beam-radius profiles after the two kinds of ZnSe lens used in our experimental study. The location and length of the tested plasma source and a scanning pitch of the laser beam

0 5 10 15 20 25 30

Distance from lens (cm)

*f* = 20 cm

course different in each IR detector and phase measuring system.

correspond to practical conditions used in our experiments.

0.0

0.2

0.4

0.6

Beam radius of CO2 laser (mm)

0.8

1.0

1.2

lock-in amplifier. Around 50 μs after the discharge ignition, the phase shift decreased rapidly in 150 μs, and then a slower change followed until the discharge termination. The 50-μs delay of the phase-shift signal is due to calculating delay time of the phase shift in the lock-in amplifier. The initial faster falling part is attributed to the increase of electron density, and the second slower part is to the decrease of gas-particle density by the Joule heating. Faster and slower slopes of the phase shift similar to the ignition timing were also observed in the termination timing. Subtracting the phase-shift component of gas-particle density, *ΔΦ*g, shown in a blue dashed-dotted curve in Fig. 2, the component of electron density, *ΔΦ*e, was obtained as shown in a red dashed curve. The absolute value of electron density can be derived from the amplitude of electron-density component.

Fig. 2. Temporal evolutions of phase-shift signal from lock-in amplifier and discharge current. Tested plasma source is small-scale discharge driven by 300-V pulsed DC high voltage at 70 Torr of He gas (Choi et al., 2009).

Fig. 3. Temporal evolutions of phase-shift signal measured changing voltage pulse duration from 60 to 700 μs (Choi et al., 2009).

lock-in amplifier. Around 50 μs after the discharge ignition, the phase shift decreased rapidly in 150 μs, and then a slower change followed until the discharge termination. The 50-μs delay of the phase-shift signal is due to calculating delay time of the phase shift in the lock-in amplifier. The initial faster falling part is attributed to the increase of electron density, and the second slower part is to the decrease of gas-particle density by the Joule heating. Faster and slower slopes of the phase shift similar to the ignition timing were also observed in the termination timing. Subtracting the phase-shift component of gas-particle density, *ΔΦ*g, shown in a blue dashed-dotted curve in Fig. 2, the component of electron density, *ΔΦ*e, was obtained as shown in a red dashed curve. The absolute value of electron

density can be derived from the amplitude of electron-density component.

ΔΦ*g*

> ΔΦ*e*

Fig. 2. Temporal evolutions of phase-shift signal from lock-in amplifier and discharge current. Tested plasma source is small-scale discharge driven by 300-V pulsed DC high

0.0 0.2 0.4 0.6 0.8 1.0

Total signal ΔΦ *e* + ΔΦ*g*

Time (ms)

Pulse duration 0.06 ms 0.10 ms 0.20 ms 0.40 ms 0.70 ms

Discharge current (mA)

Fig. 3. Temporal evolutions of phase-shift signal measured changing voltage pulse duration

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Time (ms)

voltage at 70 Torr of He gas (Choi et al., 2009).


Phase-shift signal (mV)





Phase-shift signal (mV)


0

from 60 to 700 μs (Choi et al., 2009).

As explained in the previous paragraph, because the temporal changes of electron and gasparticle density can be observed only in the discharge ignition or termination timings, there is a need to pulse modulation of continuous discharge for the separation of phase-shift components measured in the CO2-laser heterodyne interferometer. In order to understand appropriate range of duration times for the pulse modulation, especially minimum duration time, it is important to measure the phase-shift signal decreasing the modulating pulse duration. Figure 3 shows waveforms of the phase-shift signal measured in our heterodyne interferometer using five pulse duration times ranging from 60 to 700 µs. From the measured waveforms, it could be confirmed that the pulse modulation with the duration time shorter than 200 µs does not give us accurate information of electron density in our setup, and we used the modulation pulse with duration times larger than 500 µs in our studies. This temporal behavior of the output signal of the heterodyne interferometer is of course different in each IR detector and phase measuring system.

Fig. 4. Calculated beam spot radii of CO2 laser beam at 10.6 µm as a function of distance from lens (Yariv, 1997). Initial spot radius at 1.0 mm and focal lengths of lens at 5 and 20 cm correspond to practical conditions used in our experiments.

For measuring the spatial distributions of electron density, evaluation of the spot radius of the CO2 laser beam inside the tested plasma source is required. In order to measure the spatial distribution of electron density inside the high-pressure plasmas whose scale are usually below cm order, the CO2-laser beam has to be focused in μm order using a pair of ZnSe lens as shown in Fig. 1. Assuming that the laser beam is a Gaussian beam, we can calculate a profile of the beam spot radius along the laser path from the beam parameter and focal length of the ZnSe lens using an ABCD matrix analysis (Yariv, 1997). Figrue 4 shows the beam-radius profiles after the two kinds of ZnSe lens used in our experimental study. The location and length of the tested plasma source and a scanning pitch of the laser beam should be determined by reference to these kinds of beam-profile evaluations.

#### **3. Spatial distribution of electron density in high-pressure plasmas**

Some of the specific measurement results of our CO2-laser heterodyne interferometer are introduced in this section. Influence of gas heating on detected phase-shift signals, spatial

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 217

Figure 5(b) shows dependences of electron density in the short HC discharge on the discharge current measured at several He gas pressures. In the calculation of electron density from the phase shift signal, we used two assumptions that the plasma was uniform along the CO2 laser path and its effective length was 9.5 mm. The electron density in the discharge increased monotonically with the increase of the discharge current and the gas pressure. This result indicates that the CO2-laser heterodyne interferometer is able to measure appropriate dependence of electron density on the gas pressure, because the electron density inside the high-pressure plasma must be increased at higher pressure by the slower drift velocity of electrons due to frequent collisions with gas particles when the

Here, the minimum sensitivity of electron density in our CO2-laser heterodyne interferometer is introduced. The minimum electron density which we recorded in the short HC discharge was corresponds to a line integrated electron density *n*e*d* of 7×1012 cm−2 with a detected phase shift around 0.1 degree (Choi et al., 2009). However, the signal to noise ratio, for instance shown in Fig. 3, showed that the minimum sensitivity should be at least six times better than that. Therefore, it could be estimated that the minimum detectable phase shift in our system was about 0.02 degree, corresponding to *n*e*d* of 1×1012 cm−2, which is much smaller than the minimum sensitivity of Stark broadening measurement (Laux et al,

Figure 6(a) shows a schematic diagram of DC discharge in open space operated in a He gas flow ejected from a tubular cathode to a pin anode. The cylindrical tubular cathode, whose outer and inner diameters were 3.1 and 2.1 mm, and the pin anode with a 0.5-mm diameter were faced to the cathode with a 3-mm gap. The measurement point between the cathode and the anode was scanned by putting the whole discharge device on a three-dimensional mechanical movement stage. The influence of temporal evolutions of the gas-particle density on the measured phase shift can be seen in Fig. 6(b) showing the phase-shift signals observed in the atmospheric-pressure DC discharge using two different flow rates of He gas (1 and 2 L/min). This measurement result clearly suggests that the contribution of the Joule heating on temporal evolution of the phase shift becomes much greater in the discharge operated at atmospheric pressure and the gas-particle component in the phase shift, *ΔΦ*g, has large dependence on the gas flow velocity. The fast time constant and large amplitude of *ΔΦ*g in both rising and falling periods of applied voltage in lower gas flow rate was due to

In order to obtain radial distributions of electron density in the high-pressure plasmas, which cannot be evaluated by photographic observations, spatial distributions of lineintegrated electron density and inverse Abel transformation of the distributions are required. This diagnostic method of radial distribution is also applied for excited species measurements in the high-pressure plasmas by a laser absorption spectroscopy (LAS) and a laser induced fluorescence (LIF) methods (Urabe et al., 2010). Figure 7(a) shows two spatial distributions of the line-integrated electron density, e *n dl x*( ) , measured near the tubular cathode and the pin anode in the DC discharge scanning the laser beam perpendicularly to the gas-flow axis. Using the CO2-laser heterodyne interferometer with appropriate control of

discharge current is the same as that at lower pressure.

**3.2 Atmospheric-pressure DC discharge in open space** 

less cooling effect by neutral gas particles.

2003).

resolutions of the heterodyne interferometer, and the combination measurement method for AC-voltage driven APPs, will be discussed in addition to the measured electron-density distributions in the tested plasma sources.

#### **3.1 Small-scale DC discharge at high pressure**

A short hollow cathode (HC) discharge tube shown in Fig. 5(a) was used for basic experiments of our CO2-laser heterodyne interferometer system with variable pressure in pure He gas. The results can be good references to measurement of other plasmas operated at atmospheric pressure introduced in following subsections. Two electrodes for anode and cathode had a 2-mm bore and a 4-mm hole length, and these electrodes were separated by a 1.5-mm thick ceramic disk also having the 2-mm bore. Two of ZnSe windows were equipped to seal the discharge region and transmit the CO2 laser beam. Gas pressure inside the small chamber was controlled in a range from several tens to hundreds Torr.

Fig. 5. (a) Cross-sectional diagram and photograph of short hollow cathode (HC) discharge. (b) Dependence of electron density on discharge current in the short HC discharge in He gas at three values of gas pressure.

resolutions of the heterodyne interferometer, and the combination measurement method for AC-voltage driven APPs, will be discussed in addition to the measured electron-density

A short hollow cathode (HC) discharge tube shown in Fig. 5(a) was used for basic experiments of our CO2-laser heterodyne interferometer system with variable pressure in pure He gas. The results can be good references to measurement of other plasmas operated at atmospheric pressure introduced in following subsections. Two electrodes for anode and cathode had a 2-mm bore and a 4-mm hole length, and these electrodes were separated by a 1.5-mm thick ceramic disk also having the 2-mm bore. Two of ZnSe windows were equipped to seal the discharge region and transmit the CO2 laser beam. Gas pressure inside

(a)

Laser path

(b) Fig. 5. (a) Cross-sectional diagram and photograph of short hollow cathode (HC) discharge. (b) Dependence of electron density on discharge current in the short HC discharge in He gas

0 50 100 150 200 250

Current (mA)

the small chamber was controlled in a range from several tens to hundreds Torr.

Gas inlet Gas outlet

He gas pressure 35 Torr 70 Torr 140 Torr

Anode Ceramic

distributions in the tested plasma sources.

at three values of gas pressure.

Electron density (1013 cm-3

)

**3.1 Small-scale DC discharge at high pressure** 

Cathode

ZnSe window Figure 5(b) shows dependences of electron density in the short HC discharge on the discharge current measured at several He gas pressures. In the calculation of electron density from the phase shift signal, we used two assumptions that the plasma was uniform along the CO2 laser path and its effective length was 9.5 mm. The electron density in the discharge increased monotonically with the increase of the discharge current and the gas pressure. This result indicates that the CO2-laser heterodyne interferometer is able to measure appropriate dependence of electron density on the gas pressure, because the electron density inside the high-pressure plasma must be increased at higher pressure by the slower drift velocity of electrons due to frequent collisions with gas particles when the discharge current is the same as that at lower pressure.

Here, the minimum sensitivity of electron density in our CO2-laser heterodyne interferometer is introduced. The minimum electron density which we recorded in the short HC discharge was corresponds to a line integrated electron density *n*e*d* of 7×1012 cm−2 with a detected phase shift around 0.1 degree (Choi et al., 2009). However, the signal to noise ratio, for instance shown in Fig. 3, showed that the minimum sensitivity should be at least six times better than that. Therefore, it could be estimated that the minimum detectable phase shift in our system was about 0.02 degree, corresponding to *n*e*d* of 1×1012 cm−2, which is much smaller than the minimum sensitivity of Stark broadening measurement (Laux et al, 2003).

#### **3.2 Atmospheric-pressure DC discharge in open space**

Figure 6(a) shows a schematic diagram of DC discharge in open space operated in a He gas flow ejected from a tubular cathode to a pin anode. The cylindrical tubular cathode, whose outer and inner diameters were 3.1 and 2.1 mm, and the pin anode with a 0.5-mm diameter were faced to the cathode with a 3-mm gap. The measurement point between the cathode and the anode was scanned by putting the whole discharge device on a three-dimensional mechanical movement stage. The influence of temporal evolutions of the gas-particle density on the measured phase shift can be seen in Fig. 6(b) showing the phase-shift signals observed in the atmospheric-pressure DC discharge using two different flow rates of He gas (1 and 2 L/min). This measurement result clearly suggests that the contribution of the Joule heating on temporal evolution of the phase shift becomes much greater in the discharge operated at atmospheric pressure and the gas-particle component in the phase shift, *ΔΦ*g, has large dependence on the gas flow velocity. The fast time constant and large amplitude of *ΔΦ*g in both rising and falling periods of applied voltage in lower gas flow rate was due to less cooling effect by neutral gas particles.

In order to obtain radial distributions of electron density in the high-pressure plasmas, which cannot be evaluated by photographic observations, spatial distributions of lineintegrated electron density and inverse Abel transformation of the distributions are required. This diagnostic method of radial distribution is also applied for excited species measurements in the high-pressure plasmas by a laser absorption spectroscopy (LAS) and a laser induced fluorescence (LIF) methods (Urabe et al., 2010). Figure 7(a) shows two spatial distributions of the line-integrated electron density, e *n dl x*( ) , measured near the tubular cathode and the pin anode in the DC discharge scanning the laser beam perpendicularly to the gas-flow axis. Using the CO2-laser heterodyne interferometer with appropriate control of

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 219

e e ( ) 2 2 <sup>1</sup> ( ) ( ) *r*

(a)


Horizontal position *x* (mm)

(b) Fig. 7. (a) Spatial distributions of line-integrated electron density measured in DC plasma jet near tubular cathode and pin anode. (b) Radial distributions of electron density derived from line-integrated electron density using inverse Abel transformation (Choi et al., 2009).


Radial position *r* (mm)

The calculated results in Fig. 7(b) indicate that total amounts of the electrons near the cathode and the anode are significantly different in this DC discharge and there must be another kind of negatively charged particles delivering the discharge current and keeping

*n r n dl x* π

∞

= −

0.0

0.5

1.0

1.5

Electron density (1014 cm-3

)

2.0

2.5

Line-integrated electron

density (1013 cm-2

)

*d dx*

Measurement position

Measurement position

 Near tubular cathode Near pin anode

 Near tubular cathode Near pin anode

<sup>−</sup> . (7)

*dx x r*

the beam radius around the tested plasma source, the spatial distribution of electron density with enough quality for the inverse Abel transformation can be measured.

(b)

Fig. 6. (a) Schematic diagram and photograph of atmospheric-pressure DC discharge in open space. (b) Temporal evolutions of phase-shift signal in the DC discharge measured changing He gas flow rate.

Calculation results of the inverse Abel transformation corresponding to the radial distribution of electron density, *n*e(*r*), at the measurement points in the DC discharge are shown in Fig. 7(b). The calculated radial distributions showed two different structures which were a hollow shape near the cathode and a center-peaked shape near the anode, having a good agreement with the electrode structures. The inverse Abel transformation was performed using a following equation (Lochte-Holtgreven, 1968),

∞

218 CO2 Laser – Optimisation and Application

the beam radius around the tested plasma source, the spatial distribution of electron density

Atmospheric

(a)

Gas inlet

(b) Fig. 6. (a) Schematic diagram and photograph of atmospheric-pressure DC discharge in open space. (b) Temporal evolutions of phase-shift signal in the DC discharge measured

Time (ms)


Current (mA)

 He flow rate 1 L/min 2 L/min

Calculation results of the inverse Abel transformation corresponding to the radial distribution of electron density, *n*e(*r*), at the measurement points in the DC discharge are shown in Fig. 7(b). The calculated radial distributions showed two different structures which were a hollow shape near the cathode and a center-peaked shape near the anode, having a good agreement with the electrode structures. The inverse Abel transformation

was performed using a following equation (Lochte-Holtgreven, 1968),

changing He gas flow rate.






Phase-shift signal (mV)


0

with enough quality for the inverse Abel transformation can be measured.

air Laser path

Pin anode

Tubular cathode

Fig. 7. (a) Spatial distributions of line-integrated electron density measured in DC plasma jet near tubular cathode and pin anode. (b) Radial distributions of electron density derived from line-integrated electron density using inverse Abel transformation (Choi et al., 2009).

(b)

The calculated results in Fig. 7(b) indicate that total amounts of the electrons near the cathode and the anode are significantly different in this DC discharge and there must be another kind of negatively charged particles delivering the discharge current and keeping

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 221

in the APGD, and the influence of this smoothing effect on the phase-shift signal could not be resolved. Therefore, the measured phase-shift waveform should be divided into two components only at the cut-off timing of applied voltage (around 0 ms in Fig. 8(b)). Calculation procedure of the temporally-averaged electron density after dividing the two

> Power supply

**60 mm** ZnSe

Dielectric barrier Laser path

window

Modulation signal (V)

0

1

2

3

4

5

(a)

Exponential fit of ΔΦ**g**

Electrode

(b) Fig. 8. (a) Cross-sectional diagram of parallel-plate dielectric barrier discharge (DBD). (b) Example temporal evolution of phase shift by the parallel-plate DBD together with amplitude modulation signal of 30-kHz AC applied voltage (Urabe et al., 2011).


Time (ms)

ΔΦ**e**

The spatial distribution of the electron-density component in the phase shift and the calculated temporally-averaged electron density from the four signal waveforms measured under the same condition are shown in Fig. 9. The points and both ends of error bars indicate the averaged value and the maximum and minimum values in each measurement. The electron-density distribution inside the APGD was localized near the dielectric barriers, and this result had a good agreement with reported results of computational simulations in similar geometries (Massines et al., 1998, 2003; Martens et al., 2009). The electron density near the powered electrode was approximately two times larger than that near the

components is the same as the calculation in DC discharges.




0.0

Phase shift (degree)

0.2

Vacuum chamber

its continuity. Considering that electron density near the central axis of the gas flow was not different at both measurement points, there were some losing mechanisms of the electrons outside of the He gas flow where ambient air contaminates into the flow. The electron loss was mainly due to an electron attachment process with O2 molecules presenting in the ambient air in the DC discharge, because of μm-order short diffusion lengths of electrons in the atmospheric-pressure gas conditions which could be derived from calculations of electron diffusion coefficient (Hargelaar & Pitchford, 2005) and measurement results of electron lifetime (Moselhy et al., 2003). Whereas this negative-ion density, for example O2 ions, cannot be detected by the CO2-laser heterodyne interferometer, this selectivity of negatively charged particles in the interferometer enables us to distinguish kinds and fractions of the negatively charged particle inside the high-pressure plasmas with the estimation of total amount of the charged particles from the discharge current amplitude.

#### **3.3 Pulsed AC discharge at atmospheric pressure**

For the measurement of electron density inside the high-pressure plasmas driven by kHzorder AC applied voltage, the temporal resolution of CO2-laser heterodyne interferometer using the lock-in amplifier is often insufficient for direct measurement of temporal evolutions of electron density. In order to depict spatiotemporal structures of electron density inside such plasma sources, for example dielectric barrier discharges (DBDs) (Kogelschatz, 2003; Becker et al., 2005) and ns-order short pulsed discharges (Namihira et al., 2003; Walsh & Kong, 2007), it has been confirmed that an amplitude modulation of the kHz-order applied voltage at a frequency of a few hundreds Hz and additional measurement of a millimeter-wave (mm-wave) transmission method are effective.

Figure 8(a) shows a schematic diagram of atmospheric-pressure glow discharge (APGD) tested in our group. The APGD is a major kind of DBDs generating homogeneous plasmas with atmospheric-pressure He gas and kHz-order AC applied voltage (Kanazawa et al., 1988). Powered (upper side) and grounded (lower side) stainless-steel electrodes were round, and their diameters were 60 mm. Dielectric barriers of 1-mm thick alumina were placed on the electrodes' surface and a gap distance between the two barriers was set at 6.0 mm. Whole electrode setup was installed in a vacuum chamber with a pair of ZnSe windows to control the gas compositions and pressures. In the measurement of APGD, we used a pair of ZnSe lens with longer focal length (20 cm), in order to get constant beam shape in whole discharge region with 60-mm length along the CO2 laser path. Therefore, the spatial resolution of the interferometer was worse than the measurement of small-scale DC plasmas explained in above subsections.

To divide the phase-shift signal into two components of the electron and gas-particle densities in a similar way to that used for the small-scale DC discharges, we used a squarepulse amplitude modulation at 125 Hz for the 30-kHz AC applied voltage, whose modulation-signal waveform is shown in Fig. 8(b). Using this amplitude modulation, the temporal evolution of phase shift has the fall and rise slopes in the both ends of modulation signal similar to that in the measurement of pulsed DC discharges. However, in the measurement of AC discharge, the phase-shift signal at the start-up timing of applied voltage (around −3.5 ms in the abscissa axis of Fig. 8(b)) is unsuitable for the derivation of the electron-density component in the phase shift. At this timing, the signal associated with the electron density was smoothed by the step-wise increase due to intermittent discharges

its continuity. Considering that electron density near the central axis of the gas flow was not different at both measurement points, there were some losing mechanisms of the electrons outside of the He gas flow where ambient air contaminates into the flow. The electron loss was mainly due to an electron attachment process with O2 molecules presenting in the ambient air in the DC discharge, because of μm-order short diffusion lengths of electrons in the atmospheric-pressure gas conditions which could be derived from calculations of electron diffusion coefficient (Hargelaar & Pitchford, 2005) and measurement results of electron lifetime (Moselhy et al., 2003). Whereas this negative-ion density, for example O2 ions, cannot be detected by the CO2-laser heterodyne interferometer, this selectivity of negatively charged particles in the interferometer enables us to distinguish kinds and fractions of the negatively charged particle inside the high-pressure plasmas with the estimation of total amount of the charged particles from the discharge current amplitude.

For the measurement of electron density inside the high-pressure plasmas driven by kHzorder AC applied voltage, the temporal resolution of CO2-laser heterodyne interferometer using the lock-in amplifier is often insufficient for direct measurement of temporal evolutions of electron density. In order to depict spatiotemporal structures of electron density inside such plasma sources, for example dielectric barrier discharges (DBDs) (Kogelschatz, 2003; Becker et al., 2005) and ns-order short pulsed discharges (Namihira et al., 2003; Walsh & Kong, 2007), it has been confirmed that an amplitude modulation of the kHz-order applied voltage at a frequency of a few hundreds Hz and additional

Figure 8(a) shows a schematic diagram of atmospheric-pressure glow discharge (APGD) tested in our group. The APGD is a major kind of DBDs generating homogeneous plasmas with atmospheric-pressure He gas and kHz-order AC applied voltage (Kanazawa et al., 1988). Powered (upper side) and grounded (lower side) stainless-steel electrodes were round, and their diameters were 60 mm. Dielectric barriers of 1-mm thick alumina were placed on the electrodes' surface and a gap distance between the two barriers was set at 6.0 mm. Whole electrode setup was installed in a vacuum chamber with a pair of ZnSe windows to control the gas compositions and pressures. In the measurement of APGD, we used a pair of ZnSe lens with longer focal length (20 cm), in order to get constant beam shape in whole discharge region with 60-mm length along the CO2 laser path. Therefore, the spatial resolution of the interferometer was worse than the measurement of small-scale DC

To divide the phase-shift signal into two components of the electron and gas-particle densities in a similar way to that used for the small-scale DC discharges, we used a squarepulse amplitude modulation at 125 Hz for the 30-kHz AC applied voltage, whose modulation-signal waveform is shown in Fig. 8(b). Using this amplitude modulation, the temporal evolution of phase shift has the fall and rise slopes in the both ends of modulation signal similar to that in the measurement of pulsed DC discharges. However, in the measurement of AC discharge, the phase-shift signal at the start-up timing of applied voltage (around −3.5 ms in the abscissa axis of Fig. 8(b)) is unsuitable for the derivation of the electron-density component in the phase shift. At this timing, the signal associated with the electron density was smoothed by the step-wise increase due to intermittent discharges

measurement of a millimeter-wave (mm-wave) transmission method are effective.

**3.3 Pulsed AC discharge at atmospheric pressure** 

plasmas explained in above subsections.

in the APGD, and the influence of this smoothing effect on the phase-shift signal could not be resolved. Therefore, the measured phase-shift waveform should be divided into two components only at the cut-off timing of applied voltage (around 0 ms in Fig. 8(b)). Calculation procedure of the temporally-averaged electron density after dividing the two components is the same as the calculation in DC discharges.

Fig. 8. (a) Cross-sectional diagram of parallel-plate dielectric barrier discharge (DBD). (b) Example temporal evolution of phase shift by the parallel-plate DBD together with amplitude modulation signal of 30-kHz AC applied voltage (Urabe et al., 2011).

The spatial distribution of the electron-density component in the phase shift and the calculated temporally-averaged electron density from the four signal waveforms measured under the same condition are shown in Fig. 9. The points and both ends of error bars indicate the averaged value and the maximum and minimum values in each measurement. The electron-density distribution inside the APGD was localized near the dielectric barriers, and this result had a good agreement with reported results of computational simulations in similar geometries (Massines et al., 1998, 2003; Martens et al., 2009). The electron density near the powered electrode was approximately two times larger than that near the

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 223

together with the waveform of applied voltage. The electron density increased after the positive- and negative-main pulses around 2.6 and 19.0 µs in the abscissa time axis, and there were small increases in electron density after the main pulses caused by weak

From the measurement results of the CO2-laser heterodyne interferometer and the mmwave transmission method applied to the same plasma source, spatial distribution of temporal-peak electron density can be calculated dividing the temporally-averaged electron densities by a duty ratio of plasma. The duty ratio of plasma is the ratio of temporallyaveraged electron density to temporal-peak density in the result of the mm-wave transmission measurement, and it indicates the temporally averaging effects of the CO2 laser heterodyne interferometer. In an example case of the APGD measurement shown in Figs. 9 and 10, the calculated duty ratio of plasma was 0.33. Then, the temporal-peak electron densities near the dielectric barriers were derived approximately 5×1012 cm−3 on the

In this chapter, we reviewed experimental studies for electron-density measurement in small-scale plasmas operated at high and atmospheric pressures using the CO2-laser heterodyne interferometer, from brief theoretical introduction of the interferometer to specific measurement results in the high-pressure plasma sources. It should be noted that separation of the CO2 laser beam's phase shift into two components, which are due to changes of electron and gas-particle densities, is the most important procedure for the measurement in high-pressure plasmas, and pulse modulation of applied voltage is

From the experimental results of the interferometer in high-pressure plasmas driven by pulsed DC voltage, fundamental properties of our interferometer including the minimum sensitivity of line-integrated electron density and the spatial resolution could be evaluated. Because these properties are changed due to specifications of the laser source and the phase detecting system, they must be confirmed in each setup of the interferometer before practical measurements. In addition to the interferometer, a mmwave transmission method with a good temporal resolution was used to AC-voltage driven plasmas having ns-order fast temporal behavior. This novel combination method has potentials to be applied to the refractive-index measurements requiring both spatial

Our studies on the CO2-laser heterodyne interferometer were partially supported by Grantin-Aid for Scientific Research from the MEXT of Japan and Global Center of Excellence program on Photonics and Electronics Science and Engineering at Kyoto University. The authors would like to thank Prof. Osamu Sakai, Dr. Nobuhiko Takano, Dr. Joon-Young Choi, and Dr. Yosuke Ito at Kyoto University for their substantial supports. The author U.K. would like to acknowledge support of Research Fellowship from Japan Society for the

indispensable for the separation at the rise and fall timings of the modulation signal.

side of the powered electrode and 2×1012 cm−3 on the grounded electrode.

discharges in the ringing part of applied voltage.

**4. Concluding remarks** 

and temporal high resolutions.

**5. Acknowledgments** 

Promotion of Science.

grounded electrode in each gas composition. This asymmetric distribution was probably caused by diffusion of the discharge current flow into the chamber wall from the powered electrode not flowing into the grounded electrode.

To get temporally resolved information of the electron density inside the APGD, we inserted a mm-wave at 55 GHz through the vacuum chamber and measured temporal evolutions of the transmitted mm-wave intensity using a pair of horn antennas. In this mm-wave transmission method, spatial distributions of electron density cannot be measured because of the diffraction limit of the mm-wave. Details of the experimental setup and the calculation procedure of spatially-averaged electron density are introduced in our previous paper (Urabe et al., 2011). The temporal evolution of spatially-averaged electron density in the APGD derived from absorption ratio of the mm-wave in the plasma is shown in Fig. 10,

Fig. 9. Spatial distribution of electron-density component in phase shift and calculated temporally-averaged electron density in APGD (Urabe et al., 2011).

Fig. 10. Temporal evolution of spatially-averaged electron density in APGD measured by mm-wave transmission method under same conditions as interferometer measurement (Fig. 9), together with applied-voltage waveform (Urabe et al., 2011).

together with the waveform of applied voltage. The electron density increased after the positive- and negative-main pulses around 2.6 and 19.0 µs in the abscissa time axis, and there were small increases in electron density after the main pulses caused by weak discharges in the ringing part of applied voltage.

From the measurement results of the CO2-laser heterodyne interferometer and the mmwave transmission method applied to the same plasma source, spatial distribution of temporal-peak electron density can be calculated dividing the temporally-averaged electron densities by a duty ratio of plasma. The duty ratio of plasma is the ratio of temporallyaveraged electron density to temporal-peak density in the result of the mm-wave transmission measurement, and it indicates the temporally averaging effects of the CO2 laser heterodyne interferometer. In an example case of the APGD measurement shown in Figs. 9 and 10, the calculated duty ratio of plasma was 0.33. Then, the temporal-peak electron densities near the dielectric barriers were derived approximately 5×1012 cm−3 on the side of the powered electrode and 2×1012 cm−3 on the grounded electrode.

#### **4. Concluding remarks**

222 CO2 Laser – Optimisation and Application

grounded electrode in each gas composition. This asymmetric distribution was probably caused by diffusion of the discharge current flow into the chamber wall from the powered

To get temporally resolved information of the electron density inside the APGD, we inserted a mm-wave at 55 GHz through the vacuum chamber and measured temporal evolutions of the transmitted mm-wave intensity using a pair of horn antennas. In this mm-wave transmission method, spatial distributions of electron density cannot be measured because of the diffraction limit of the mm-wave. Details of the experimental setup and the calculation procedure of spatially-averaged electron density are introduced in our previous paper (Urabe et al., 2011). The temporal evolution of spatially-averaged electron density in the APGD derived from absorption ratio of the mm-wave in the plasma is shown in Fig. 10,

Fig. 9. Spatial distribution of electron-density component in phase shift and calculated

0123456

0.0


0

Applied voltage (kV)

2

4

6

8

10

0.5

1.0

Temporally-averaged

electron density (1012 cm-3

)

1.5

2.0

Position (mm)

Fig. 10. Temporal evolution of spatially-averaged electron density in APGD measured by mm-wave transmission method under same conditions as interferometer measurement (Fig.

0 10 20 30 40 50

Time (μs)

temporally-averaged electron density in APGD (Urabe et al., 2011).

0.00


0.05

0.10

Electron-density component in

Spatially-averaged

electron density (1012 cm-3

)

phase shift, ΔΦe (degree)

0.15

0.20

0.25

9), together with applied-voltage waveform (Urabe et al., 2011).

electrode not flowing into the grounded electrode.

In this chapter, we reviewed experimental studies for electron-density measurement in small-scale plasmas operated at high and atmospheric pressures using the CO2-laser heterodyne interferometer, from brief theoretical introduction of the interferometer to specific measurement results in the high-pressure plasma sources. It should be noted that separation of the CO2 laser beam's phase shift into two components, which are due to changes of electron and gas-particle densities, is the most important procedure for the measurement in high-pressure plasmas, and pulse modulation of applied voltage is indispensable for the separation at the rise and fall timings of the modulation signal.

From the experimental results of the interferometer in high-pressure plasmas driven by pulsed DC voltage, fundamental properties of our interferometer including the minimum sensitivity of line-integrated electron density and the spatial resolution could be evaluated. Because these properties are changed due to specifications of the laser source and the phase detecting system, they must be confirmed in each setup of the interferometer before practical measurements. In addition to the interferometer, a mmwave transmission method with a good temporal resolution was used to AC-voltage driven plasmas having ns-order fast temporal behavior. This novel combination method has potentials to be applied to the refractive-index measurements requiring both spatial and temporal high resolutions.

#### **5. Acknowledgments**

Our studies on the CO2-laser heterodyne interferometer were partially supported by Grantin-Aid for Scientific Research from the MEXT of Japan and Global Center of Excellence program on Photonics and Electronics Science and Engineering at Kyoto University. The authors would like to thank Prof. Osamu Sakai, Dr. Nobuhiko Takano, Dr. Joon-Young Choi, and Dr. Yosuke Ito at Kyoto University for their substantial supports. The author U.K. would like to acknowledge support of Research Fellowship from Japan Society for the Promotion of Science.

Heterodyne Interferometer for Measurement of Electron Density in High-Pressure Plasmas 225

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Leipold, F.; Stark, R.H.; El-Habachi, A. & Schoenbach, K.H. (2000). Electron density

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Massines, F.; Rabehi, A.; Decomps, P.; Gadri, R.B.; Segur, P. & Mayoux, C. (1998).

Namihira, T.; Wang, D.; Katsuki, S.; Hackam, R. & Akiyama, H. (2003). Propagation Velocity

Nozaki, T.; Sasaki, K.; Ogino, T.; Asahi, D. & Okazaki, K. (2007). Microplasma synthesis of

Paschen, F. (1889). Ueber die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure

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Tachibana, K.; Kishimoto, Y. & Sakai, O. (2005(a)). Measurement of metastable He\*(23S1)

Urabe, K.; Morita, T.; Tachibana, K. & Ganguly, B.N. (2010). Investigation of discharge

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measurements in an atmospheric pressure air plasma by means of infrared heterodyne interferometry. *Journal of Physics D: Applied Physics,* Vol. 33, pp. 2268-

during the formation of an atmospheric pressure dielectric barrier glow discharge.

Experimental and theoretical study of a glow discharge at atmospheric pressure controlled by dielectric barrier. *Journal of Applied Physics,* Vol. 83, pp. 2950-2957 Massines, F.; Segur, P.; Gherardi, N.; Khamphan, C. & Ricard, A. (2003). Physics and

chemistry in a glow dielectric barrier discharge at atmospheric pressure: diagnostics and modeling. *Surface and Coatings Technology,* Vol. 174–175, pp. 8-14 Moselhy, M.; Petzenhauser, I.; Frank, K. & Schoenbach, K.H. (2003). Excimer emission from

microhollow cathode argon discharges. *Journal of Physics D: Applied Physics,* Vol. 36,

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tunable photoluminescent silicon nanocrystals. *Nanotechnology,* Vol. 18, pp. 235603-

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Ichiki, T.; Taura, R. & Horiike, Y. (2004). Localized and ultrahigh-rate etching of silicon

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**8** 

*Russian Federation* 

**Transmission of CO2 Laser Radiation Through** 

A. D. Pryamikov, A. F. Kosolapov, V. G. Plotnichenko and E. M. Dianov

In this chapter we would like to highlight and analyze the main problems of transmission and propagation of CO2 laser radiation in the hollow core microstructured fibers (HC MFs). It is well known that there is a strong need for the fiber delivery systems for 10.6 μm CO2 lasers due to a wide range of CO2 laser applications in medicine, spectrometry, industry, military applications and in other fields of science and technology. Research into the possibility of the mid IR laser radiation transmission (especially, CO and CO2 lasers) with the help of optical fibers as well as with crystalline or glass cores made of different materials has been going hand with hand with the technological development. However, until recently these fibers haven't been used for industrial applications due to a relatively high level of optical losses at the lasers wavelengths and certain physicochemical properties of the fiber materials. These problems mainly arise from a low laser damage threshold, low

melting temperatures of most IR transmitting materials and their high nonlinearity.

Hollow waveguides are exempt from many problems that are common to all types of the solid waveguides in this spectral region and thus can serve as much more reliable delivery systems. Glass hollow waveguides, crystalline hollow waveguides, dielectric – coated cylindrical hollow waveguides, polycrystalline fibers are well known examples of such systems. Here we consider only the glass HC MFs with their characteristics and physical phenomena laying the basis for their waveguide mechanisms. In particular, we propose a new type of HC MF for CO2 laser radiation delivery with the cladding consisting of one row of the glass capillaries. We show that due to complicated boundary conditions and optical properties of an individual capillary it is possible to obtain low loss waveguide regimes for CO2 laser radiation. Moreover, we show that the HC MFs with a determined symmetry type of a capillary arrangement in the cladding exhibit low bend losses when such low loss

The chapter is organized as follows. In Section 2 we consider all types of proposed hollow waveguides for CO2 laser radiation transmission and give a short historical overview to highlight the problem of CO2 laser beam delivery in the hollow core waveguides. In Section 3 we consider physical mechanisms of the light guiding in the glass HC MFs with cladding consisting of capillaries due to which, in our opinion, it becomes possible to guide the light in the mid IR including CO2 laser radiation. In Section 4 we offer some numerical analyses

**1. Introduction** 

waveguide regimes occur.

**Glass Hollow Core Microstructured Fibers** 

*Fiber Optics Research Center of Russian Academy of Sciences* 


### **Transmission of CO2 Laser Radiation Through Glass Hollow Core Microstructured Fibers**

A. D. Pryamikov, A. F. Kosolapov, V. G. Plotnichenko and E. M. Dianov *Fiber Optics Research Center of Russian Academy of Sciences Russian Federation* 

#### **1. Introduction**

226 CO2 Laser – Optimisation and Application

Urabe, K.; Sakai, O. & Tachibana, K. (2011). Combined spectroscopic methods for electron-

Walsh, J.L. & Kong, M.G. (2007). 10 ns pulsed atmospheric air plasma for uniform treatment of polymeric surfaces. *Applied Physics Letters,* Vol. 91, pp. 241504-1-3 Yariv, A. (1997). *Optical Electronics in Modern Communications,* Oxford University Press, New

mixture. *Journal of Physics D: Applied Physics,* Vol. 44, pp. 115203-1-11 von Engel, A. (1994). *Ionized Gases,* American Institute of Physics, New York, USA

York, USA

density diagnostics inside atmospheric-pressure glow discharge using He/N2 gas

In this chapter we would like to highlight and analyze the main problems of transmission and propagation of CO2 laser radiation in the hollow core microstructured fibers (HC MFs). It is well known that there is a strong need for the fiber delivery systems for 10.6 μm CO2 lasers due to a wide range of CO2 laser applications in medicine, spectrometry, industry, military applications and in other fields of science and technology. Research into the possibility of the mid IR laser radiation transmission (especially, CO and CO2 lasers) with the help of optical fibers as well as with crystalline or glass cores made of different materials has been going hand with hand with the technological development. However, until recently these fibers haven't been used for industrial applications due to a relatively high level of optical losses at the lasers wavelengths and certain physicochemical properties of the fiber materials. These problems mainly arise from a low laser damage threshold, low melting temperatures of most IR transmitting materials and their high nonlinearity.

Hollow waveguides are exempt from many problems that are common to all types of the solid waveguides in this spectral region and thus can serve as much more reliable delivery systems. Glass hollow waveguides, crystalline hollow waveguides, dielectric – coated cylindrical hollow waveguides, polycrystalline fibers are well known examples of such systems. Here we consider only the glass HC MFs with their characteristics and physical phenomena laying the basis for their waveguide mechanisms. In particular, we propose a new type of HC MF for CO2 laser radiation delivery with the cladding consisting of one row of the glass capillaries. We show that due to complicated boundary conditions and optical properties of an individual capillary it is possible to obtain low loss waveguide regimes for CO2 laser radiation. Moreover, we show that the HC MFs with a determined symmetry type of a capillary arrangement in the cladding exhibit low bend losses when such low loss waveguide regimes occur.

The chapter is organized as follows. In Section 2 we consider all types of proposed hollow waveguides for CO2 laser radiation transmission and give a short historical overview to highlight the problem of CO2 laser beam delivery in the hollow core waveguides. In Section 3 we consider physical mechanisms of the light guiding in the glass HC MFs with cladding consisting of capillaries due to which, in our opinion, it becomes possible to guide the light in the mid IR including CO2 laser radiation. In Section 4 we offer some numerical analyses

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 229

core materials with a refractive index less than 1. Due to this fact, the angle of incident radiation in the core is greater than the critical angle and the light experiences the total internal reflection. An example of such fiber operating at the CO2 laser wavelength is the

For our part, in the following subsections we will consider the second group of the circular cross section hollow waveguides, previously classified as leaky waveguides, in particular, HC MFs. This group of hollow waveguides has inner wall surface with refractive indices greater than 1. Leaky hollow waveguides have metallic or dielectric layers deposited on the inside metallic, plastic or glass tubing to enhance their surface reflectivity. Creation of such dielectric coated cylindrical hollow waveguides presented a complicated technological problem since high quality reflective coatings are not compatible with circular cross section geometry. Traditional vapor deposition techniques don't produce good quality coatings on the inside of a capillary. The theoretical calculated attenuation of a dielectric coated hollow waveguide for the IR region was obtained in [Miyagi & Kawakami, 1984]. The authors have shown that the attenuation is very sensitive to the material and geometry of a dielectric film. Also, the attenuation is very sensitive to the properties of the metal under the dielectric film. A metal should have a low refractive index and a very high extinction coefficient. For example, these can be silver, nickel, copper. A dielectric should be selected with a maximum refractive index, for example, KCl, ZnSe, ZnS etc. The first demonstration of a dielectric coated cylindrical hollow waveguide was perfomed by Prof. Miyagi's group [Miyagi et. al., 1983] in 1983. The 1.2 m – long mandrel of polished aluminum tubing was coated with approximately 0.45 μm of germanium. Then, a layer of nickel up to 200 μm was deposited on the top of germanium before the aluminum mandrel was removed by leaching. The final structure was a nickel tube with optically thick dielectric layers on the inner wall. The fabricated waveguide had a core diameter of 1.5 mm and length of about 1 m. The measured attenuation was ~ 0.4 dB/m in the straight waveguide but the bend loss was very high.

Authors in [Croitoru et. al., U.S. Patent, 1990] have used polyethylene and Teflon tubing as a substrate in which thin and flexible metallic layers of Al followed by AgI were deposited. They reported attenuation in a straight waveguide of about 0.6 dB/m at the bore size value of 4 mm [Croitoru et. al., 1990]. Authors of [Morrow & Gu, 1994] reported a cylindrical hollow waveguide in which Ag and Ag halide coatings were deposited inside Ag tubes. The

At the end of this subsection, we will turn to the currently most popular hollow circular cross section waveguides for CO2 laser radiation transmission. These are hollow glass waveguides developed initially by Prof. Harrington's group [Abel et. al., 1994]. There are two main advantages of the glass tubing substrate. First, it is easier to make a long, uniform tubing from glass having considerably smoother wall surfaces than metal or plastic tubings. As a result, the scattered losses are less. The second advantage is that the technology of making glass capillary tubings is common and inexpensive. The authors fabricated a hollow glass waveguide using wet chemistry methods. First, an Ag layer was deposited on the inside of a silica glass tubing. Then, an AgI layer was formed over the metallic film. The thickness of the layer was optimized to obtain a high reflectivity at the required wavelength. A straight waveguide with a bore of 530 μm demonstrated a loss of 0.3 dB/m at CO2 laser wavelength. This fiber could maintain a loss level under 2 dB/m at a bend radius as small as

λ

= 10.6 μm which

waveguide with 1 – mm – bore size had attenuation below 0.1 dB/m at

was still below 0.8 dB/m at a bend radius up to 25 cm.

sapphire fiber with a refractive index of *n* = 0.67 [Harrington & Gregory, 1990].

and show a possibility to achieve low loss waveguide regimes in such HC MFs by careful selection of geometry parameters characterizing the fibers and a glass refractive index. Section 5 contains conclusions.

#### **2. CO2 laser radiation transmission through hollow core waveguides**

A variety of waveguides has been studied for the delivery of CO2 laser energy. In this section we consider briefly all types and properties of hollow waveguides and HC MFs for the CO2 laser radiation transmission known up to now.

#### **2.1 Historical overview of CO2 laser radiation transmission through hollow waveguides**

Rectangular core hollow waveguide structures were the first suggested for the delivery of CO2 laser radiation [Nishihara et. al., 1974]. The first publication on the IR spectral transmission measurements of a rectangular hollow waveguide dates back to [Garmire, 1976]. The hollow waveguide described was made of aluminium strips with heights greater than 0.5 mm demonstrating a delivery over 200 W of continuous CO2 laser radiation with no damage to the structure [Garmire et. al., 1979]. However, such metallic rectangular waveguides are not suitable for many practical applications due to their relatively big outer dimensions ~ 1 mm\*10mm in cross section while smaller dimensions made the loss was too high for any practical use. Thus the search for materials and waveguides more suitable for practical applications continued and, a few years later, in [Laakmann, 1987] there was proposed a way to decrease the outside dimensions of HC waveguides to under 2 mm in diameter and to increase the reflectivity of the bore inside surface. Silver was used as a substrate metallic material of the rectangular core on which several dielectric coatings were deposited. By doing so, the author succeeded in maintaining a practical transmission level for the hollow rectangular waveguides. However, as imperfections of the inside geometry and surfaces affected the transmission, the design of the rectangular hollow waveguide proposed in [Laakmann, 1987] had to be improved [Mashida et. al., 1991]. The authors proposed a hollow waveguide having the same cross section design as in [Laakmann, 1987] but with multiple dielectric coatings on the inside surfaces to increase its reflectivity. As a result, 1 – mm – core straight rectangular hollow waveguide of such construction had a loss ~ 0.1 dB/m for circularly polarized CO2 laser radiation. Moreover, the waveguide demonstrated the low loss for a bend. The next attempt to decrease loss for the rectangular core hollow waveguides was described in [Karasawa et. al., 1990]. The authors proposed and fabricated a germanium coated rectangular hollow waveguide with a cross section of 2 mm2, a length of 80 cm and a loss of less than 0.1 dB/m was fabricated. The resulting waveguide had a relatively low loss even for a bend.

However, the main disadvantage of the rectangular hollow waveguides is their relatively large outer dimensions and low flexibility which has led to a greater popularity of circular hollow waveguides. These waveguides made of glass, metal or plastic are those most commonly used today. Along general lines, circular cross section hollow waveguides for CO2 laser radiation transmission can be divided into two groups: attenuating total reflecting and leaky waveguides. The metallic or dielectric films are deposited on the inside of metallic, plastic or glass tubing. Attenuating total reflecting hollow waveguides have inner

and show a possibility to achieve low loss waveguide regimes in such HC MFs by careful selection of geometry parameters characterizing the fibers and a glass refractive index.

A variety of waveguides has been studied for the delivery of CO2 laser energy. In this section we consider briefly all types and properties of hollow waveguides and HC MFs for

Rectangular core hollow waveguide structures were the first suggested for the delivery of CO2 laser radiation [Nishihara et. al., 1974]. The first publication on the IR spectral transmission measurements of a rectangular hollow waveguide dates back to [Garmire, 1976]. The hollow waveguide described was made of aluminium strips with heights greater than 0.5 mm demonstrating a delivery over 200 W of continuous CO2 laser radiation with no damage to the structure [Garmire et. al., 1979]. However, such metallic rectangular waveguides are not suitable for many practical applications due to their relatively big outer dimensions ~ 1 mm\*10mm in cross section while smaller dimensions made the loss was too high for any practical use. Thus the search for materials and waveguides more suitable for practical applications continued and, a few years later, in [Laakmann, 1987] there was proposed a way to decrease the outside dimensions of HC waveguides to under 2 mm in diameter and to increase the reflectivity of the bore inside surface. Silver was used as a substrate metallic material of the rectangular core on which several dielectric coatings were deposited. By doing so, the author succeeded in maintaining a practical transmission level for the hollow rectangular waveguides. However, as imperfections of the inside geometry and surfaces affected the transmission, the design of the rectangular hollow waveguide proposed in [Laakmann, 1987] had to be improved [Mashida et. al., 1991]. The authors proposed a hollow waveguide having the same cross section design as in [Laakmann, 1987] but with multiple dielectric coatings on the inside surfaces to increase its reflectivity. As a result, 1 – mm – core straight rectangular hollow waveguide of such construction had a loss ~ 0.1 dB/m for circularly polarized CO2 laser radiation. Moreover, the waveguide demonstrated the low loss for a bend. The next attempt to decrease loss for the rectangular core hollow waveguides was described in [Karasawa et. al., 1990]. The authors proposed and fabricated a germanium coated rectangular hollow waveguide with a cross section of 2 mm2, a length of 80 cm and a loss of less than 0.1 dB/m was fabricated. The resulting

However, the main disadvantage of the rectangular hollow waveguides is their relatively large outer dimensions and low flexibility which has led to a greater popularity of circular hollow waveguides. These waveguides made of glass, metal or plastic are those most commonly used today. Along general lines, circular cross section hollow waveguides for CO2 laser radiation transmission can be divided into two groups: attenuating total reflecting and leaky waveguides. The metallic or dielectric films are deposited on the inside of metallic, plastic or glass tubing. Attenuating total reflecting hollow waveguides have inner

**2. CO2 laser radiation transmission through hollow core waveguides** 

**2.1 Historical overview of CO2 laser radiation transmission through hollow** 

the CO2 laser radiation transmission known up to now.

waveguide had a relatively low loss even for a bend.

Section 5 contains conclusions.

**waveguides** 

core materials with a refractive index less than 1. Due to this fact, the angle of incident radiation in the core is greater than the critical angle and the light experiences the total internal reflection. An example of such fiber operating at the CO2 laser wavelength is the sapphire fiber with a refractive index of *n* = 0.67 [Harrington & Gregory, 1990].

For our part, in the following subsections we will consider the second group of the circular cross section hollow waveguides, previously classified as leaky waveguides, in particular, HC MFs. This group of hollow waveguides has inner wall surface with refractive indices greater than 1. Leaky hollow waveguides have metallic or dielectric layers deposited on the inside metallic, plastic or glass tubing to enhance their surface reflectivity. Creation of such dielectric coated cylindrical hollow waveguides presented a complicated technological problem since high quality reflective coatings are not compatible with circular cross section geometry. Traditional vapor deposition techniques don't produce good quality coatings on the inside of a capillary. The theoretical calculated attenuation of a dielectric coated hollow waveguide for the IR region was obtained in [Miyagi & Kawakami, 1984]. The authors have shown that the attenuation is very sensitive to the material and geometry of a dielectric film. Also, the attenuation is very sensitive to the properties of the metal under the dielectric film. A metal should have a low refractive index and a very high extinction coefficient. For example, these can be silver, nickel, copper. A dielectric should be selected with a maximum refractive index, for example, KCl, ZnSe, ZnS etc. The first demonstration of a dielectric coated cylindrical hollow waveguide was perfomed by Prof. Miyagi's group [Miyagi et. al., 1983] in 1983. The 1.2 m – long mandrel of polished aluminum tubing was coated with approximately 0.45 μm of germanium. Then, a layer of nickel up to 200 μm was deposited on the top of germanium before the aluminum mandrel was removed by leaching. The final structure was a nickel tube with optically thick dielectric layers on the inner wall. The fabricated waveguide had a core diameter of 1.5 mm and length of about 1 m. The measured attenuation was ~ 0.4 dB/m in the straight waveguide but the bend loss was very high.

Authors in [Croitoru et. al., U.S. Patent, 1990] have used polyethylene and Teflon tubing as a substrate in which thin and flexible metallic layers of Al followed by AgI were deposited. They reported attenuation in a straight waveguide of about 0.6 dB/m at the bore size value of 4 mm [Croitoru et. al., 1990]. Authors of [Morrow & Gu, 1994] reported a cylindrical hollow waveguide in which Ag and Ag halide coatings were deposited inside Ag tubes. The waveguide with 1 – mm – bore size had attenuation below 0.1 dB/m at λ = 10.6 μm which was still below 0.8 dB/m at a bend radius up to 25 cm.

At the end of this subsection, we will turn to the currently most popular hollow circular cross section waveguides for CO2 laser radiation transmission. These are hollow glass waveguides developed initially by Prof. Harrington's group [Abel et. al., 1994]. There are two main advantages of the glass tubing substrate. First, it is easier to make a long, uniform tubing from glass having considerably smoother wall surfaces than metal or plastic tubings. As a result, the scattered losses are less. The second advantage is that the technology of making glass capillary tubings is common and inexpensive. The authors fabricated a hollow glass waveguide using wet chemistry methods. First, an Ag layer was deposited on the inside of a silica glass tubing. Then, an AgI layer was formed over the metallic film. The thickness of the layer was optimized to obtain a high reflectivity at the required wavelength. A straight waveguide with a bore of 530 μm demonstrated a loss of 0.3 dB/m at CO2 laser wavelength. This fiber could maintain a loss level under 2 dB/m at a bend radius as small as

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 231

chalcogenide glasses. These glasses are composed of the chalcogen elements Se and Te with an addition of such elements as Ge, As, Sb. The transparency windows of these glasses

Modeling of BG HC PCFs made of nonsilica glasses was performed by a number of authors [Shaw et. al., 2003; Pottage et. al., 2003; Pearce et. al., 2005]. In this paper [Shaw et. al., 2003] BG HC PCFs made of As – S (refractive index ~ 2.4) and As – Se (refractive index ~ 2.8) were analyzed. It was shown that there exist several spectral regions with bandgaps for an air filling fraction > 40% in both As – S and As – Se BG HC PCFs. These BG HC PCFs have large bandgap widths at the air filling fraction of 45% to 60%. BG HC PCFs with high air filling fractions > 80% also exhibited large bandgap widths. In the author' opinion, all these results show a possibility of a light transmission in the mid IR using halcogenide BG HC PCFs. The authors of [Pottage et. al., 2003] have carried out a numerical analyses of BG HC PCFs for a wide range of refractive indices from *n* = 1.5 to *n* =3.6 and for different values of air filling fractions from 33% to 87%. They discovered a new type of the bandgap which was called type 2 bandgap at an air filling fraction ~ 60% for any glass index beyond 2. The results

Another important aspect of the problem of the mid IR radiation transmission was discussed in [Pearce et. al., 2005]. Apart from a limitation to attaining a low loss guidance in BG HC PCFs connected with the intrinsic roughness of the air glass interfaces, there is another problem connected with an existence of surface guided modes that are trapped in the core surroundings. Experimental and theoretical studies [Smith et. al., 2003; Humbert et. al., 2004; West et. al., 2004; Saitoh et. al., 2004] carried out for silica BG HC PCFs have shown that the anticrossing between dispersion curves of the surface modes and the air core modes is the main factor leading to a transmission loss in BG HC PCFs. Several methods were proposed to suppress the surface modes. The first method is used to reduce the distortion of the core by including 'fingers' of glass [West et. al., 2004]. The second method is to use thin core walls [Saitoh et. al., 2004] and the third one is to use 'antiresonance' walls [Roberts, Williams et. al., 2005]. The authors of [Pearce et. al., 2005] modeled a realistic design of distorted cores for BG HC PCFs which can guide the light in the type 2 bandgap. They have demonstrated that BG HC PCFs made of high index glass can guide a fundamental air core

In their paper [Hu & Menyuk, 2007] the authors analyzed BG HC PCFs for refractive indices between 1.4 and 2.8. They found two maxima of the relative bandgap as a function of the air filling fraction and refractive index. The authors also found that the relative bandgap and the level of loss are interrelated. When the relative bandgap increases the loss decreases and

Despite the promising results of modeling obtained in the above listed works a practical realization of BG HC PCFs made completely of chalcogenide glass for the mid IR spectral region has not been reported. The only successful realization of a photonic band gap hollow core fiber for the CO2 laser radiation transmission was 'Omniguide' fiber where the cladding is a Bragg reflector (hollow core Bragg fiber) made of soft glass and polymer [Temelkuran et. al., 2002]. The authors of [Bowden & Harrington, 2009] have studied low and high index chalcogenide glasses for their potential use in the fabrication of all glass hollow core Bragg

showed a possibility of obtaining a satisfactory guidance in such BG HC PCFs.

correspond approximately to the mid IR region 2 – 25 μm.

mode with a fraction of power in the air of up to 98%.

vice versa.

fiber.

5 cm. Hollow glass waveguides have been used successfully for a modest CO2 laser power delivery below ~ 80 W. For the higher power delivery it is necessary to place a water – cooled jacket around the guides. The highest CO2 laser power delivered through the water – cooled hollow glass waveguide with 700 μm bore was 1040 W [Nubling & Harrington, 1996]. This is comparable to CO2 laser power delivered through the water – cooled hollow metallic waveguide with 1800 μm bore which was 2700 W [Hongo et. al., 1992].

#### **2.2 CO2 laser radiation transmission through hollow core microstructured fibers**

In this subsection we will consider a new approach to solving the problem of the mid IR transmission (in particular, CO2 laser radiation) through the glass hollow core microstructured fibers (HC MFs). The possibility of the light confinement in the air core of HC MFs with the cladding consisting of two dimensional periodic array of air holes was predicted by Russell at the beginning of 1990s and theoretically demonstrated by Birks et. al. [Birks et. al., 1995]. The most advanced HC MFs are hollow core photonic crystal fibers (HC PCFs). HC PCFs in turn can be divided into two main groups. The HC PCFs from the first group guide the light by virtue of photonic band gap (BG HC PCFs). The HC PCFs from the second group have no band gaps and guide the light due to an inhibited coupling between the core guided modes and modes associated with a cladding [Benabid et. al., 2002]. They are called inhibited coupling HC PCFs (IC HC PCFs). Both types of HC PCFs have the claddings with very little solid material, usually, with a filling fraction less than 10%.

The guidance mechanism for BG HC PCFs is based on the concept of 'out of plane' band gap. The microstructure of BG HC PCF cladding consists of air holes packed in a triangular arrangement. It gives rise to a full two dimensional photonic band gap [Birks et. al., 1995]. As a result, forbidden frequencies occur for optical waves whose wave vector (axial) component is not equal to zero. Such frequency ranges constitute bands. The first experimental demonstration of light transmission in the BG HC PCF was made in 1999 [Gregan et. al., 1999]. Up to now, considerable efforts have been put forth in experimental and theoretical studies of BG HC PCFs made of silica glass [Humbert et. al., 2004; Benabid et. al., 2004]. This special interest can be partly explained by a need to find a way of yielding a loss level less than 0.2 dB/km for telecommunication spectral region. So far, the BG HC PCFs loss was reduced only to 1.2 dB/km due to intrinsic roughness of the air – glass interfaces in the structure [Roberts, Couny et. al., 2005].

As it was mentioned above, BG HC PCFs made of silica glass have claddings with very little solid material. The bandgap located between 4th and 5th bands is used for guiding in HC PCFs with such high air – filling fraction ( ≥ 80%) [Humbert et. al., 2004]. The number of each band is counted from the band with the largest value of the propagation constant of the air core mode. However, there is an important need for BG HC PCFs which can be used in the mid and far IR. BG HC PCF made of silica glass with a core diameter of 40 μm demonstrated single mode waveguide regime in a narrow transmission window near the wavelength of λ = 3.14 μm with an attenuation of ~ 2.6 dB/m [Shephard et. al., 2005]. But silica glass BG HC PCFs cannot be used for CO2 laser radiation transmission due to a very high material loss of silica. Transmission of light in the mid IR region becomes possible with BG HC PCFs made of glasses which are transparent in this spectral region such as

5 cm. Hollow glass waveguides have been used successfully for a modest CO2 laser power delivery below ~ 80 W. For the higher power delivery it is necessary to place a water – cooled jacket around the guides. The highest CO2 laser power delivered through the water – cooled hollow glass waveguide with 700 μm bore was 1040 W [Nubling & Harrington, 1996]. This is comparable to CO2 laser power delivered through the water – cooled hollow

metallic waveguide with 1800 μm bore which was 2700 W [Hongo et. al., 1992].

10%.

**2.2 CO2 laser radiation transmission through hollow core microstructured fibers** 

In this subsection we will consider a new approach to solving the problem of the mid IR transmission (in particular, CO2 laser radiation) through the glass hollow core microstructured fibers (HC MFs). The possibility of the light confinement in the air core of HC MFs with the cladding consisting of two dimensional periodic array of air holes was predicted by Russell at the beginning of 1990s and theoretically demonstrated by Birks et. al. [Birks et. al., 1995]. The most advanced HC MFs are hollow core photonic crystal fibers (HC PCFs). HC PCFs in turn can be divided into two main groups. The HC PCFs from the first group guide the light by virtue of photonic band gap (BG HC PCFs). The HC PCFs from the second group have no band gaps and guide the light due to an inhibited coupling between the core guided modes and modes associated with a cladding [Benabid et. al., 2002]. They are called inhibited coupling HC PCFs (IC HC PCFs). Both types of HC PCFs have the claddings with very little solid material, usually, with a filling fraction less than

The guidance mechanism for BG HC PCFs is based on the concept of 'out of plane' band gap. The microstructure of BG HC PCF cladding consists of air holes packed in a triangular arrangement. It gives rise to a full two dimensional photonic band gap [Birks et. al., 1995]. As a result, forbidden frequencies occur for optical waves whose wave vector (axial) component is not equal to zero. Such frequency ranges constitute bands. The first experimental demonstration of light transmission in the BG HC PCF was made in 1999 [Gregan et. al., 1999]. Up to now, considerable efforts have been put forth in experimental and theoretical studies of BG HC PCFs made of silica glass [Humbert et. al., 2004; Benabid et. al., 2004]. This special interest can be partly explained by a need to find a way of yielding a loss level less than 0.2 dB/km for telecommunication spectral region. So far, the BG HC PCFs loss was reduced only to 1.2 dB/km due to intrinsic roughness of the air – glass

As it was mentioned above, BG HC PCFs made of silica glass have claddings with very little solid material. The bandgap located between 4th and 5th bands is used for guiding in HC PCFs with such high air – filling fraction ( ≥ 80%) [Humbert et. al., 2004]. The number of each band is counted from the band with the largest value of the propagation constant of the air core mode. However, there is an important need for BG HC PCFs which can be used in the mid and far IR. BG HC PCF made of silica glass with a core diameter of 40 μm demonstrated single mode waveguide regime in a narrow transmission window near the wavelength of λ = 3.14 μm with an attenuation of ~ 2.6 dB/m [Shephard et. al., 2005]. But silica glass BG HC PCFs cannot be used for CO2 laser radiation transmission due to a very high material loss of silica. Transmission of light in the mid IR region becomes possible with BG HC PCFs made of glasses which are transparent in this spectral region such as

interfaces in the structure [Roberts, Couny et. al., 2005].

chalcogenide glasses. These glasses are composed of the chalcogen elements Se and Te with an addition of such elements as Ge, As, Sb. The transparency windows of these glasses correspond approximately to the mid IR region 2 – 25 μm.

Modeling of BG HC PCFs made of nonsilica glasses was performed by a number of authors [Shaw et. al., 2003; Pottage et. al., 2003; Pearce et. al., 2005]. In this paper [Shaw et. al., 2003] BG HC PCFs made of As – S (refractive index ~ 2.4) and As – Se (refractive index ~ 2.8) were analyzed. It was shown that there exist several spectral regions with bandgaps for an air filling fraction > 40% in both As – S and As – Se BG HC PCFs. These BG HC PCFs have large bandgap widths at the air filling fraction of 45% to 60%. BG HC PCFs with high air filling fractions > 80% also exhibited large bandgap widths. In the author' opinion, all these results show a possibility of a light transmission in the mid IR using halcogenide BG HC PCFs. The authors of [Pottage et. al., 2003] have carried out a numerical analyses of BG HC PCFs for a wide range of refractive indices from *n* = 1.5 to *n* =3.6 and for different values of air filling fractions from 33% to 87%. They discovered a new type of the bandgap which was called type 2 bandgap at an air filling fraction ~ 60% for any glass index beyond 2. The results showed a possibility of obtaining a satisfactory guidance in such BG HC PCFs.

Another important aspect of the problem of the mid IR radiation transmission was discussed in [Pearce et. al., 2005]. Apart from a limitation to attaining a low loss guidance in BG HC PCFs connected with the intrinsic roughness of the air glass interfaces, there is another problem connected with an existence of surface guided modes that are trapped in the core surroundings. Experimental and theoretical studies [Smith et. al., 2003; Humbert et. al., 2004; West et. al., 2004; Saitoh et. al., 2004] carried out for silica BG HC PCFs have shown that the anticrossing between dispersion curves of the surface modes and the air core modes is the main factor leading to a transmission loss in BG HC PCFs. Several methods were proposed to suppress the surface modes. The first method is used to reduce the distortion of the core by including 'fingers' of glass [West et. al., 2004]. The second method is to use thin core walls [Saitoh et. al., 2004] and the third one is to use 'antiresonance' walls [Roberts, Williams et. al., 2005]. The authors of [Pearce et. al., 2005] modeled a realistic design of distorted cores for BG HC PCFs which can guide the light in the type 2 bandgap. They have demonstrated that BG HC PCFs made of high index glass can guide a fundamental air core mode with a fraction of power in the air of up to 98%.

In their paper [Hu & Menyuk, 2007] the authors analyzed BG HC PCFs for refractive indices between 1.4 and 2.8. They found two maxima of the relative bandgap as a function of the air filling fraction and refractive index. The authors also found that the relative bandgap and the level of loss are interrelated. When the relative bandgap increases the loss decreases and vice versa.

Despite the promising results of modeling obtained in the above listed works a practical realization of BG HC PCFs made completely of chalcogenide glass for the mid IR spectral region has not been reported. The only successful realization of a photonic band gap hollow core fiber for the CO2 laser radiation transmission was 'Omniguide' fiber where the cladding is a Bragg reflector (hollow core Bragg fiber) made of soft glass and polymer [Temelkuran et. al., 2002]. The authors of [Bowden & Harrington, 2009] have studied low and high index chalcogenide glasses for their potential use in the fabrication of all glass hollow core Bragg fiber.

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 233

Fig. 1. (left) HC MF with the cladding consisting of eight capillaries (right) HC MF with the

In [Pryamikov et. al., 2011] the authors have made a calculation mistake when they were trying to justify their assumptions on the role of the negative curvature of the core boundary. The mistake was made when calculating the waveguide loss for a dielectric tube using an analytical formula from [Marcatili & Schmeltzer, 1964]. Indeed, the loss levels for the dielectric tube and silica HC MF with the cladding consisting of solid rods with equal air core diameters are approximately the same. Despite this fact, the main conclusion of the paper remains accurate, i.e. that to obtain a long wavelength waveguide regime in the mid IR with silica HC MF it is necessary to combine two factors, namely, the negative curvature of the core boundary and the low density of eigenstates of the individual elements of the

To clarify a role of the negative curvature of the core boundary we should consider a plane wave scattering on the curved surface, for example, of a solid rod. This problem was solved by many authors [Wait, 1955; Lind & Greenberg, 1966]. Depending on the polarization state of the incident plane wave *z* – component of the electric (TM polarization) or magnetic field (TE polarization) is parallel to the incident plane. Suppose the refractive index of the solid rod is *n*1 and the outer space is *n*<sup>2</sup> . In the following, only TE polarized plane wave will be considered. Its z – component of the magnetic field can be expanded according to addition

*i n in i z*

=−∞

 λ

<sup>=</sup>

<sup>∞</sup> − −

ϕ β

<sup>=</sup> is a wavevector in the outer space *k*2 2

= 0 *<sup>i</sup> Ez* , (1)

λ

λ2 2 = −

and *r* are an azimuthal and radial cylindrical

is its axial component. In such a way, the incident

ωone can

*2r)* are the Bessel

β

is its

theorem for Bessel functions and taking into account the temporal dependence as *i t e*

*z n n H H i J re e* 0 2 sin [ ( ) ]

ϕ

θ

coordinates, *H0* is an amplitude of the incident plane wave and *Jn(*

2π

β= cos

λ

θ

cladding consisting of eight solid rods.

cladding.

obtain:

where

θ

is an angle of incidence,

functions of first kind . If *k n* 2 2

transverse component and *k*<sup>2</sup>

The first work devoted to the fabrication and experimental investigation of BG HC PCF for CO2 laser radiation transmission has appeared only in 2010 [Deseveday et. al., 2010]. The authors designed BG HC PCF made of chalcogenide glass to guide the light in the air core at λ = 9.3 μm. They also fabricated two BG HC PCFs which could potentially guide CO2 laser radiation but no guidance was observed. The authors explained this fact by technological difficulties in the fabrication process. They hope to improve the process by avoiding air tightness anomalies and by decreasing the core's wall thickness.

In the next section we will represent our approach to solving the problem of CO2 laser radiation transmission through the glass HC MFs.

#### **3. Mechanisms of CO2 laser radiation transmission through the glass hollow core microstructured fiber with the cladding consisting of capillaries**

In this section, we will consider physical mechanisms and principles which enable, in our opinion, to obtain a loss level much lower than the material loss of the glass of HC MFs with a negative curvature of the core boundary [Pryamikov et. al., 2011]. The negative curvature of the core boundary is obtained by the cladding consisting of one or several rows of glass capillaries. Such microstructure design leads to a significant complication of the boundary conditions for the air - core modes. To justify our assumptions it will be necessary to consider a plane wave scattering on a cylindrical surface to show an analogy between this phenomenon and the light scattering on the plane optical diffraction grating. An analogy between discrete rotational symmetry of the capillary arrangement in the cladding and the plane diffraction grating will also be outlined. We will also consider the second main factor leading to a loss reduction of the air core modes of the HC MFs and to an increase in the width of transmission regions. It is connected with the geometry parameters of an individual capillary and the glass refractive index. In the end, we will try to justify the statement how these factors can result in the loss reduction of the air core mode in HC MF with the cladding consisting of capillaries with respect to the BG HC PCFs and kagome lattice IC HC PCFs.

#### **3.1 The cylindrical surface as a diffraction grating**

In this subsection, we will offer a reason which, in our opinion, lies behind the low loss waveguide regimes for the glass HC MFs with negative curvature of the core boundary. For the first time, an effect of the loss level decrease resulting from the negative curvature of the core boundary was observed for a large pitch kagome – lattice IC HC PCF with a hypocycloid – shaped core structure (the second group of PCFs) [Wang et. al., 2011]. We have used a simple cladding structure of the HC MF consisting of eight silica capillaries (Fig. 1(left)). Such HC MF guided light in the mid IR up to 4 μm despite of very high material losses of silica in this spectral region. In this case, the negative curvature of the core boundary was created by the capillary surfaces. Of course, such long a wavelength guiding is determined by not only the negative curvature of the core boundary but (may be to a greater extent) also by the optical properties of an individual capillary of the cladding. For example, the simple cladding structure consisting of one row of the capillaries has a lower density of eigenstates with respect to the cladding consisting of the solid rods (Fig. 1(right)).

The first work devoted to the fabrication and experimental investigation of BG HC PCF for CO2 laser radiation transmission has appeared only in 2010 [Deseveday et. al., 2010]. The authors designed BG HC PCF made of chalcogenide glass to guide the light in the air core at λ = 9.3 μm. They also fabricated two BG HC PCFs which could potentially guide CO2 laser radiation but no guidance was observed. The authors explained this fact by technological difficulties in the fabrication process. They hope to improve the process by avoiding air

In the next section we will represent our approach to solving the problem of CO2 laser

**3. Mechanisms of CO2 laser radiation transmission through the glass hollow** 

In this section, we will consider physical mechanisms and principles which enable, in our opinion, to obtain a loss level much lower than the material loss of the glass of HC MFs with a negative curvature of the core boundary [Pryamikov et. al., 2011]. The negative curvature of the core boundary is obtained by the cladding consisting of one or several rows of glass capillaries. Such microstructure design leads to a significant complication of the boundary conditions for the air - core modes. To justify our assumptions it will be necessary to consider a plane wave scattering on a cylindrical surface to show an analogy between this phenomenon and the light scattering on the plane optical diffraction grating. An analogy between discrete rotational symmetry of the capillary arrangement in the cladding and the plane diffraction grating will also be outlined. We will also consider the second main factor leading to a loss reduction of the air core modes of the HC MFs and to an increase in the width of transmission regions. It is connected with the geometry parameters of an individual capillary and the glass refractive index. In the end, we will try to justify the statement how these factors can result in the loss reduction of the air core mode in HC MF with the cladding consisting of capillaries with respect to the BG HC PCFs and kagome

In this subsection, we will offer a reason which, in our opinion, lies behind the low loss waveguide regimes for the glass HC MFs with negative curvature of the core boundary. For the first time, an effect of the loss level decrease resulting from the negative curvature of the core boundary was observed for a large pitch kagome – lattice IC HC PCF with a hypocycloid – shaped core structure (the second group of PCFs) [Wang et. al., 2011]. We have used a simple cladding structure of the HC MF consisting of eight silica capillaries (Fig. 1(left)). Such HC MF guided light in the mid IR up to 4 μm despite of very high material losses of silica in this spectral region. In this case, the negative curvature of the core boundary was created by the capillary surfaces. Of course, such long a wavelength guiding is determined by not only the negative curvature of the core boundary but (may be to a greater extent) also by the optical properties of an individual capillary of the cladding. For example, the simple cladding structure consisting of one row of the capillaries has a lower density of eigenstates with respect to the cladding consisting of the solid rods (Fig.

**core microstructured fiber with the cladding consisting of capillaries** 

tightness anomalies and by decreasing the core's wall thickness.

radiation transmission through the glass HC MFs.

**3.1 The cylindrical surface as a diffraction grating** 

lattice IC HC PCFs.

1(right)).

Fig. 1. (left) HC MF with the cladding consisting of eight capillaries (right) HC MF with the cladding consisting of eight solid rods.

In [Pryamikov et. al., 2011] the authors have made a calculation mistake when they were trying to justify their assumptions on the role of the negative curvature of the core boundary. The mistake was made when calculating the waveguide loss for a dielectric tube using an analytical formula from [Marcatili & Schmeltzer, 1964]. Indeed, the loss levels for the dielectric tube and silica HC MF with the cladding consisting of solid rods with equal air core diameters are approximately the same. Despite this fact, the main conclusion of the paper remains accurate, i.e. that to obtain a long wavelength waveguide regime in the mid IR with silica HC MF it is necessary to combine two factors, namely, the negative curvature of the core boundary and the low density of eigenstates of the individual elements of the cladding.

To clarify a role of the negative curvature of the core boundary we should consider a plane wave scattering on the curved surface, for example, of a solid rod. This problem was solved by many authors [Wait, 1955; Lind & Greenberg, 1966]. Depending on the polarization state of the incident plane wave *z* – component of the electric (TM polarization) or magnetic field (TE polarization) is parallel to the incident plane. Suppose the refractive index of the solid rod is *n*1 and the outer space is *n*<sup>2</sup> . In the following, only TE polarized plane wave will be considered. Its z – component of the magnetic field can be expanded according to addition theorem for Bessel functions and taking into account the temporal dependence as *i t e* ω one can obtain:

$$H\_z^i = H\_0 \sin \theta [\sum\_{n=-\omega}^{\omega} i^n] I\_n(\lambda\_2 r) e^{-i\nu \rho} \left[ e^{-i\beta z} \right]$$

$$E\_z^i = 0 \quad \tag{1}$$

where θ is an angle of incidence, ϕ and *r* are an azimuthal and radial cylindrical coordinates, *H0* is an amplitude of the incident plane wave and *Jn(*λ*2r)* are the Bessel functions of first kind . If *k n* 2 2 2π λ <sup>=</sup> is a wavevector in the outer space *k*2 2 λ2 2 = − β is its transverse component and *k*<sup>2</sup> β = cosθis its axial component. In such a way, the incident

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 235

Suppose the diffraction grating extends infinitely in the *y* and *z* directions, with the period *d* in the *z* direction only. The refractive index of the outer medium is again <sup>2</sup> *n* . The magnetic

*<sup>x</sup> <sup>i</sup> ik x i z H He e <sup>y</sup>* <sup>0</sup>

Then, due to periodicity the scattered magnetic field can be represented as [Hessel & Oliner,

[ () ]

transverse components of the wavevector of the scattered field. Applying boundary conditions one obtains an infinite inhomogeneous set of simultaneous linear equations

coupled between each other as in the case of the plane wave scattering on the rod and a set of resonances Lorentzian and Fano types known as Wood anomalies [Wood, 1902; Lord Rayleigh, 1907; Hessel & Oliner, 1965] also occur. In the case of optical grating the

*<sup>n</sup> <sup>k</sup>*

In the case of the plane wave scattering on a dielectric rod there is also a conservation of the angular momentum of the light. The fields of the source plane wave are expanded into a set of the 'space' channels with an angular momentum determined by the number of *n* in *in e*<sup>−</sup>

(1) and each continuous (radiation) mode of the dielectric rod has the same angular momentum (1, 2). Note, that this is (4) of the same form as an expression (2a) for the scattered field *<sup>s</sup> Hz* in the case of the dielectric rod. Comparing expressions (2a) and (4) one can state that the process of the plane wave scattering on the rod can be represented as scattering on the diffraction quasi – grating. The surface of the dielectric rod can be

conservation of the angular momentum of the light. But instead of one incident plane wave as in the case of the plane diffraction grating (3) there is an infinite set of incident cylindrical harmonics with their own angular momentums of the light. It can also be shown that the

analogous to Wood anomalies as in the case of the plane diffraction grating. This problem and its application to the waveguide mechanism in all solid band gap fibers will be considered by us thoroughly in our future publication. In the same way, it is possible to consider a cylindrical surface of the capillary as a diffraction quasi - grating in the

The main conclusion to draw is that the plane wave incidence on a curved cylindrical surface leads to the appearance of an infinite set of cylindrical harmonics with different

*n n b a*, in expansions (2a) demonstrate the resonance behaviour

= + β.

*d* 2π

conservation of light momentum for the scattered light in the *z* - direction looks like:

*s n*

considered as an azimuthal diffraction grating with periodicity in

direction instead of *z* – direction in the case of the plane diffraction grating.

*H A ee e*

β

*y n n*

[Hessel & Oliner, 1965] for the scattered field amplitudes *An*( )

=−∞

are the amplitudes of the various spectral orders and *<sup>n</sup>*

*n x <sup>n</sup> i z <sup>s</sup> ik x <sup>d</sup> i z*

<sup>∞</sup> <sup>−</sup> <sup>−</sup>

2

π

β

<sup>=</sup> , (4)

− β

= (3)

*x*

β

*<sup>n</sup> k k*

. These amplitudes are

= −+ β

2

ϕ


*d* 2 2

are

φ

ϕ

<sup>2</sup> ( ) π

field of this incident wave of *S* polarization is represented as:

1965]:

where *An*( )

β

spectral dependencies of *s s*

plane wave is expanded into an infinite number of cylindrical harmonics due to the curvature of the cylinder surface. The z – components of the scattered field and field inside the cylinder can be expressed in the same manner:

$$H\_z^s = \[\sum\_{n=-\infty}^{\infty} b\_n^s H\_n^{(2)}(\lambda\_2 r) e^{-i\alpha \rho} \} e^{-i\beta z}$$

$$E\_z^s = \[\sum\_{n=-\infty}^{\infty} a\_n^s H\_n^{(2)}(\lambda\_2 r) e^{-i\alpha \rho} \} e^{-i\beta z} \tag{2a}$$

$$H\_z^{\text{ins}} = \[\sum\_{n=-\infty}^{\infty} b\_n f\_n(\lambda\_1 r) e^{-i\alpha \rho} \} e^{-i\beta z}$$

$$E\_z^{\text{ins}} = \[\sum\_{n=-\infty}^{\infty} a\_n f\_n(\lambda\_1 r) e^{-i\alpha \rho} \} e^{-i\beta z} \tag{2b}$$

where *H r <sup>n</sup>* (2) <sup>2</sup> ( ) λ is Hankel function, *k*2 2 λ1 1 = − β is a transverse components of the wavevector *k n* 1 1 2π λ <sup>=</sup> for the field inside the rod. On the basis of these expressions for *z* – components of the incident, scattered and inside fields it is possible to calculate ϕ and *r* components of the fields [Adler, 1952]. In other words, the field of the incident wave is represented by an infinite number of space 'channels' (harmonics) through which the energy of the incident wave is transferred to the scattered fields and the fields inside the dielectric rod. It is seen, that such sets of cylindrical harmonics (1) - (2) have a mode structure and can be considered as radiation or continuous modes of ITE (incident transverse electric) type of the individual dielectric rod [Snyder, 1971].

To calculate the coefficients *s s nnnn baba* ,,, it is necessary to apply boundary conditions for *z* and ϕ - components of the incident, scattered fields and the fields inside the cylinder. Because of the mode structure of the total field it is not necessary to solve an infinite set of simultaneous linear equations. To obtain the *n*th order coefficients one needs to solve 4\*4 inhomogeneous system of linear equations. For a solid cylinder rod it is possible to obtain analytical expression for the coefficients which includes such terms as *n n J aJ a* ' 1 1 ( )/ ( ) λ λ [ Wait, 1955]. These terms have resonances (poles) corresponding to zeros of *nJ a*<sup>1</sup> ( ) λ . It is necessary to point out that the resonances of the *n*th order coefficients of the scattered field are determined not only by *n*th order functions *nJ a*<sup>1</sup> ( ) λ but also by *nJ a* 1 1 <sup>+</sup> ( ) λ and *nJ a* 1 1 <sup>−</sup> ( ) λ due to recurrent relations for the derivatives of the Bessel functions. In other words, the different diffraction orders are coupled between each other. Due to this fact, it is possible to observe not only Lorentzian – like resonances for the spectral dependencies of absolute values of the amplitudes *s s n n b a*, but also Fano type resonances [Fano, 1961]. For example, Fano type resonances were analysed in the case of all solid band gap fibers [Steinvurzel et. al., 2006] with the cladding consisting of solid dielectric cylinders with a refractive index higher than the background.

A similar phenomenon occurs when the plane wave is scattered on optical diffraction grating. A short analysis can be carried out based on the work [Hessel & Oliner, 1965].

plane wave is expanded into an infinite number of cylindrical harmonics due to the curvature of the cylinder surface. The z – components of the scattered field and field inside

*ss in i z*

λ

<sup>∞</sup> − −

ϕ β

ϕ β

> ϕ β

ϕ β

<sup>=</sup> for the field inside the rod. On the basis of these expressions for *z* –

<sup>=</sup> (2a)

<sup>=</sup> , (2b)

*nnnn baba* ,,, it is necessary to apply boundary conditions for *z*

λ

is a transverse components of the

'

λ

λ

and *nJ a* 1 1 <sup>−</sup> ( )

λ

1 1 ( )/ ( )

 λ

. It is necessary to

due to recurrent

[ Wait,

ϕ

and *r* -

*H bH re e* (2) <sup>2</sup> [ () ]

*ss in i z*

λ

<sup>∞</sup> − −

*ins in i z*

λ

<sup>=</sup>

<sup>∞</sup> − −

*H bJ re e* <sup>1</sup> [ () ]

*ins in i z*

components of the fields [Adler, 1952]. In other words, the field of the incident wave is represented by an infinite number of space 'channels' (harmonics) through which the energy of the incident wave is transferred to the scattered fields and the fields inside the dielectric rod. It is seen, that such sets of cylindrical harmonics (1) - (2) have a mode structure and can be considered as radiation or continuous modes of ITE (incident transverse electric) type of

λ

<sup>∞</sup> − −

β

 - components of the incident, scattered fields and the fields inside the cylinder. Because of the mode structure of the total field it is not necessary to solve an infinite set of simultaneous linear equations. To obtain the *n*th order coefficients one needs to solve 4\*4 inhomogeneous system of linear equations. For a solid cylinder rod it is possible to obtain

*E a J re e* <sup>1</sup> [ () ]

*E aH re e* (2) <sup>2</sup> [ () ]

*z nn n*

=−∞ <sup>=</sup>

*z nn n*

=−∞

*z n n n*

*z n n n*

> λ1 1 = −

is Hankel function, *k*2 2

=−∞

components of the incident, scattered and inside fields it is possible to calculate

analytical expression for the coefficients which includes such terms as *n n J aJ a*

point out that the resonances of the *n*th order coefficients of the scattered field are determined

relations for the derivatives of the Bessel functions. In other words, the different diffraction orders are coupled between each other. Due to this fact, it is possible to observe not only Lorentzian – like resonances for the spectral dependencies of absolute values of the amplitudes

*n n b a*, but also Fano type resonances [Fano, 1961]. For example, Fano type resonances were analysed in the case of all solid band gap fibers [Steinvurzel et. al., 2006] with the cladding consisting of solid dielectric cylinders with a refractive index higher than the background.

A similar phenomenon occurs when the plane wave is scattered on optical diffraction grating. A short analysis can be carried out based on the work [Hessel & Oliner, 1965].

but also by *nJ a* 1 1 <sup>+</sup> ( )

1955]. These terms have resonances (poles) corresponding to zeros of *nJ a*<sup>1</sup> ( )

λ

=−∞

the cylinder can be expressed in the same manner:

where *H r <sup>n</sup>* (2) <sup>2</sup> ( ) λ

and ϕ

*s s*

wavevector *k n* 1 1

2π

λ

the individual dielectric rod [Snyder, 1971].

not only by *n*th order functions *nJ a*<sup>1</sup> ( )

To calculate the coefficients *s s*

Suppose the diffraction grating extends infinitely in the *y* and *z* directions, with the period *d* in the *z* direction only. The refractive index of the outer medium is again <sup>2</sup> *n* . The magnetic field of this incident wave of *S* polarization is represented as:

$$H\_y^i = H\_0 e^{k\_x x} e^{-i\beta z} \tag{3}$$

Then, due to periodicity the scattered magnetic field can be represented as [Hessel & Oliner, 1965]:

$$H\_y^s = \left[\sum\_{n=-\omega}^{\omega} A\_n(\mathcal{J}) e^{i\lambda\_n^n z} e^{-i\frac{2\pi n}{d}z}\right] e^{-i\beta z} \,, \tag{4}$$

where *An*( ) β are the amplitudes of the various spectral orders and *<sup>n</sup> x <sup>n</sup> k k d* 2 2 2 <sup>2</sup> ( ) π = −+ βare

transverse components of the wavevector of the scattered field. Applying boundary conditions one obtains an infinite inhomogeneous set of simultaneous linear equations [Hessel & Oliner, 1965] for the scattered field amplitudes *An*( ) β . These amplitudes are coupled between each other as in the case of the plane wave scattering on the rod and a set of resonances Lorentzian and Fano types known as Wood anomalies [Wood, 1902; Lord Rayleigh, 1907; Hessel & Oliner, 1965] also occur. In the case of optical grating the conservation of light momentum for the scattered light in the *z* - direction looks like:

$$k\_u^s = \beta + \frac{2\pi n}{d} \dots$$

In the case of the plane wave scattering on a dielectric rod there is also a conservation of the angular momentum of the light. The fields of the source plane wave are expanded into a set of the 'space' channels with an angular momentum determined by the number of *n* in *in e*<sup>−</sup> φ (1) and each continuous (radiation) mode of the dielectric rod has the same angular momentum (1, 2). Note, that this is (4) of the same form as an expression (2a) for the scattered field *<sup>s</sup> Hz* in the case of the dielectric rod. Comparing expressions (2a) and (4) one can state that the process of the plane wave scattering on the rod can be represented as scattering on the diffraction quasi – grating. The surface of the dielectric rod can be considered as an azimuthal diffraction grating with periodicity in ϕ - direction and conservation of the angular momentum of the light. But instead of one incident plane wave as in the case of the plane diffraction grating (3) there is an infinite set of incident cylindrical harmonics with their own angular momentums of the light. It can also be shown that the spectral dependencies of *s s n n b a*, in expansions (2a) demonstrate the resonance behaviour analogous to Wood anomalies as in the case of the plane diffraction grating. This problem and its application to the waveguide mechanism in all solid band gap fibers will be considered by us thoroughly in our future publication. In the same way, it is possible to consider a cylindrical surface of the capillary as a diffraction quasi - grating in the ϕ direction instead of *z* – direction in the case of the plane diffraction grating.

The main conclusion to draw is that the plane wave incidence on a curved cylindrical surface leads to the appearance of an infinite set of cylindrical harmonics with different

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 237

cylindrical surface of an individual capillary but also by the discrete rotational symmetry of

Summarizing the conclusions of the two previous subsections one can state that the air core modes of HC MFs with the cladding consisting of capillaries are formed by a superposition (interference) of several space cylindrical harmonics originated from the azimuthal diffraction quasi - gratings occurred in the cladding. The main factors affecting the air core mode formation are geometry parameters of an individual capillary and the type of a periodic arrangement of the capillaries in the cladding. All these space harmonics interact with the capillary walls in stronger or weaker ways depending on their radial and azimuthal distribution. In this case, the material loss of the capillary walls doesn't have the same affect on the attenuation of each harmonic. In such a way, the energy of the air core mode at the core boundary for HC MF with the cladding consisting of capillaries is distributed in much more complicated way than in the case of BG HC PCFs or kagome

BG HC PCFs and kagome lattice IC HC PCFs do not have such complicated mechanism of the air core modes formation because of a quasi continuous rotational symmetry of the core boundary and the boundaries of succeeding layers in the cladding. Kagome lattices IC HC PCFs sometimes have the discrete symmetry of the core boundary but just with a polygonal shape of the core without a negative curvature of the core boundary. The authors in [Pearce et al., 2007] have shown that the loss behavior of a hollow core fiber with the cladding consisting of concentric glass rings or hexagons explain the qualitative features in the loss curves associated with kagome lattice IC HC PCF. The hollow core photonic band gap fiber with the cladding consisting of concentric glass rings has a continuous rotational symmetry of the core modes and is analogous to solid Bragg fibers [Fevrier et. al., 2006]. In this case, the air core is formed by the boundaries of the concentric glass rings which cannot play the role of the azimuthal diffraction gratings. Applying boundary conditions to each concentric ring of the cladding one obtains a homogeneous system of linear equations determinant of which is a dispersion relation for the air core modes. Each air core mode is formed and described by only one space cylindrical harmonic with the propagation constant

determined from the corresponding dispersion relation. These space harmonics don't interact with each other's as in the case of all solid band gap fibers and Fano type resonances cannot be observed (an exception can be kagome lattice IC HC PCF with a polygonal shape of the air core). As a consequence, all energy of each air core mode is concentrated in one 'space' channel (cylindrical harmonic) which interacts with glass rings of the cladding in the

above. All resonances in high index layers for this mode are radial and can be described by

The other very important moment is that the geometry parameters of the capillaries *ins out d d*, and the glass refractive index at the determined value of *Dcore* (Fig .1(left)) should be chosen

ϕ

is determined from the dispersion relation mentioned

. This air core mode is

same way according to its azimuthal angular dependence of *in e*<sup>−</sup>

β

leaky and its imaginary part of

the ARROW model [Litchinitser et. al., 2002].

β

**3.3 Complicated boundary conditions for the air core mode of HC MF with the** 

**cladding consisting of capillaries and low loss guidance** 

the core boundary.

lattice IC HC PCFs.

angular momentums of the light. As the source of the incident wave is outside of a solid cylinder or a capillary one obtains an inhomogeneous set of linear equations for determining amplitudes of the scattered field harmonics. These scattered field harmonics have the same values of the angular momentums of the light as the harmonics of the incident field. Different orders of these harmonics (diffraction orders) are coupled between each other due to the properties of the Bessel functions. It leads to appearance of Wood anomalies in the spectral dependencies of their amplitudes. As a consequence, the curved cylindrical surface can be considered as an azimuthal diffraction grating with modulation in ϕ - direction [Pryamikov, to be prepared]. This fact leads to a loss of simplicity of the boundary conditions for the air core modes of the HC MF with the cladding consisting of capillaries compared with BG HC PCF, for example. Similar situation occurs if one considers the boundary conditions for the core modes of all solid photonic band gap fibers [White et. al., 2002] and Bragg fibers [Yeh et. al., 1978].

#### **3.2 Discrete rotational symmetry of the core boundary**

Another aspect of the problem of complicated boundary conditions for HC MF with the cladding consisting of *N* capillaries is that the capillary location in the cladding is also periodic in the azimuthal coordinate ϕ (Fig.1). As a result, the boundary conditions for the air core modes are also periodic. It is known that if the system transforms into itself for a set of discrete rotations δϕ = 2 / π *k N* , *k N* ∈ − (0, 1) around axial vector *z* the eigenfunctions of the system (in other words, the air core modes) can be represented as [Skorobogatiy & Yang, 2009]:

*in i z n n* (, ,) () *r z e U re* ϕ β ψ ϕ− − = , (5)

and their eigenvalues are:

$$\mathbf{X} = e^{i n \frac{2\pi k}{N}} \mathbf{.}$$

These eigenvalues are the same for any *n n Nm* = + , where *m* is an integer and the eigenfunctions characterized by an integer *n* are degenerate ones [Skorobogatiy & Yang, 2009]. As a consequence, such eigenstates of the system with a discrete rotational symmetry can be expressed as a superposition of all the degenerate states:

$$\Psi\_n(r,\varphi,z) = \left[\sum\_{m=-\omega}^{\omega} A(m)\mathcal{U}\_{n+\text{Min}}(r)e^{-i(n+\text{Min})\varphi}\right]e^{-i\beta z},\tag{6}$$

where an expression under the sum sign is a periodic function in ϕ with a period *<sup>N</sup>* 2π and *n N* ∈ − [0, 1] . Note that this is (6) of the same form as an expression (2a) and (4) for the scattered field *<sup>s</sup> Hz* in the case of the dielectric rod and the plane diffraction grating. The discrete symmetry of the core boundary gives one more type of azimuthal diffraction grating in the considered HC MFs.

In such a way, the boundary conditions for the air core modes of the HC MF with the cladding consisting of capillaries are complicated not only by the curvature of the

angular momentums of the light. As the source of the incident wave is outside of a solid cylinder or a capillary one obtains an inhomogeneous set of linear equations for determining amplitudes of the scattered field harmonics. These scattered field harmonics have the same values of the angular momentums of the light as the harmonics of the incident field. Different orders of these harmonics (diffraction orders) are coupled between each other due to the properties of the Bessel functions. It leads to appearance of Wood anomalies in the spectral dependencies of their amplitudes. As a consequence, the curved cylindrical surface

[Pryamikov, to be prepared]. This fact leads to a loss of simplicity of the boundary conditions for the air core modes of the HC MF with the cladding consisting of capillaries compared with BG HC PCF, for example. Similar situation occurs if one considers the boundary conditions for the core modes of all solid photonic band gap fibers [White et. al.,

Another aspect of the problem of complicated boundary conditions for HC MF with the cladding consisting of *N* capillaries is that the capillary location in the cladding is also

air core modes are also periodic. It is known that if the system transforms into itself for a set

the system (in other words, the air core modes) can be represented as [Skorobogatiy & Yang,

*n n* (, ,) () *r z e U re* ϕ

*k N* , *k N* ∈ − (0, 1) around axial vector *z*

*<sup>k</sup> in <sup>N</sup> <sup>e</sup>* 2π

Χ = .

These eigenvalues are the same for any *n n Nm* = + , where *m* is an integer and the eigenfunctions characterized by an integer *n* are degenerate ones [Skorobogatiy & Yang, 2009]. As a consequence, such eigenstates of the system with a discrete rotational symmetry

*r z AmU r e e* ( ) (, ,) [ ( ) () ]

*n N* ∈ − [0, 1] . Note that this is (6) of the same form as an expression (2a) and (4) for the scattered field *<sup>s</sup> Hz* in the case of the dielectric rod and the plane diffraction grating. The discrete symmetry of the core boundary gives one more type of azimuthal diffraction

In such a way, the boundary conditions for the air core modes of the HC MF with the cladding consisting of capillaries are complicated not only by the curvature of the

<sup>∞</sup> − + <sup>−</sup> +

*in i z*

 β ϕ

the eigenfunctions of

(Fig.1). As a result, the boundary conditions for the

− − = , (5)

*i n Nm i z*

ϕ β

<sup>=</sup> , (6)

ϕ

with a period *<sup>N</sup>*

2πand


can be considered as an azimuthal diffraction grating with modulation in

ϕ

ψ ϕ

can be expressed as a superposition of all the degenerate states:

where an expression under the sum sign is a periodic function in

ψ ϕ

grating in the considered HC MFs.

*n n Nm m*

=−∞

2002] and Bragg fibers [Yeh et. al., 1978].

periodic in the azimuthal coordinate

δϕ = 2 / π

of discrete rotations

and their eigenvalues are:

2009]:

**3.2 Discrete rotational symmetry of the core boundary** 

cylindrical surface of an individual capillary but also by the discrete rotational symmetry of the core boundary.

#### **3.3 Complicated boundary conditions for the air core mode of HC MF with the cladding consisting of capillaries and low loss guidance**

Summarizing the conclusions of the two previous subsections one can state that the air core modes of HC MFs with the cladding consisting of capillaries are formed by a superposition (interference) of several space cylindrical harmonics originated from the azimuthal diffraction quasi - gratings occurred in the cladding. The main factors affecting the air core mode formation are geometry parameters of an individual capillary and the type of a periodic arrangement of the capillaries in the cladding. All these space harmonics interact with the capillary walls in stronger or weaker ways depending on their radial and azimuthal distribution. In this case, the material loss of the capillary walls doesn't have the same affect on the attenuation of each harmonic. In such a way, the energy of the air core mode at the core boundary for HC MF with the cladding consisting of capillaries is distributed in much more complicated way than in the case of BG HC PCFs or kagome lattice IC HC PCFs.

BG HC PCFs and kagome lattice IC HC PCFs do not have such complicated mechanism of the air core modes formation because of a quasi continuous rotational symmetry of the core boundary and the boundaries of succeeding layers in the cladding. Kagome lattices IC HC PCFs sometimes have the discrete symmetry of the core boundary but just with a polygonal shape of the core without a negative curvature of the core boundary. The authors in [Pearce et al., 2007] have shown that the loss behavior of a hollow core fiber with the cladding consisting of concentric glass rings or hexagons explain the qualitative features in the loss curves associated with kagome lattice IC HC PCF. The hollow core photonic band gap fiber with the cladding consisting of concentric glass rings has a continuous rotational symmetry of the core modes and is analogous to solid Bragg fibers [Fevrier et. al., 2006]. In this case, the air core is formed by the boundaries of the concentric glass rings which cannot play the role of the azimuthal diffraction gratings. Applying boundary conditions to each concentric ring of the cladding one obtains a homogeneous system of linear equations determinant of which is a dispersion relation for the air core modes. Each air core mode is formed and described by only one space cylindrical harmonic with the propagation constant β determined from the corresponding dispersion relation. These space harmonics don't interact with each other's as in the case of all solid band gap fibers and Fano type resonances cannot be observed (an exception can be kagome lattice IC HC PCF with a polygonal shape of the air core). As a consequence, all energy of each air core mode is concentrated in one 'space' channel (cylindrical harmonic) which interacts with glass rings of the cladding in the same way according to its azimuthal angular dependence of *in e*<sup>−</sup> ϕ . This air core mode is leaky and its imaginary part of β is determined from the dispersion relation mentioned above. All resonances in high index layers for this mode are radial and can be described by the ARROW model [Litchinitser et. al., 2002].

The other very important moment is that the geometry parameters of the capillaries *ins out d d*, and the glass refractive index at the determined value of *Dcore* (Fig .1(left)) should be chosen

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 239

These capillary modes have a lower azimuthal index and a different radial dependence (Fig. 3(right)). It is worth pointing out that these two types of the individual capillary leaky modes are the main reason for occurring high loss regions for the considered HC MFs made

Fig. 2. (a) loss dependence for HC MF with *Dcore* = 220 μm and 6 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares); (b) loss dependence for HC MF with *Dcore* =

Fig. 3. (left) a typical Pointing vector distribution for a capillary leaky mode in the cladding with a high azimuthal index; (right) the Pointing vector distribution for the second type of

Further, we will consider HC MF with eight capillaries in the cladding. The air core diameters and the glass refractive indices will be the same as in the case of HC MFs with six

As one can see from Fig. 4(a) HC MF with *ins out d d* / = 0.85 and *n* = 2.8 has the highest loss due to the excitation of the leaky modes with a lower azimuthal index in this spectral region (Fig. 3(b)). The HC MF with *ins out d d* / = 0.85 and *n* = 2.4 has a high loss for the same reason. Losses for HC MFs with other parameters in Fig. 4(a) are relatively low, especially, in the case of HC MF with *ins out d d* / = 0.8 and *n* = 2.4. The losses for HC MFs with *Dcore* = 320 μm are very high due to the strong coupling of the air core modes with the capillary modes having a lower azimuthal index (Fig.3(right)) in this spectral range with the exception of the

capillaries in the cladding. In Fig. 4 the loss dependencies for this HC MF are shown.

of high index glasses.

320 μm the other notations are the same as in (a).

the capillary leaky modes with a lower azimuthal index.

HC MF with *ins out d d* / = 0.85 and *n* = 2.8.

in such a way so as to excite leaky modes with high quality factor. These modes usually have high radial and azimuthal indices. To this end, the capillary wall thickness must be thin enough and comparable with the wavelength. In this case, it is possible to obtain large widths of the transmission regions for the air core modes. Moreover, it seems possible to choose all parameters of the considered HC MF including glass refractive index in such a way so as to obtain a very weak interaction (coupling) of each cylindrical harmonic constituting the air core mode with capillary walls inside the transmission regions. All these factors can give rise to a low loss waveguide regime for CO2 laser radiation. Several examples of such waveguide regimes will be given in the next section.

#### **4. Numerical modelling of HC MFs with different types of discrete rotational symmetry of the core boundary and glass composition of the capillaries**

In the following subsections four types of HC MFs with the claddings consisting of 6, 8, 10 and 12 capillaries will be considered. The calculations will be carried out for two values of the glass refractive indices *n* = 2.4, 2.8 and with three values of *ins out d d* / = 0.8, 0.85, 0.9. All calculations will be made in the narrow spectral region near λ = 10.6 μm. This fact is connected with high density of the individual capillary eigenstates (leaky modes with high azimuthal indices [Vincetti & Setti, 2010]) which occur at such high values of the glass refractive indices and individual capillary dimensions with respect to the wavelength. We will show that the way of obtaining a low loss waveguide regime in the glass HC MFs with the cladding consisting of capillaries presents a complicated multiparameter task. Unusual behaviour of the bend loss depending on the bend radii for high index glass HC MFs with the cladding consisting of capillaries will be demonstrated.

#### **4.1 Loss dependencies for HC MF with different number of capillaries in the cladding**

First, we will consider the loss dependencies for HC MF with six capillaries in the cladding. As was mentioned above, all loss dependencies are calculated in the narrow spectral range from 10.59 μm to 10.61 μm with a wavelength step equals to 1 nm. The calculations will be made for two values of the ratio of *ins out d d* / 0.85 = and 0.9 because the losses are very high at lower values of the one. In Fig. 2 these dependencies are shown for two values of the air core diameter *Dcore* = 220 μm and 320 μm.

As one can see from Fig. 2(a) HC MF with *n* = 2.4 and *ins out d d* / = 0.9 has the minimal loss level in the considered spectral range. In our opinion, it can be explained by the minimal value of density of individual capillary states. In this case, the capillary has a minimal capillary wall thickness with respect to the wavelength and the lowest refractive index. The loss dependence for HC MF with *n* = 2.8 and *ins out d d* / = 0.9 is relatively inhomogeneous and has a strong peak at λ = 10.601 μm caused by the excitation of a capillary leaky mode with high azimuthal and radial indices. This mode is shown in Fig. 3(left).

Other curves in Fig.2 (a) for *ins out d d* / = 0.85 have a higher loss level due to thicker capillary walls compared to the previous case. In Fig. 2(b) HC MF with *n* = 2.8 and *ins out d d* / = 0.85 has the maximal loss due to the excitation of the second type of the capillary leaky modes.

in such a way so as to excite leaky modes with high quality factor. These modes usually have high radial and azimuthal indices. To this end, the capillary wall thickness must be thin enough and comparable with the wavelength. In this case, it is possible to obtain large widths of the transmission regions for the air core modes. Moreover, it seems possible to choose all parameters of the considered HC MF including glass refractive index in such a way so as to obtain a very weak interaction (coupling) of each cylindrical harmonic constituting the air core mode with capillary walls inside the transmission regions. All these factors can give rise to a low loss waveguide regime for CO2 laser radiation. Several

**4. Numerical modelling of HC MFs with different types of discrete rotational symmetry of the core boundary and glass composition of the capillaries** 

In the following subsections four types of HC MFs with the claddings consisting of 6, 8, 10 and 12 capillaries will be considered. The calculations will be carried out for two values of the glass refractive indices *n* = 2.4, 2.8 and with three values of *ins out d d* / = 0.8, 0.85, 0.9. All

connected with high density of the individual capillary eigenstates (leaky modes with high azimuthal indices [Vincetti & Setti, 2010]) which occur at such high values of the glass refractive indices and individual capillary dimensions with respect to the wavelength. We will show that the way of obtaining a low loss waveguide regime in the glass HC MFs with the cladding consisting of capillaries presents a complicated multiparameter task. Unusual behaviour of the bend loss depending on the bend radii for high index glass HC MFs with

**4.1 Loss dependencies for HC MF with different number of capillaries in the cladding**  First, we will consider the loss dependencies for HC MF with six capillaries in the cladding. As was mentioned above, all loss dependencies are calculated in the narrow spectral range from 10.59 μm to 10.61 μm with a wavelength step equals to 1 nm. The calculations will be made for two values of the ratio of *ins out d d* / 0.85 = and 0.9 because the losses are very high at lower values of the one. In Fig. 2 these dependencies are shown for two values of the air

As one can see from Fig. 2(a) HC MF with *n* = 2.4 and *ins out d d* / = 0.9 has the minimal loss level in the considered spectral range. In our opinion, it can be explained by the minimal value of density of individual capillary states. In this case, the capillary has a minimal capillary wall thickness with respect to the wavelength and the lowest refractive index. The loss dependence for HC MF with *n* = 2.8 and *ins out d d* / = 0.9 is relatively inhomogeneous and has a strong peak at λ = 10.601 μm caused by the excitation of a capillary leaky mode

Other curves in Fig.2 (a) for *ins out d d* / = 0.85 have a higher loss level due to thicker capillary walls compared to the previous case. In Fig. 2(b) HC MF with *n* = 2.8 and *ins out d d* / = 0.85 has the maximal loss due to the excitation of the second type of the capillary leaky modes.

with high azimuthal and radial indices. This mode is shown in Fig. 3(left).

λ

= 10.6 μm. This fact is

examples of such waveguide regimes will be given in the next section.

calculations will be made in the narrow spectral region near

the cladding consisting of capillaries will be demonstrated.

core diameter *Dcore* = 220 μm and 320 μm.

These capillary modes have a lower azimuthal index and a different radial dependence (Fig. 3(right)). It is worth pointing out that these two types of the individual capillary leaky modes are the main reason for occurring high loss regions for the considered HC MFs made of high index glasses.

Fig. 2. (a) loss dependence for HC MF with *Dcore* = 220 μm and 6 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares); (b) loss dependence for HC MF with *Dcore* = 320 μm the other notations are the same as in (a).

Fig. 3. (left) a typical Pointing vector distribution for a capillary leaky mode in the cladding with a high azimuthal index; (right) the Pointing vector distribution for the second type of the capillary leaky modes with a lower azimuthal index.

Further, we will consider HC MF with eight capillaries in the cladding. The air core diameters and the glass refractive indices will be the same as in the case of HC MFs with six capillaries in the cladding. In Fig. 4 the loss dependencies for this HC MF are shown.

As one can see from Fig. 4(a) HC MF with *ins out d d* / = 0.85 and *n* = 2.8 has the highest loss due to the excitation of the leaky modes with a lower azimuthal index in this spectral region (Fig. 3(b)). The HC MF with *ins out d d* / = 0.85 and *n* = 2.4 has a high loss for the same reason. Losses for HC MFs with other parameters in Fig. 4(a) are relatively low, especially, in the case of HC MF with *ins out d d* / = 0.8 and *n* = 2.4. The losses for HC MFs with *Dcore* = 320 μm are very high due to the strong coupling of the air core modes with the capillary modes having a lower azimuthal index (Fig.3(right)) in this spectral range with the exception of the HC MF with *ins out d d* / = 0.85 and *n* = 2.8.

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 241

The loss dependencies in Fig. 5 show that a low loss regime for the high index glass HC MFs with the cladding consisting of capillaries can be obtained by the right selection of many

At the end of this subsection, the loss dependencies for HC MFs with the cladding

Fig. 6. (a) loss dependence for HC MF with *Dcore* = 220 μm and 12 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm

It has thus been shown that the achievement of a low loss waveguide regime for HC MFs with the cladding consisting of capillaries is complicated multi parameter task. All the parameters characterizing the HC MFs such as *Dcore, dins, dout, n, N* (number of the capillaries in the cladding) have an effect on the waveguide regime in the considered spectral range. In this way, two main factors affect the loss level of the HC MFs. The first is the density of eigenstates of the individual capillary and the second is the discrete rotational symmetry of the core boundary. The density of eigenstates of the individual capillary is determined by geometry parameters of a capillary and the value of a glass refractive index. The second factor is connected to the symmetry of the capillary arrangement in the cladding. By comparing the figures in this subsection one can make a conclusion that by decreasing the number of capillaries in the cladding one obtains a stronger dependence on the *Dcore*. It seems possible to find a balance between the number of capillaries and the air core diameter. With the increase in the capillary number the role of the discrete rotational symmetry

**4.2 Bend loss dependencies on a bend radius for HC MF with a different number of** 

In this subsection we will consider characteristics of the bend loss behaviour for HC MFs with a different number of capillaries in the cladding. To reveal the special features of the bend loss one analyses the bend loss behaviour for HC MFs with optimal waveguide

parameters characterizing HC MF including *Dcore*.

consisting of 12 capillaries will be shown (Fig. 6).

the other notations are the same as in (a).

weakens.

**capillaries in the cladding** 

Fig. 4. (a) loss dependence for HC MF with *Dcore* = 220 μm and 8 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm the other notations are the same as in (a).

The loss dependencies for HC MFs with ten capillaries in the cladding are shown in Fig. 5. The values of *dins*, *dout* and consequently the capillary wall thicknesses are lower compared to the cases considered above. The loss level for all HC MFs (Fig. 5(a)) is very high due to a strong coupling to the individual capillary leaky modes of both types. Low loss curves correspond only to HC MFs with *ins out d d* / = 0.8, 0.85 and *n* = 2.8. The other picture is observed in the case of HC MFs with *Dcore* = 320 μm. All loss dependencies have low losses with the exception of HC MF with *ins out d d* / = 0.8 and *n* = 2.8 which has strong coupling with the cladding and, consequently, a non propagating regime in this spectral range.

Fig. 5. (a) loss dependence for HC MF with *Dcore* = 220 μm and 10 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm the other notations are the same as in (a).

Fig. 4. (a) loss dependence for HC MF with *Dcore* = 220 μm and 8 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm

The loss dependencies for HC MFs with ten capillaries in the cladding are shown in Fig. 5. The values of *dins*, *dout* and consequently the capillary wall thicknesses are lower compared to the cases considered above. The loss level for all HC MFs (Fig. 5(a)) is very high due to a strong coupling to the individual capillary leaky modes of both types. Low loss curves correspond only to HC MFs with *ins out d d* / = 0.8, 0.85 and *n* = 2.8. The other picture is observed in the case of HC MFs with *Dcore* = 320 μm. All loss dependencies have low losses with the exception of HC MF with *ins out d d* / = 0.8 and *n* = 2.8 which has strong coupling with

Fig. 5. (a) loss dependence for HC MF with *Dcore* = 220 μm and 10 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm

the cladding and, consequently, a non propagating regime in this spectral range.

the other notations are the same as in (a).

the other notations are the same as in (a).

The loss dependencies in Fig. 5 show that a low loss regime for the high index glass HC MFs with the cladding consisting of capillaries can be obtained by the right selection of many parameters characterizing HC MF including *Dcore*.

At the end of this subsection, the loss dependencies for HC MFs with the cladding consisting of 12 capillaries will be shown (Fig. 6).

Fig. 6. (a) loss dependence for HC MF with *Dcore* = 220 μm and 12 capillaries in the cladding, *ins out d d* / = 0.9 (*n* = 2.4, circles), *ins out d d* / = 0.9 (*n* = 2.8, triangles), *ins out d d* / = 0.85 (*n* = 2.4, rhombuses), *ins out d d* / = 0.85 (*n* = 2.8, squares), *ins out d d* / = 0.8 (*n* = 2.4, white rhombuses), *ins out d d* / = 0.8 (*n* = 2.8, white squares); (b) loss dependence for HC MF with *Dcore* = 320 μm the other notations are the same as in (a).

It has thus been shown that the achievement of a low loss waveguide regime for HC MFs with the cladding consisting of capillaries is complicated multi parameter task. All the parameters characterizing the HC MFs such as *Dcore, dins, dout, n, N* (number of the capillaries in the cladding) have an effect on the waveguide regime in the considered spectral range. In this way, two main factors affect the loss level of the HC MFs. The first is the density of eigenstates of the individual capillary and the second is the discrete rotational symmetry of the core boundary. The density of eigenstates of the individual capillary is determined by geometry parameters of a capillary and the value of a glass refractive index. The second factor is connected to the symmetry of the capillary arrangement in the cladding. By comparing the figures in this subsection one can make a conclusion that by decreasing the number of capillaries in the cladding one obtains a stronger dependence on the *Dcore*. It seems possible to find a balance between the number of capillaries and the air core diameter. With the increase in the capillary number the role of the discrete rotational symmetry weakens.

#### **4.2 Bend loss dependencies on a bend radius for HC MF with a different number of capillaries in the cladding**

In this subsection we will consider characteristics of the bend loss behaviour for HC MFs with a different number of capillaries in the cladding. To reveal the special features of the bend loss one analyses the bend loss behaviour for HC MFs with optimal waveguide

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 243

Such resonance behaviour of the bend loss occurs due to a very high density of dielectric modes (eigenstates) of an individual capillary at such values of *n*, *dins, dout*. The energy of the air core mode of the HC MFs is tunnelled by these dielectric modes into the capillary 'airy' modes. The higher the values of *n*, *dins, dout* with respect to the wavelength the more effective tunnelling is observed and the excited 'airy' modes of the individual capillary have higher quality factor. For example, the bend loss dependence for HC MF with the cladding consisting of 8 capillaries and *Dcore* = 220 μm has no resonance peaks due to suppressing the

To confirm the above conclusions, bend losses for HC MFs with the cladding consisting of 10 and 12 capillaries were calculated (Fig. 9). As in the case of Fig. 7, HC MFs with the

Fig. 9. (a) bend loss dependence on the bend radius for HC MFs with 10 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.85 (*n* = 2.8, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.85 (*n* = 2.4, circles); (b) bend loss dependence on the bend radius for HC MFs with 12 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.8 (*n* = 2.8, squares) and *Dcore* = 320

All curves in Fig. 9 have no resonance peaks except for the HC MF with *Dcore* = 320 μm, *ins out d d* / = 0.85 and *n* = 2.4. In this case, the dielectric capillary mode with a high azimuthal index (Fig. 3(left)) was excited at the bend radius *R* = 18 cm and a weak tunnelling process into the 'airy' mode occurred. The level of the bend losses for all considered bent HC MFs

In conclusion, one can state that the optimal waveguide regime in the spectral region near λ = 10.6 μm for HC MFs made of high index glass (*n* > 2) is possible at *N* > 8, where *N* is a number of capillaries in the cladding. In this case, the process of tunnelling of the air core modes of HC MF into the 'airy' modes of an individual capillary is suppressed due to low quality factor of the 'airy' modes and thus a low loss waveguide regime for a bend becomes

The guidance of CO2 laser radiation in HC MFs with the cladding consisting of capillaries was analysed. Two main factors affecting the waveguide mechanism in these waveguide

tunnelling through the capillary walls due to a decrease in the values of *dins, dout* or *n*.

lowest waveguide losses were taken for the bend loss calculations.

μm, *ins out d d* / = 0.8 (*n* = 2.4, circles).

possible.

**5. Conclusion** 

(Fig. 9) is very close to that of the straight HC MFs.

regimes found in the previous subsection and, correspondingly, with minimal waveguide losses.

In Fig.7 the bend loss dependencies for two low loss waveguide regimes in the case of HC MF with the cladding consisting of 6 capillaries and 8 capillaries are shown.

Fig. 7. (a) bend loss dependence on the bend radius for HC MFs with 6 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.9 (*n* = 2.4, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.9 (*n* = 2.4, circles); (b) bend loss dependence on the bend radius for HC MFs with 8 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.8 (*n* = 2.4, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.85 (*n* = 2.8, circles).

As one can see from Fig. 7(a), the bend loss dependencies have resonance peaks in the case of both values of *Dcore*. Just as in the case of HC MF with 8 capillaries in the cladding this resonance behaviour exists only for HC MF with *Dcore* = 320 μm (Fig. 7(b)). These resonances are connected with the excitation of capillary eigenstates modes called 'airy' modes [Vincetti&Setti, 2010]. An example of such a resonance tunnelling with the excitation of the 'airy' mode of the individual capillary under bending is shown in Fig. 8 for HC MF with 8 capillaries in the cladding.

Fig. 8. (left) the air core mode of HC MF with 8 capillaries in the cladding begin to couple with an 'airy' mode of an individual capillary of the cladding at a certain value of the bend radius; (right) the resonance excitation of the 'airy' mode of an individual capillary occurs at a lower value of the bend radius.

Such resonance behaviour of the bend loss occurs due to a very high density of dielectric modes (eigenstates) of an individual capillary at such values of *n*, *dins, dout*. The energy of the air core mode of the HC MFs is tunnelled by these dielectric modes into the capillary 'airy' modes. The higher the values of *n*, *dins, dout* with respect to the wavelength the more effective tunnelling is observed and the excited 'airy' modes of the individual capillary have higher quality factor. For example, the bend loss dependence for HC MF with the cladding consisting of 8 capillaries and *Dcore* = 220 μm has no resonance peaks due to suppressing the tunnelling through the capillary walls due to a decrease in the values of *dins, dout* or *n*.

To confirm the above conclusions, bend losses for HC MFs with the cladding consisting of 10 and 12 capillaries were calculated (Fig. 9). As in the case of Fig. 7, HC MFs with the lowest waveguide losses were taken for the bend loss calculations.

Fig. 9. (a) bend loss dependence on the bend radius for HC MFs with 10 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.85 (*n* = 2.8, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.85 (*n* = 2.4, circles); (b) bend loss dependence on the bend radius for HC MFs with 12 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.8 (*n* = 2.8, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.8 (*n* = 2.4, circles).

All curves in Fig. 9 have no resonance peaks except for the HC MF with *Dcore* = 320 μm, *ins out d d* / = 0.85 and *n* = 2.4. In this case, the dielectric capillary mode with a high azimuthal index (Fig. 3(left)) was excited at the bend radius *R* = 18 cm and a weak tunnelling process into the 'airy' mode occurred. The level of the bend losses for all considered bent HC MFs (Fig. 9) is very close to that of the straight HC MFs.

In conclusion, one can state that the optimal waveguide regime in the spectral region near λ = 10.6 μm for HC MFs made of high index glass (*n* > 2) is possible at *N* > 8, where *N* is a number of capillaries in the cladding. In this case, the process of tunnelling of the air core modes of HC MF into the 'airy' modes of an individual capillary is suppressed due to low quality factor of the 'airy' modes and thus a low loss waveguide regime for a bend becomes possible.

#### **5. Conclusion**

242 CO2 Laser – Optimisation and Application

regimes found in the previous subsection and, correspondingly, with minimal waveguide

In Fig.7 the bend loss dependencies for two low loss waveguide regimes in the case of HC

Fig. 7. (a) bend loss dependence on the bend radius for HC MFs with 6 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.9 (*n* = 2.4, squares) and *Dcore* = 320 μm, *ins out d d* / = 0.9 (*n* = 2.4, circles); (b) bend loss dependence on the bend radius for HC MFs with 8 capillaries in the cladding: *Dcore* = 220 μm, *ins out d d* / = 0.8 (*n* = 2.4, squares) and *Dcore* = 320 μm, *ins out d d* /

As one can see from Fig. 7(a), the bend loss dependencies have resonance peaks in the case of both values of *Dcore*. Just as in the case of HC MF with 8 capillaries in the cladding this resonance behaviour exists only for HC MF with *Dcore* = 320 μm (Fig. 7(b)). These resonances are connected with the excitation of capillary eigenstates modes called 'airy' modes [Vincetti&Setti, 2010]. An example of such a resonance tunnelling with the excitation of the 'airy' mode of the individual capillary under bending is shown in Fig. 8 for HC MF with 8

Fig. 8. (left) the air core mode of HC MF with 8 capillaries in the cladding begin to couple with an 'airy' mode of an individual capillary of the cladding at a certain value of the bend radius; (right) the resonance excitation of the 'airy' mode of an individual capillary occurs at

MF with the cladding consisting of 6 capillaries and 8 capillaries are shown.

losses.

= 0.85 (*n* = 2.8, circles).

capillaries in the cladding.

a lower value of the bend radius.

The guidance of CO2 laser radiation in HC MFs with the cladding consisting of capillaries was analysed. Two main factors affecting the waveguide mechanism in these waveguide

Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 245

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structures were proposed. The first factor is connected with the representation of the curved air core boundary of the HC MFs as azimuthal diffraction quasi - gratings. These azimuthal diffraction gratings occur due to the cylindrical surface of an individual capillary of the cladding as well as to a discrete rotational symmetry of their arrangement in the cladding. In this way, the air core mode of the HC MF is formed by the interference of space cylindrical harmonics originated from the light scattering on these quasi - diffraction gratings. The process of the air core mode formation is much more complicated compared to the one for the HC MFs with continuous rotational symmetry of the air core boundary. The interaction of cylindrical harmonics forming the air core mode of the HC MF with the capillary walls is different from each other. It leads to a weakened material loss effect on the waveguide regime in comparison with the HC MF with a continuous rotational symmetry of the air core boundary, for example, IC HC PCFs. The second factor is connected with the optical properties of an individual capillary, in particular, with the density of its eigenstates (leaky modes). This factor determines the widths of the transmission regions and the level of waveguide losses. Numerical analyses have shown that a low loss waveguide regime in the spectral region near λ = 10.6 μm for the HC MFs with the cladding consisting of high index glass capillaries becomes possible. The optimisation of the HC MF structure to achieve these regimes is a complicated multiparameter task depending on all geometry parameters characterizing the HC MFs and the value of a glass refractive index. The bend loss of the HC MFs with the cladding consisting of capillaries made of high index glasses has a resonance character depending on the bend radius. To suppress such resonances it is necessary to increase the number of capillaries in the cladding. It leads to a decrease in the capillary sizes and to a decrease in the quality factor of the 'airy' modes of the capillaries.

In the end, we would like to outline the prospects of future investigations in this field. In our opinion, to improve the waveguide properties of the HC MFs it is necessary to study the process of the air core mode formation more carefully. An effect of different types of symmetries of the capillaries arrangements in the cladding and the value of *Dcore* on the level of waveguide loss should be investigated. The optical properties of an individual capillary made of high index glass, in particular, its optical eigenstates and the density of these eigenstates depending on the geometry parameters of the capillary and glass refractive indices should be studied. To achieve a low loss guidance it is necessary to perform an optimisation of the HC MFs structure. This complicated optimisation task can be performed by powerful numerical algorithms which have already been applied, for example, to optimisation of the Bragg fibers structures [Biriukov et. al., 2008]. Also, it is necessary to improve the technology of making high index glasses with a low material loss and a technology of the HC MFs fabrication. It is worth mentioning that the early experiments demonstrated the possibility of obtaining waveguide regimes for such HC MFs made of high index chalcogenide glasses at CO2 laser wavelengths [Kosolapov et. al., 2011]. As the light was well localized in the core, such fibers hold much promise for the delivery of CO2 laser radiation.

#### **6. Acknowledgment**

The authors thank Alexandra Nikolskaya for her assistance in translating this chapter into English.

#### **7. References**

244 CO2 Laser – Optimisation and Application

structures were proposed. The first factor is connected with the representation of the curved air core boundary of the HC MFs as azimuthal diffraction quasi - gratings. These azimuthal diffraction gratings occur due to the cylindrical surface of an individual capillary of the cladding as well as to a discrete rotational symmetry of their arrangement in the cladding. In this way, the air core mode of the HC MF is formed by the interference of space cylindrical harmonics originated from the light scattering on these quasi - diffraction gratings. The process of the air core mode formation is much more complicated compared to the one for the HC MFs with continuous rotational symmetry of the air core boundary. The interaction of cylindrical harmonics forming the air core mode of the HC MF with the capillary walls is different from each other. It leads to a weakened material loss effect on the waveguide regime in comparison with the HC MF with a continuous rotational symmetry of the air core boundary, for example, IC HC PCFs. The second factor is connected with the optical properties of an individual capillary, in particular, with the density of its eigenstates (leaky modes). This factor determines the widths of the transmission regions and the level of waveguide losses. Numerical analyses have shown that a low loss waveguide regime in the

glass capillaries becomes possible. The optimisation of the HC MF structure to achieve these regimes is a complicated multiparameter task depending on all geometry parameters characterizing the HC MFs and the value of a glass refractive index. The bend loss of the HC MFs with the cladding consisting of capillaries made of high index glasses has a resonance character depending on the bend radius. To suppress such resonances it is necessary to increase the number of capillaries in the cladding. It leads to a decrease in the capillary sizes

In the end, we would like to outline the prospects of future investigations in this field. In our opinion, to improve the waveguide properties of the HC MFs it is necessary to study the process of the air core mode formation more carefully. An effect of different types of symmetries of the capillaries arrangements in the cladding and the value of *Dcore* on the level of waveguide loss should be investigated. The optical properties of an individual capillary made of high index glass, in particular, its optical eigenstates and the density of these eigenstates depending on the geometry parameters of the capillary and glass refractive indices should be studied. To achieve a low loss guidance it is necessary to perform an optimisation of the HC MFs structure. This complicated optimisation task can be performed by powerful numerical algorithms which have already been applied, for example, to optimisation of the Bragg fibers structures [Biriukov et. al., 2008]. Also, it is necessary to improve the technology of making high index glasses with a low material loss and a technology of the HC MFs fabrication. It is worth mentioning that the early experiments demonstrated the possibility of obtaining waveguide regimes for such HC MFs made of high index chalcogenide glasses at CO2 laser wavelengths [Kosolapov et. al., 2011]. As the light was well localized in the core, such fibers hold much promise for the delivery of CO2

The authors thank Alexandra Nikolskaya for her assistance in translating this chapter into

and to a decrease in the quality factor of the 'airy' modes of the capillaries.

= 10.6 μm for the HC MFs with the cladding consisting of high index

spectral region near

laser radiation.

English.

**6. Acknowledgment** 

λ


Transmission of CO2 Laser Radiation Through Hollow Core Microstructured Fibers 247

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**Part 3** 

**Material Processing**

