1. Introduction

Femtosecond laser micromachining and inscription have attracted significant attention in the past decade, not only for material processing applications, such as cutting or drilling [1, 2], but also for the fabrication of 3D photonic devices in transparent materials. When focusing a high-power femtosecond pulse inside a transparent dielectric material, the intensity at the focal region is high enough to initiate multiphoton ionization, which eventually leads to structural changes and permanent refractive index changes [3–7]. This technique has some advantages over current photonic device fabrication methods: (i) the nonlinear nature of the laser-matter interaction confines any induced index change to the focal volume, enabling 3D fabrication of photonic devices in a relatively short time compared to planar semiconductor-based fabrication methods; (ii) the nonlinear absorption process does not require any photosensitivity of the material, facilitating fabrication in glasses, crystals, polymers, and practically any optical material. Although preprocessing of the materials to be inscribed is not necessary, it can be helpful. Hydrogen loading, for example, can enhance the sensitivity to inscription of fiber Bragg gratings [8, 9].

Different categories of index change have been defined in the literature, mostly with respect to grating fabrication. Type I index changes happen for pulse energies close to the nonlinear ionization threshold (1013 W=cm2) and cause an accumulative change in the refractive index of the order of 10<sup>3</sup> (in silica glass). The change in the refractive index is isotropic and is mostly attributed to localized material melting and rapid resolidification [10, 11], although other explanations (such as color center formations) are also considered [12]. This type of index change is most useful for the fabrication of waveguides [13], couplers [14], and FBGs [15].

From a mechanical perspective, the fiber core must be maintained in the focal plane through the entire fabrication process. This requires high-end air-bearing translation stages. An extension of the PbP method to reduce the mechanical complexity is the line-by-line method, in which the beam is scanned across the fiber axis and forms a rectangular "snake" pattern [28], or plane-by-plane method in which the

The PbP method offers the highest flexibility in grating fabrication. Uniform gratings, phase-shifted gratings [30], apodization [31], and more [32] have been demonstrated. The tight focusing condition also enables inscription through the fiber jacket without damage [33]. The same inscription system can be used for the fabrication of waveguides and long-period gratings as well [34–36]. Gratings fabricated by this method have been shown to have superior thermal properties [37] than UV gratings and better performance as fiber laser mirrors [38–40].

In 2003, Mihailov et al. demonstrated the fabrication of FBGs with a femtosecond laser and a phase mask [41, 42]. The optical configuration is similar to its UV counterpart. The beam is focused on the fiber core using a cylindrical lens and through a phase mask. The mask period defines the Bragg grating period. In the phase mask configuration, the grating is inscribed as a whole rather than plane by plane. It is robust, repeatable, and typically stationary. As the period is defined by the phase mask, relatively long-focus lenses can be used, which greatly eases alignment and makes this configuration suitable for large core fibers as well. With this technique, grating inscription has been demonstrated in various types of fibers [43–46]. The main drawback of this configuration is the lack of flexibility, as the period is predetermined by the phase mask. Nevertheless, it is possible to tune the Bragg wavelength by introducing defocusing and other aberrations into the inscribing beam. Shifts of more than 300 nm, as well as chirp gratings, have been demonstrated with this method [47, 48]. Inscription through the coating is also feasible in this method with "of the shelf" high-NA cylinder lenses [49–51].

Both methods have been used for fabrication of fiber Bragg grating with superior properties than grating fabrication with UV sources. Femtosecond laser can be used to fabricate gratings in any type of fibers and can withstand higher temperature than UV gratings. The most notable feature is the ability to inscribe grating through the fiber coating, thus maintaining its mechanical strength, and avoid handling

All-optical switching has been investigated for a long time by the optical community, in particular for optical communication applications. If successful, it will dramatically increase the throughput in optical links and will enable data switching

Recently, there has been a growing interest in FBGs for optical switching applications. Several works reported implementations of an optical switch by tuning a pre-inscribed grating by means of heat, stress, and other relatively slow processes [55–58]. These methods are based on permanent FBGs, in which any change in the refractive index (heat, cross-phase modulation) or period (induced stress) will shift the grating resonance from the signal wavelength. Such switching mechanisms have several drawbacks due to the inherent physical properties of their operation, which limits their applicability and performance. In the wider context, there have been several reports on the switching of various photonic crystal structures, both for fundamental and for applicative purposes (see, e.g., [59, 60] for some recent

at speeds and rates far beyond the capabilities of current electronic devices.

issues such as stripping, cleaning, and recoating [52–54].

3. Transient fiber Bragg grating optical switching

reviews).

25

beam is focused to an elliptic sheet, creating 2D index change [29].

Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

Type II interaction happens at intensities beyond the damage threshold, which can lead to the formation of voids [16]. Voids are submicron features, microexplosions in matter, or air bubbles, with larger refractive index contrast compared to their surroundings. They are achieved by extremely tight focusing with power densities of the order of 10<sup>15</sup> W=cm2. Voids attract interest mainly due to their potential as permanent highly dense 3D optical data storage materials. In such schemes, each void represents a bit, which can be read with transmitted or scattered light. It was found that voids can also be seized, moved, and merged by femtosecond laser radiation [17]. Type II FBGs, also termed "damage" gratings, have been shown to withstand higher temperatures and can be used as harsh environment sensors [18].

On applying intensities between the above regimes, an anisotropic, polarizationdependent, index change is induced, and the glass material becomes birefringent [19, 20]. The magnitude of the reported index change is the same as for type I changes, but it is not isotropic. The intensity boundaries for this interaction are not well defined, as they depend on the laser source, the focusing lens, and the material itself. The anisotropy of the refractive index change is believed to originate from the nanogratings observed inside the focal volume. The planes of these gratings are perpendicular to the light polarization and behave as negative uniaxial crystals [21–24].

In the following we will focus on fabrication of FBGs using femtosecond laser. Section 2 briefly describes methods of fabrications using femtosecond laser and references to a more detailed work on the subject. Section 3 introduces the main concept of this chapter—transient fiber Bragg gratings for optical switching. The theory of transient grating is outlined, and an overview of various works on the subject is described. Section 4 provides experimental results achieved by our group on generation and characterization of transient FBGs. Finally, we summarize and discuss possible future research direction of transient Bragg grating switching.

## 2. Femtosecond inscription of fiber Bragg gratings

FBG fabricated with femtosecond laser was first demonstrated by the point-bypoint (PbP) method [25, 26]. In this method, the beam is tightly focused into the fiber core to a spot size radius smaller than half of the desired grating period. To achieve this, a microscope objective with a high numerical aperture must be used, as well as pulse energies just above the inscription threshold. The induced index change happens on the pulse peak intensity only, which can be smaller than the diffraction limit of the focusing objective lens. To fabricate the grating, the fiber is aligned and translated in the focal plane at constant velocity. The scan velocity matches the grating period to the laser pulse rate, so that each pulse inscribes a single grating "plane."

The PbP method requires tight control on all-optical and mechanical parameters of the system. The optical system must be carefully aligned to avoid aberrations and achieve the smallest spot size. The pulse width and energy should be controlled as well, since they affect the actual spot size. For this reason, most PbP systems use 800 nm femtosecond laser, rather than its harmonics, to avoid dispersions [27].

#### Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

close to the nonlinear ionization threshold (1013 W=cm2) and cause an accumulative change in the refractive index of the order of 10<sup>3</sup> (in silica glass). The change in the refractive index is isotropic and is mostly attributed to localized material melting and rapid resolidification [10, 11], although other explanations (such as color center formations) are also considered [12]. This type of index change is most useful for

Type II interaction happens at intensities beyond the damage threshold, which

On applying intensities between the above regimes, an anisotropic, polarizationdependent, index change is induced, and the glass material becomes birefringent [19, 20]. The magnitude of the reported index change is the same as for type I changes, but it is not isotropic. The intensity boundaries for this interaction are not well defined, as they depend on the laser source, the focusing lens, and the material itself. The anisotropy of the refractive index change is believed to originate from the nanogratings observed inside the focal volume. The planes of these gratings are perpendicular to the light polarization and behave as negative uniaxial crystals [21–24]. In the following we will focus on fabrication of FBGs using femtosecond laser. Section 2 briefly describes methods of fabrications using femtosecond laser and references to a more detailed work on the subject. Section 3 introduces the main concept of this chapter—transient fiber Bragg gratings for optical switching. The theory of transient grating is outlined, and an overview of various works on the subject is described. Section 4 provides experimental results achieved by our group on generation and characterization of transient FBGs. Finally, we summarize and discuss possible future research direction of transient Bragg grating switching.

FBG fabricated with femtosecond laser was first demonstrated by the point-bypoint (PbP) method [25, 26]. In this method, the beam is tightly focused into the fiber core to a spot size radius smaller than half of the desired grating period. To achieve this, a microscope objective with a high numerical aperture must be used, as well as pulse energies just above the inscription threshold. The induced index change happens on the pulse peak intensity only, which can be smaller than the diffraction limit of the focusing objective lens. To fabricate the grating, the fiber is aligned and translated in the focal plane at constant velocity. The scan velocity matches the grating period to the laser pulse rate, so that each pulse inscribes a

The PbP method requires tight control on all-optical and mechanical parameters of the system. The optical system must be carefully aligned to avoid aberrations and achieve the smallest spot size. The pulse width and energy should be controlled as well, since they affect the actual spot size. For this reason, most PbP systems use 800 nm femtosecond laser, rather than its harmonics, to avoid dispersions [27].

can lead to the formation of voids [16]. Voids are submicron features, microexplosions in matter, or air bubbles, with larger refractive index contrast compared to their surroundings. They are achieved by extremely tight focusing with power densities of the order of 10<sup>15</sup> W=cm2. Voids attract interest mainly due to their potential as permanent highly dense 3D optical data storage materials. In such schemes, each void represents a bit, which can be read with transmitted or scattered light. It was found that voids can also be seized, moved, and merged by femtosecond laser radiation [17]. Type II FBGs, also termed "damage" gratings, have been shown to withstand higher temperatures and can be used as harsh environment

the fabrication of waveguides [13], couplers [14], and FBGs [15].

Fiber Optic Sensing - Principle, Measurement and Applications

2. Femtosecond inscription of fiber Bragg gratings

sensors [18].

single grating "plane."

24

From a mechanical perspective, the fiber core must be maintained in the focal plane through the entire fabrication process. This requires high-end air-bearing translation stages. An extension of the PbP method to reduce the mechanical complexity is the line-by-line method, in which the beam is scanned across the fiber axis and forms a rectangular "snake" pattern [28], or plane-by-plane method in which the beam is focused to an elliptic sheet, creating 2D index change [29].

The PbP method offers the highest flexibility in grating fabrication. Uniform gratings, phase-shifted gratings [30], apodization [31], and more [32] have been demonstrated. The tight focusing condition also enables inscription through the fiber jacket without damage [33]. The same inscription system can be used for the fabrication of waveguides and long-period gratings as well [34–36]. Gratings fabricated by this method have been shown to have superior thermal properties [37] than UV gratings and better performance as fiber laser mirrors [38–40].

In 2003, Mihailov et al. demonstrated the fabrication of FBGs with a femtosecond laser and a phase mask [41, 42]. The optical configuration is similar to its UV counterpart. The beam is focused on the fiber core using a cylindrical lens and through a phase mask. The mask period defines the Bragg grating period. In the phase mask configuration, the grating is inscribed as a whole rather than plane by plane. It is robust, repeatable, and typically stationary. As the period is defined by the phase mask, relatively long-focus lenses can be used, which greatly eases alignment and makes this configuration suitable for large core fibers as well. With this technique, grating inscription has been demonstrated in various types of fibers [43–46]. The main drawback of this configuration is the lack of flexibility, as the period is predetermined by the phase mask. Nevertheless, it is possible to tune the Bragg wavelength by introducing defocusing and other aberrations into the inscribing beam. Shifts of more than 300 nm, as well as chirp gratings, have been demonstrated with this method [47, 48]. Inscription through the coating is also feasible in this method with "of the shelf" high-NA cylinder lenses [49–51].

Both methods have been used for fabrication of fiber Bragg grating with superior properties than grating fabrication with UV sources. Femtosecond laser can be used to fabricate gratings in any type of fibers and can withstand higher temperature than UV gratings. The most notable feature is the ability to inscribe grating through the fiber coating, thus maintaining its mechanical strength, and avoid handling issues such as stripping, cleaning, and recoating [52–54].

## 3. Transient fiber Bragg grating optical switching

All-optical switching has been investigated for a long time by the optical community, in particular for optical communication applications. If successful, it will dramatically increase the throughput in optical links and will enable data switching at speeds and rates far beyond the capabilities of current electronic devices.

Recently, there has been a growing interest in FBGs for optical switching applications. Several works reported implementations of an optical switch by tuning a pre-inscribed grating by means of heat, stress, and other relatively slow processes [55–58]. These methods are based on permanent FBGs, in which any change in the refractive index (heat, cross-phase modulation) or period (induced stress) will shift the grating resonance from the signal wavelength. Such switching mechanisms have several drawbacks due to the inherent physical properties of their operation, which limits their applicability and performance. In the wider context, there have been several reports on the switching of various photonic crystal structures, both for fundamental and for applicative purposes (see, e.g., [59, 60] for some recent reviews).

Transient Bragg gratings (TBGs) can overcome these limitations. These are Bragg gratings of finite duration. In the case of femtosecond gratings in materials, they are expected to be formed at intensities below the threshold for permanent index modification and to exist for the inscribing pulse duration only. Transient gratings in fibers or waveguides are expected to act as a fast switch or modulator by implementing a Bragg mirror with (ultra-) fast decay time.

(800 nm); therefore, a transient thermal grating may only be realized through

Another mechanism is to form dynamic population gratings in active fibers. This was implemented via counter propagating waves and resulted in millisecond time

TBGs of a few centimeter lengths were implemented using 193 nm, nanosecond, excimer laser pulses, and a phase mask in phosphosilicate fibers without hydrogen loading. In passive fibers, extremely slow reflection of tens of seconds' duration was demonstrated [80], while in active fibers, the grating was based on population inversion, and the time response was estimated to be milliseconds long [81]. In both cases the expected rise time of such switching mechanism cannot be shorter than

Transient grating-based switching was suggested numerically by coupling light from the fundamental mode to high-order modes [82]. Nanosecond switching was implemented using the Kerr effect with a highly nonlinear polymer layer deposited close to the core of a polished fiber [83]. It was suggested, theoretically, that a TBG would result in an ultrafast switching response [84]. Thermal phenomena are typically associated with relatively long (microsecond) time scales. Recently, it was suggested, theoretically, that picosecond scale switching is achievable with thermal gratings, using metal nanoparticles in waveguides [85]. Nanosecond switching of a permanent FBG was demonstrated by introducing electrodes into a special two-hole fiber [86]; however, this device suffers from nanosecond rise time and a millisecond

TBGs essentially enable pulse extraction from CW source. This can lead to several photonic applications such as all-optical switching and modulator at any wavelength, all-fiber Q-switching mechanism, and sub-ns pulse sources.

literature [87, 88] starting from the wave equation. Here, we provide a short description of the theory starting from its derived coupled mode equation for transient grating. The analysis begins from the well-known coupled mode equations for forward and backward propagating waves in grating media, adapted to the case

dz Af <sup>þ</sup> <sup>2</sup> ivgκq zð Þm tð ÞAf <sup>¼</sup> iCvgκq zð Þm tð Þ<sup>e</sup>

Here, Af and Ab represent the envelopes of the forward and backward pulses, respectively, vg is the group velocity, q zð Þ is the spatial shape of the inscribed Bragg grating, and m tð Þ is its temporal profile. C is the grating contrast, and δk ¼ δω=vg is the detuning of the incident pulse from the center of the spectral gap. The forwardbackward mode coupling coefficient, κ ¼ k0n0Δn=4nneff , is a product of the free space wavevector k0, the waveguide material refractive index n0, and its maximal

dz Ab <sup>þ</sup> <sup>2</sup> ivgκq zð Þm tð ÞAb ¼ �iCvgκq zð Þm tð Þ exp ð Þ <sup>2</sup>iδκ<sup>z</sup> Af (2)

ð Þ �2iδκ<sup>z</sup> Ab (1)

In the following, we will shortly describe the theory of transient Bragg grating. A detailed derivation of the suitable coupled mode equations, and their numerical solution can be found in literature. Here, we begin our discussion from the coupled mode equations and limit the discussion to specific case where analytical solution is possible to gain physical insight. Next, we will describe our group experimental work on transient Bragg gratings in silica fibers. We will show the dynamic of permanent grating switching and describe an immunization technique that enable, for the first time to our knowledge, thermal grating-based nonlinear absorption. The theory of transient Bragg gratings is fully developed and described in the

nonlinear absorption.

Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

responses [79].

the ns pulse length.

of transient grating:

d dt Ab � vg

27

d dt Af <sup>þ</sup> vg d

d

time scale to return to its original state.

Several mechanisms are available to implement transient Bragg gratings: the optical Kerr effect, free-carrier recombination in semiconductor materials, and diffusion of thermal gratings. The different mechanisms differ from one to another by the rise and decay time of the switch and by the extinction ratio, i.e., the contrast between on and off states. Such transient gratings can be turned on/off by modulating the illumination beam.

The Kerr effect describes the refractive index change in the presence of high intensities, such as those that are available from high-power femtosecond lasers [61]. The refractive index changes by an amount of n2I, where n<sup>2</sup> is the material nonlinear index and I is the intensity. The response of the material is instantaneous. For silica fibers, <sup>n</sup><sup>2</sup> � <sup>3</sup> � <sup>10</sup>�<sup>16</sup> cm2=W; thus, for an intensity of <sup>I</sup> <sup>¼</sup> <sup>10</sup><sup>11</sup> <sup>W</sup>=cm2, the refractive index change is of the order of 10�<sup>5</sup> . Stronger index change is feasible for materials with higher Kerr nonlinearity, such as Chalcogenide or Bismuth fibers [43, 62]. The Kerr grating has a periodic pattern, with the index modulation as described above. A Kerr grating switch is expected to be weak yet with a femtosecond time scale response. Several publications reported on transient Kerr gratings in gas for the purpose of spectroscopy and in bulk semiconductors for studying freecarrier recombination rates [63]. An optical grating based on the nonlinear Kerr effect has been used in the past for parametric wavelength conversion [64] and for chemical spectroscopy [65]. An optical switch based on an optical Kerr grating has only been investigated numerically until now [66–68].

Free-carriers in semiconductor materials are formed upon pulse irradiation followed by excessive charge concentrations. In this case, the refractive index changes due to different charge densities are much higher than due to the Kerr effect. The transient index change of the semiconductor is described by the Drude model of excited free-carriers [69–71] reaching values as high as <sup>δ</sup>n=<sup>n</sup> � <sup>10</sup>�<sup>1</sup> [59, 60]. Unlike the Kerr effect, which is instantaneous, the FC excitation is "turned on" fast but typically persists for a time scale of several tens of picosecond to several ns depending on the recombination rate of the generated electron-hole pairs and the diffusion length [63, 72–74]. An optical switch-based free-carrier transient Bragg grating is expected to have better contrast and stronger reflection but on a much shorter switching time. As the reflection is very sensitive to the grating period (typically 1 μm), extremely small diffusion is sufficient to wash out the grating and its reflection. Sivan et al. showed theoretically that when exciting a transient grating based on FC, the turn-off times are very fast (<ps) due to diffusion of the excited FCs that erases the grating structure [75]. This is a key point that will allow for switching times several orders of magnitude faster than in bulk FC switching configurations, thus potentially revolutionizing switching technology. Such an optical switch is expected to have a better extinction ratio than a Kerr grating and slower (picosecond) time scale switching.

The same principle can be applied for transient thermal gratings, in which the index changes as a response to localized heat or increased temperature and the diffusion length is determined by the material properties. Transient thermal gratings are used as a method for measuring the diffusion coefficient of materials and were implemented in opaque materials with linear absorption at the laser wavelength [76–78]. Optical materials are mostly transparent to NIR femtosecond lasers

## Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

Transient Bragg gratings (TBGs) can overcome these limitations. These are Bragg gratings of finite duration. In the case of femtosecond gratings in materials, they are expected to be formed at intensities below the threshold for permanent index modification and to exist for the inscribing pulse duration only. Transient gratings in fibers or waveguides are expected to act as a fast switch or modulator by

Several mechanisms are available to implement transient Bragg gratings: the optical Kerr effect, free-carrier recombination in semiconductor materials, and diffusion of thermal gratings. The different mechanisms differ from one to another by the rise and decay time of the switch and by the extinction ratio, i.e., the contrast between on and off states. Such transient gratings can be turned on/off by modu-

The Kerr effect describes the refractive index change in the presence of high intensities, such as those that are available from high-power femtosecond lasers [61]. The refractive index changes by an amount of n2I, where n<sup>2</sup> is the material nonlinear index and I is the intensity. The response of the material is instantaneous. For silica fibers, <sup>n</sup><sup>2</sup> � <sup>3</sup> � <sup>10</sup>�<sup>16</sup> cm2=W; thus, for an intensity of <sup>I</sup> <sup>¼</sup> <sup>10</sup><sup>11</sup> <sup>W</sup>=cm2, the

materials with higher Kerr nonlinearity, such as Chalcogenide or Bismuth fibers [43, 62]. The Kerr grating has a periodic pattern, with the index modulation as described above. A Kerr grating switch is expected to be weak yet with a femtosecond time scale response. Several publications reported on transient Kerr gratings in gas for the purpose of spectroscopy and in bulk semiconductors for studying freecarrier recombination rates [63]. An optical grating based on the nonlinear Kerr effect has been used in the past for parametric wavelength conversion [64] and for chemical spectroscopy [65]. An optical switch based on an optical Kerr grating has

Free-carriers in semiconductor materials are formed upon pulse irradiation followed by excessive charge concentrations. In this case, the refractive index changes due to different charge densities are much higher than due to the Kerr effect. The transient index change of the semiconductor is described by the Drude model of excited free-carriers [69–71] reaching values as high as <sup>δ</sup>n=<sup>n</sup> � <sup>10</sup>�<sup>1</sup> [59, 60]. Unlike the Kerr effect, which is instantaneous, the FC excitation is "turned on" fast but typically persists for a time scale of several tens of picosecond to several ns depending on the recombination rate of the generated electron-hole pairs and the diffusion length [63, 72–74]. An optical switch-based free-carrier transient Bragg grating is expected to have better contrast and stronger reflection but on a much shorter switching time. As the reflection is very sensitive to the grating period (typically 1 μm), extremely small diffusion is sufficient to wash out the grating and its reflection. Sivan et al. showed theoretically that when exciting a transient grating based on FC, the turn-off times are very fast (<ps) due to diffusion of the excited FCs that erases the grating structure [75]. This is a key point that will allow for switching times several orders of magnitude faster than in bulk FC switching configurations, thus potentially revolutionizing switching technology. Such an optical switch is expected to have a better extinction ratio than a Kerr grating and

The same principle can be applied for transient thermal gratings, in which the index changes as a response to localized heat or increased temperature and the diffusion length is determined by the material properties. Transient thermal gratings are used as a method for measuring the diffusion coefficient of materials and were implemented in opaque materials with linear absorption at the laser wavelength [76–78]. Optical materials are mostly transparent to NIR femtosecond lasers

. Stronger index change is feasible for

implementing a Bragg mirror with (ultra-) fast decay time.

Fiber Optic Sensing - Principle, Measurement and Applications

lating the illumination beam.

refractive index change is of the order of 10�<sup>5</sup>

only been investigated numerically until now [66–68].

slower (picosecond) time scale switching.

26

(800 nm); therefore, a transient thermal grating may only be realized through nonlinear absorption.

Another mechanism is to form dynamic population gratings in active fibers. This was implemented via counter propagating waves and resulted in millisecond time responses [79].

TBGs of a few centimeter lengths were implemented using 193 nm, nanosecond, excimer laser pulses, and a phase mask in phosphosilicate fibers without hydrogen loading. In passive fibers, extremely slow reflection of tens of seconds' duration was demonstrated [80], while in active fibers, the grating was based on population inversion, and the time response was estimated to be milliseconds long [81]. In both cases the expected rise time of such switching mechanism cannot be shorter than the ns pulse length.

Transient grating-based switching was suggested numerically by coupling light from the fundamental mode to high-order modes [82]. Nanosecond switching was implemented using the Kerr effect with a highly nonlinear polymer layer deposited close to the core of a polished fiber [83]. It was suggested, theoretically, that a TBG would result in an ultrafast switching response [84]. Thermal phenomena are typically associated with relatively long (microsecond) time scales. Recently, it was suggested, theoretically, that picosecond scale switching is achievable with thermal gratings, using metal nanoparticles in waveguides [85]. Nanosecond switching of a permanent FBG was demonstrated by introducing electrodes into a special two-hole fiber [86]; however, this device suffers from nanosecond rise time and a millisecond time scale to return to its original state.

TBGs essentially enable pulse extraction from CW source. This can lead to several photonic applications such as all-optical switching and modulator at any wavelength, all-fiber Q-switching mechanism, and sub-ns pulse sources.

In the following, we will shortly describe the theory of transient Bragg grating. A detailed derivation of the suitable coupled mode equations, and their numerical solution can be found in literature. Here, we begin our discussion from the coupled mode equations and limit the discussion to specific case where analytical solution is possible to gain physical insight. Next, we will describe our group experimental work on transient Bragg gratings in silica fibers. We will show the dynamic of permanent grating switching and describe an immunization technique that enable, for the first time to our knowledge, thermal grating-based nonlinear absorption.

The theory of transient Bragg gratings is fully developed and described in the literature [87, 88] starting from the wave equation. Here, we provide a short description of the theory starting from its derived coupled mode equation for transient grating. The analysis begins from the well-known coupled mode equations for forward and backward propagating waves in grating media, adapted to the case of transient grating:

$$\frac{d}{dt}A\_f + v\_\text{g.}\frac{d}{dz}A\_f + 2\operatorname{i}v\_\text{g.}\kappa q(z)m(t)A\_f = \mathrm{iCv}\_\text{g.}\kappa q(z)m(t)e^{(-2i\hbar\text{cz})}A\_b\tag{1}$$

$$\frac{d}{dt}A\_b - v\_g \frac{d}{dz}A\_b + 2\operatorname{i}v\_g \kappa q(z)m(t)A\_b = -i\mathcal{C}v\_g \kappa q(z)m(t) \exp^{(2i\delta \text{ex})}A\_f \tag{2}$$

Here, Af and Ab represent the envelopes of the forward and backward pulses, respectively, vg is the group velocity, q zð Þ is the spatial shape of the inscribed Bragg grating, and m tð Þ is its temporal profile. C is the grating contrast, and δk ¼ δω=vg is the detuning of the incident pulse from the center of the spectral gap. The forwardbackward mode coupling coefficient, κ ¼ k0n0Δn=4nneff , is a product of the free space wavevector k0, the waveguide material refractive index n0, and its maximal

modulation amplitude Δn, divided by the effective mode index nneff . These equations are similar to those obtained in [87]; however, they account for non-zero mean index modulations, absorption, imperfect grating contrast, and nonuniform pumping (via q zð Þ).

An exact solution of Eqs. (1) and (2) is possible only numerically. However, if one assumes uniform pump spot (q ¼ 1) and ignores the spatial derivatives (justified for short modulations during which the pulse is nearly stationary), Eqs. (1) and (2) can be solved analytically—this yields the well-known Rabi solution (see, e.g., [87, 89]). This was shown to give a reasonable accuracy in measurements with spin waves [87], at least in this limit, and to lead to envelope reversal [90–92].

Alternatively, Eqs. (1) and (2) can also be solved analytically in the low conversion efficiency limit, without neglecting the spatial derivatives. In this case, the efficiency of the backward pulse generation is given approximately by a convolution of the incoming pulse with meffð Þt , where Meffð Þt is an effective modulation, and the forward wave is (nearly) monochromatic (e.g., for a CW or nanosecond source —AfðÞ!t 1):

$$A\_b(z,t) = i\mathcal{C}\nu\_\mathcal{g}\kappa q(z)m(t)\mathbf{e}^{\{2i8\text{k}\mathbf{z}\}}M\_{\text{eff}}(t) \tag{3}$$

<sup>∣</sup>Abð Þ <sup>t</sup>; <sup>z</sup> <sup>∣</sup> � ffiffiffi

spond to the above solutions.

Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

also feasible.

experiments.

29

4.2 Transient Kerr grating

4.1 Experimental setup

results.

exception of non-Gaussian response.

<sup>π</sup> <sup>p</sup> <sup>C</sup> <sup>n</sup><sup>0</sup> 4n<sup>2</sup> eff

Δnω0Tpasse

Thus, the reflected wave duration and spectrum follow that of the pump pulse. The above approximations are valid for low reflection efficiency, i.e., undepleted pump. Transient Kerr grating is expected to have a very low efficiency, and an order of magnitude difference between Tpass and Tmod is expected to corre-

In silica fibers, there is also the possibility for thermal gratings. In this case the index modulation time varies on the microsecond and nanosecond time scales, which is considerably longer than the passage time for a typical 5-mm grating (�25 ps). The expected reflectivity should behave as in the first case above with the

The results indicate that with the Kerr mechanism high reflection efficiencies are feasible for Chalcogenide fibers and semiconductor waveguides; however, silica fibers are more challenging. Furthermore, as the reflection from transient Bragg gratings is dependent on the pumping configuration, e.g., grating length and pump pulse duration, and it is possible to control the signal modulation. In the theory, generation pulses on time scale such as tens of ps, currently not available from fiber lasers, are possible. Other interesting applications such as in-fiber Q-switching are

In the next sections, we will describe experimental results achieved by our group on the subject of transient Bragg gratings in standard silica fibers for switching and modulation applications. We will describe methods to generate them and their

The experimental setup is standard for FBG inscription with the phase mask technique and is shown schematically below (Figure 1). A femtosecond laser (800 nm, 35 fs, 1 KHz) is focused on the fiber core, through a phase mask. The mask period is 2.14 μm, suitable for second-order Bragg gratings at 1550 nm. The fiber to be inscribed is connected to a probe signal source and an Optical Spectrum Analyzer (OSA) to monitor the FBG spectrum or to a fast photodiode (Thorlabs DETO8CFC) to monitor the dynamic effects. The signal source can be a broadband ASE source when characterize permanent FBG inscription or an amplified DFB laser when observing transient, dynamic effect. The probe laser mostly operated in CW mode providing 1 W output power and was operated in pulse mode for Kerr grating

We tried to observe a transient Kerr grating with pulse energies below the inscription threshold in standard SMFs. In these experiments, we monitor the reflection from the grating with a photodiode. We found the permanent inscription threshold to be 160 μJ; thus, our pulse energy is limited below this value. For 100 μJ

35 fs only. The expected reflection from such a grating is extremely weak; the

, which will exist for

pulse energy, we expect grating index modulation of 8 � <sup>10</sup>�<sup>7</sup>

4. Experimental results of femtosecond transient FBGs

�ð Þ <sup>z</sup>þvg <sup>t</sup> <sup>2</sup> v2 g T2 mod � �

(6)

MeffðÞ¼ t q zð Þ ∗ m tð Þ is the convolution of the (transverse) spatial and temporal profiles of the pump pulse. These equations can be solved analytically assuming symmetric Gaussian shape for the pump pulse: q zð Þ¼ <sup>e</sup>ð Þ �z=Lg 2 and m tðÞ¼ <sup>e</sup>ð Þ �t=Tmod <sup>2</sup> :

The complex analytical solution for the backward reflected pulse depends on two time scales: (i) the modulation time Tmod, which, for a Kerr grating, is the pump pulse duration, and (ii) the grating pass time Tpass ¼ L=vg, where L is the grating length and has the form:

$$|A\_b(t,x)| \sim \sqrt{\pi} C \frac{\eta\_0}{4n\_{eff}^2} \Delta n o\_o \sqrt{\frac{T\_{pas}^2 T\_{mod}^2}{T\_{pas}^2 + T\_{mod}^2}} e^{\left\{-\frac{\left(x+\eta\_T t\right)^2}{\eta\_T^2 \left(T\_{pm}^2 + T\_{mod}^2\right)}\right\}}\tag{4}$$

Significant physical insight is achieved under the assumption that Tmod≪Tpass. The solution for the reflected wave is then

$$|A\_b(t, z)| \sim \sqrt{\pi} C \frac{n\_0}{4n\_{eff}^2} \Delta n o\_0 T\_{mod} e^{\left\{-\frac{\left(t + \eta\_f t\right)^2}{n\_f^2 T\_{pm}^2}\right\}}\tag{5}$$

This reveals unique spatial-temporal dependency. The reflected wave has the temporal duration of the longer time scale, and the power is scaled as the shorter time scale. This occurs because the reflections occur from within the grating rather than outside of it. Note that the grating length only influences the temporal duration and not the power efficiency. The reflected efficiency can be approximated to

$$\mathbf{be} \sim \left(\frac{\pi^2}{2\lambda\_{0}n\_0}\Delta n c\_0 T\_p\right)^2 \cdot$$

For a 10�<sup>4</sup> index change and a 50-fs pump duration with a 1500-nm signal wavelength, we get an efficiency of � <sup>4</sup> � <sup>10</sup>�6. Since vgTp � <sup>10</sup> <sup>μ</sup>m, then the minimal length of the grating for this limit to hold is about 0.1 mm. The backward pulse is then at least 500 fs long.

In the opposite case of a very short grating, Tmod ≫ Tpass, as is feasible in semiconductors, the reflected pulse power is

Femtosecond Transient Bragg Gratings DOI: http://dx.doi.org/10.5772/intechopen.84448

modulation amplitude Δn, divided by the effective mode index nneff . These equations are similar to those obtained in [87]; however, they account for non-zero mean index modulations, absorption, imperfect grating contrast, and nonuniform

Fiber Optic Sensing - Principle, Measurement and Applications

An exact solution of Eqs. (1) and (2) is possible only numerically. However, if one assumes uniform pump spot (q ¼ 1) and ignores the spatial derivatives (justified for short modulations during which the pulse is nearly stationary), Eqs. (1) and (2) can be solved analytically—this yields the well-known Rabi solution (see, e.g., [87, 89]). This was shown to give a reasonable accuracy in measurements with spin

Alternatively, Eqs. (1) and (2) can also be solved analytically in the low conversion efficiency limit, without neglecting the spatial derivatives. In this case, the efficiency of the backward pulse generation is given approximately by a convolution of the incoming pulse with meffð Þt , where Meffð Þt is an effective modulation, and the forward wave is (nearly) monochromatic (e.g., for a CW or nanosecond source

MeffðÞ¼ t q zð Þ ∗ m tð Þ is the convolution of the (transverse) spatial and temporal profiles of the pump pulse. These equations can be solved analytically assuming

The complex analytical solution for the backward reflected pulse depends on two time scales: (i) the modulation time Tmod, which, for a Kerr grating, is the pump pulse duration, and (ii) the grating pass time Tpass ¼ L=vg, where L is the grating

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T2 passT<sup>2</sup> mod

vuut <sup>e</sup>

Δnω0Tmode

mod

T2 pass <sup>þ</sup> <sup>T</sup><sup>2</sup>

Significant physical insight is achieved under the assumption that Tmod≪Tpass.

This reveals unique spatial-temporal dependency. The reflected wave has the temporal duration of the longer time scale, and the power is scaled as the shorter time scale. This occurs because the reflections occur from within the grating rather than outside of it. Note that the grating length only influences the temporal duration and not the power efficiency. The reflected efficiency can be approximated to

For a 10�<sup>4</sup> index change and a 50-fs pump duration with a 1500-nm signal wavelength, we get an efficiency of � <sup>4</sup> � <sup>10</sup>�6. Since vgTp � <sup>10</sup> <sup>μ</sup>m, then the minimal length of the grating for this limit to hold is about 0.1 mm. The backward pulse

In the opposite case of a very short grating, Tmod ≫ Tpass, as is feasible in semi-

Δnω<sup>o</sup>

<sup>π</sup> <sup>p</sup> <sup>C</sup> <sup>n</sup><sup>0</sup> 4n<sup>2</sup> eff

Abð Þ¼ <sup>z</sup>; <sup>t</sup> iCvgκq zð Þm tð Þef g 2iδkz Meffð Þ<sup>t</sup> (3)

2 and

� ð Þ <sup>z</sup>þvg <sup>t</sup> <sup>2</sup> v2 <sup>g</sup> <sup>T</sup><sup>2</sup> passþT<sup>2</sup> mod ð Þ � �

�ð Þ <sup>z</sup>þvg <sup>t</sup> <sup>2</sup> v2 g T2 pass � � (4)

(5)

waves [87], at least in this limit, and to lead to envelope reversal [90–92].

symmetric Gaussian shape for the pump pulse: q zð Þ¼ <sup>e</sup>ð Þ �z=Lg

<sup>π</sup> <sup>p</sup> <sup>C</sup> <sup>n</sup><sup>0</sup> 4n<sup>2</sup> eff

<sup>∣</sup>Abð Þ <sup>t</sup>; <sup>z</sup> <sup>∣</sup> � ffiffiffi

pumping (via q zð Þ).

—AfðÞ!t 1):

m tðÞ¼ <sup>e</sup>ð Þ �t=Tmod <sup>2</sup>

be � <sup>π</sup>

28

3 2 <sup>2</sup>λ0n<sup>0</sup> Δnc0Tp � �<sup>2</sup>

is then at least 500 fs long.

length and has the form:

:

<sup>∣</sup>Abð Þ <sup>t</sup>; <sup>z</sup> <sup>∣</sup> � ffiffiffi

The solution for the reflected wave is then

.

conductors, the reflected pulse power is

$$|A\_b(t, z)| \sim \sqrt{\pi} C \frac{n\_0}{4n\_{\text{eff}}^2} \Delta n o\_0 T\_{pas} e^{\left\{-\frac{\left(t + n\_{\text{fl}}t\right)^2}{n\_{\text{fl}}^2 T\_{md}^2}\right\}}\tag{6}$$

Thus, the reflected wave duration and spectrum follow that of the pump pulse.

The above approximations are valid for low reflection efficiency, i.e., undepleted pump. Transient Kerr grating is expected to have a very low efficiency, and an order of magnitude difference between Tpass and Tmod is expected to correspond to the above solutions.

In silica fibers, there is also the possibility for thermal gratings. In this case the index modulation time varies on the microsecond and nanosecond time scales, which is considerably longer than the passage time for a typical 5-mm grating (�25 ps). The expected reflectivity should behave as in the first case above with the exception of non-Gaussian response.

The results indicate that with the Kerr mechanism high reflection efficiencies are feasible for Chalcogenide fibers and semiconductor waveguides; however, silica fibers are more challenging. Furthermore, as the reflection from transient Bragg gratings is dependent on the pumping configuration, e.g., grating length and pump pulse duration, and it is possible to control the signal modulation. In the theory, generation pulses on time scale such as tens of ps, currently not available from fiber lasers, are possible. Other interesting applications such as in-fiber Q-switching are also feasible.

In the next sections, we will describe experimental results achieved by our group on the subject of transient Bragg gratings in standard silica fibers for switching and modulation applications. We will describe methods to generate them and their results.
