**3. Photonic integrated interferometers for chemical and biological sensing**

Actually, due to the relatively simple design, the Mach-Zehnder Interferometer, (MZI), is the most adequate configuration for the monolithic fabrication of integrated optics microsensors. In fact, this structure is particularly suitable for sensing problems as it can combine high resolution and high sensitivity performances together with an excellent insensitiveness on mechanical vibration or other environmental effects. Many applications of optical sensors based on MZ interferometer have been reported in literature, both in the case of already cited Fourier Transform, (FT), and spectroscopy. In the case of Bio-chemical analyses, the phase shift between the electromagnetic waves propagating in the two arms of the MZI is generated by the adhesion of the analyte molecules on the surface of one (sensing) arm that has been left uncovered by the cladding protecting the whole device from the environment [4–6]. The working principle, in this case, is based on the optical path variation, *Δp = ΔnL,* generated by the change of the refractive index in the uncovered sensing arm, having a length *L*. A relatively limiting factor of this instrumental architecture is originated from the

### *Integrated Optics and Photonics for Optical Interferometric Sensing DOI: http://dx.doi.org/10.5772/intechopen.103770*

need for a relatively large value of the sensing interferometric arm *L*, to have a good sensitivity of the device. Moreover, to obtain the best performances of an MZI in terms of sensitivity, requires working with monochromatic light, for this reason, it has been suggested [6] to design a hybrid detection architecture, specifically oriented to biochemical applications, allowing both high sensitivity and a high selectivity in the case of multi-analyte detection. This performance can be obtained by integrating an MZ interferometer with a spectrum analyser and using a multi-wavelength 'white' light source to distinguish the spectral 'signature' of the different species. **Figure 4** is redrawn the device originally suggested in Ref. [7].

As previously anticipated, when the monolithic interferometer is fabricated on Electro-optic material, typically LiNbO3, the phase shift can be generated by exploiting the Pockels effect to modify the refractive index in one of the two arms, through the application of an electric field using two electrodes placed in a suitable position close to the optical waveguide (see **Figure 3(b)**).

If a continuous variation of the phase shift is generated, it is realised a so-called scanning interferometer and the whole set of intensity data measured as a function of the phase shifts gives rise to the so-called Interferogram. The Fourier Transform of the Interferogram gives rise to the frequency spectrum of the light containing the spectral information on the element to be detected [3, 4]. In the traditional instrument of **Figure 3(a)** the scanning effect is usually produced by uniformly moving one of the two mirrors giving rise to a corresponding optical path variation in one arm of the interferometer generating the desired phase shift variation. On the contrary, in an integrated microdevice, the scanning effect can be simply obtained by applying a voltage ramp to the electrodes (see **Figure 3(b)**), without the need for moving parts.

The detailed description of the Fourier Transform Spectroscopy principle and the detailed mathematical considerations have been extensively reported in a number of articles and textbooks [2, 3, 6]. In this work, we only report a concise description of the operation system of a scanning integrated MZI (see **Figure 3(b)**).

In order to achieve good spectral resolution, the scanning Interferometer needs phase shifts suitable to produce interferograms of many tens of interference fringes. This involves the need that the substrate material has an electro-optical coefficient as high as possible. In our case, the output intensity is monitored as a function of the optical path variation induced by a suitable variable electric field, applied to the arms. The interferometric output *Iout* represents the Fourier Transform of the input spectral distribution *I(k)* and is given by the following relationship:

*Hybrid MZI with a sensing pad in one arm integrated with a wavelength dispersive system [7].*

$$I\_{out}(\Delta p) = \int I(k) \left[ \mathbb{1} + \cos \left( 2\pi \Delta p(k) \right) \right] dk,\tag{1}$$

where k = 1/λ is the wavenumber of the incident radiation, and Δp is the optical path difference.

In our case, the optical path difference can be expressed by the linear relationship

$$
\Delta p = L \,\Delta n,\tag{2}
$$

where: L is the arm length, and

$$
\Delta n = r\_{\mathfrak{P}\mathfrak{J}} \cdot n\_{\mathfrak{e}}^{\mathfrak{J}} \cdot \operatorname{E}/\mathfrak{Z},\tag{3}
$$

where *r33* is the linear electro-optic coefficient along the optical c-axis, *ne* is the LiNbO3 extraordinary refractive index when x or y propagation is considered. Finally, *E* is the electric field applied to the driving electrodes.

From Eq. (1) it appears that in the case of monochromatic light, the intensities recorded by the detector, (i.e. the Interferogram), has a sinusoidal shape. In the real case, we deal with quasi-monochromatic light and the MZI output are somehow distorted as reported in **Figure 5** in the case of the incident light generated by a diode laser emitting in a narrow window around 635 nm.

When dealing with a wideband ('white') light, the conceptual behaviour is the same. Even if the interferogram is remarkably modified and several corrections must be applied to the over-simplified scheme previously reported [3], it is always possible to perform the spectrometric analysis of the incoming light. **Figure 6** reports an example of a real case of E131 dye (Patent Blue) detection with an integrated MZI.

More recently, a new generation of integrated architectures has been suggested for spectroscopic analyses, in particular the integrated monolithic version of the Young interferometer (YI) and the integrated monolithic version of the Michelson's ('Echelle') Diffractometer. **Figure 7** reports the sketch of the Young geometry in the integrated version. In this case, the waveguides' geometries are geometrically arranged like in the MZI, the only difference is at the detection side that is here based on an arrayed detector.

A more recent architecture has been realised on the basis of Michelson's echelle grating that, when fabricated with electro-optic material (LiNbO3), becomes a Programmable Micro diffractive Grating (PMDG) extending the range of this kind of micro-optical device to an extremely large field of applications. **Figure 8** reports the

#### **Figure 5.**

*(a) Raw signal detected during the scanning cycle, (interferogram) and (b) the Fourier transform of the interferogram, giving the wavelength spectrum of the incident light.*

*Integrated Optics and Photonics for Optical Interferometric Sensing DOI: http://dx.doi.org/10.5772/intechopen.103770*

**Figure 6.** *Example of densitometry performed with an IO micro-interferometer on an E131 dye solution.*

#### **Figure 7.**

*Integrated version of the young interferometric geometry the far-field geometry for the detection of the modifications of the interference pattern, originated by the analyte adhesion on the sensing pad in one of the two arms.*

comparison between the original static diffractive grating proposed by Michelson and the integrated PMDG, fabricated for high sensitivity detection systems based on the correlation spectroscopy technique. In Michelson's original device, the wavefront portions emerging from the different steps crosses different glass thicknesses, so the different optical paths acquire different phase shift as a function of the glass thickness crossed. The different wavefront emerging from each step interfere with each other giving rise to a far-field diffraction pattern that can be observed in far-field conditions on screen S, of **Figure 8(a)**.

If the integrated waveguides array sketched in **Figure 8(b)** is fabricated on electrooptical substrate, it can have the same behaviour as the Michelson's echelle device.

#### **Figure 8.**

*(a) Michelson's echelle diffraction grating. (b) Integrated programmable diffractive grating (PMDG) based on LiNbO3 substrate.*

In fact, each waveguide may have a different refractive index as a function of the electric field applied to the electrodes so, each portion of the wavefront emerging from each waveguide has a different phase and, in far-field conditions, they interfere with each other generating a diffraction pattern like in the case of Michelson's device.

The great difference between the two cases is that the device shown in **Figure 8(a)** is static and the diffractive properties are fixed by the construction parameters, whereas the PMDG device, the diffractive properties are programmable simply by changing the voltage applied at each electrode. This feature enormously expands the field of the applications of this Integrated Optics microdevice that can go far beyond the sensing systems arriving to have implications in many strategic areas such as optical fibre transmission, cryptography, quantum optic devices, optical computing, etc.

#### **3.1 Holographic correlation spectroscopy with PMDG device**

Correlation spectroscopy architectures have been widely studied for at least 2030 years and are now argument described in the textbooks [8–10]. Therefore, in the present work, we will not enter in detail in the presentation of this technique and we will take as a reference the 'holographic correlation spectroscopy' architecture [11] treating in detail the subject of correlation spectroscopy in connection with the use of computer-generated optical elements. In particular, we will consider the conclusion of reference [11] when discussing the use of the PMDG to create synthetic spectra of several compounds, some of which are of interest for Environmental control, Food production and transportation, Bio-Chemical hazard, safety and security problems.

In particular, due to its programmability, the device can generate, at least in principle, synthetic spectra of almost any analyte of interest. The PMDG may have hundreds of diffractive elements in very small overall dimensions and, with the suitable software, it can generate a digital library containing the synthetic spectra of plenty of molecules. When the PMDG is exploited in this architecture, the sensing instrument described here can be considered as an example of a new sensor concept, in fact, in traditional instruments, the optical spectrum processing is determined by the correlation between the light transmitted through an unknown sample and the light transmitted through a reference cell containing a known mixture of the chemical molecule to be detected. In this case, due to the PMDG properties, the optical

#### *Integrated Optics and Photonics for Optical Interferometric Sensing DOI: http://dx.doi.org/10.5772/intechopen.103770*

spectrum processing is based only on the correlation between the light transmission through an unknown sample and the data of a digital library. This trait greatly increases the sensor flexibility if compared with other recent instruments in which the spectrally dispersed light is delivered onto a coded mask to provide spectral filtering of the sample spectrum light [11].

In conclusion, this new sensor is particularly suited for safety and security applications because it avoids the use of a reference cell containing reference materials that can be difficult and hazardous to handle, in the case of detection of dangerous, poisoning, or explosive targets. Furthermore, it allows great flexibility if compared with the coded mask filtering described in Ref. 11, because the number of molecules that can be detected is now only limited by the wavelength transmission window of the electro-optic material used as a substrate for the PMDG device and by the sensitivity range of the detector used. Finally, exploiting during the data collection the dark-field correlation technique, it can be obtained a remarkable increase in the sensitivity of the whole system. In fact, by using shrewdness to construct the reference synthetic spectrum to be the complement of the target transmission spectrum, the signal-to-noise ratio becomes very large. Actually, with this shrewdness, all the wavelengths different from those matching the absorbance of the target, are blocked creating a programmable filter that allows the transmission of only a very small fraction of the incident light in correspondence of the desired wavelengths exclusively. So, when the spectral absorption lines match the planned transmission complement it is obtained a very large signal-to-noise ratio, allowing extremely high sensitivity detection.

The architecture of 'holographic correlation spectroscopy' is schematically reproduced in **Figure 9**, is particularly simple and takes advantage of the intrinsic PMDG flexibility and reconfigurability features. In the geometry of **Figure 9**, a broadband 'white' light coming from an external source crosses, (one or several times), a sample cell containing the analyte to be investigated. Then the radiation crosses the PMDG optical element, placed in transmission architecture. In the present case, the external broadband light source could cover the whole transparency range of the LiNbO3 base material ranging from 0.450 μm to 5.5 μm.

The wideband radiation coming from the external source is then transmitted through the PMDG device and precisely defined by the ensemble of the programmed driving electrical potentials applied to the different waveguides. The degree of correlation between the sample cell spectrum, (unknown), and the synthetic spectrum

#### **Figure 9.**

*Schematic of a holographic correlation spectrometer set-up including the PMDG which acts as the reference cell. The light coming from a broadband source passes through the measurement cell which contains the unknown analyte. The diffraction pattern generated by the PMDG at the diffraction angle* ϑd *is perfectly matched to the spectrum of the target compound within the measurement cell.*

programmed through the reference (PMDG) cell is then measured on a photodetector placed at a suitable diffraction angle *ϑd*.

To increase the sensitivity and the selectivity of the set-up, the usual techniques can be adopted, in particular: (i) Lock-in techniques are applied by modulating the transmission spectrum through the PMDG and recording the detector output at the same modulation frequency or/and (ii) Darkfield technique, i.e. applying a suitable map of the driving electrical potentials, the PMDG can be configured to synthetize the complement of the real target to be analysed, so obtaining a much larger signal-tonoise ratio and a consequent remarkable increase of both sensitivity and selectivity of the detection system.

#### **3.2 Synthetic spectra generation mathematical approach**

The key point in the programming of a waveguide-based PMDG for a synthetic spectra generation is the determination of a driving voltage pattern able to introduce the required phase shifts on each of the M waveguides, (Typically *M* can range from 50 to 200 waveguide/cm). In this way, the electromagnetic radiation emerging from the output face of the grating will generate the desired synthetic spectrum at a predetermined diffraction angle *ϑd*.

In this section, a mathematical framework for the specific case in which the functional elements are electro-optical waveguides is presented and discussed [12].

Under the hypothesis of working in the Fraunhofer approximation, the diffracted field at an angle *ϑd*, (see **Figure 9**) can be described by the following Fouriertransform integral:

$$U(\theta\_d, \lambda) = \int\_{-\infty}^{+\infty} \int\_{\lambda}^{\lambda\_2} \frac{\mathbf{C}A}{\lambda} U'(\mathbf{x}, \lambda) \exp\left(-\frac{i2\pi \sin\left(\theta\_d\right)}{\lambda}\right) d\lambda d\mathbf{x} \tag{4}$$

where *C* is a constant of proportionality, *A* is the amplitude of the incident wave, supposed to be independent of the wavelength *λ* and *x* is the spatial transverse coordinate of the PMDG output facet whereas, *λ<sup>1</sup>* and *λ<sup>2</sup>* are the lower and upper limit of the spectral band of interest, respectively (**Figure 10**).

In Eq. (4), *U*<sup>0</sup> *(x, λ)* is the near-field distribution emerging from the output facet of the PMDG. For a grating with *M* waveguides of width *W* and periodicity *P*, this distribution can be described by the following expression:

**Figure 10.** *Framework for the solution of the PMDG diffraction problem.* *Integrated Optics and Photonics for Optical Interferometric Sensing DOI: http://dx.doi.org/10.5772/intechopen.103770*

where *L* is the electrode length, *d* is the device thickness, *Vm* is the voltage applied to the *m-th* waveguide and *γ* is a constant depending both on the electrooptical characteristics and the crystallographic orientation of the substrate. In Eq. (5), the first exponential term of the summation describes the phase shift induced on the *m-th* waveguide by the local driving voltage *Vm*, whereas the second exponential term describes the mode profile emerging from each waveguide that, as a first approximation, is supposed to follow a Gaussian shape. Eq. (5) clearly shows how the local phase of the field emitted by the grating and, consequently, the diffracted pattern at angle *ϑd*, can be controlled through the application of a suitable set of *M* potentials *Vm*=1, … , M. The PMDG design and programming procedure is therefore reduced to the determination of a suitable voltage pattern, which minimises the difference between the target spectrum of interest and the synthetic one calculated with Eqs. (4) and (5). The difference between the target and the synthetic spectra can be quantified by introducing an error function ℇ of the form:

$$\mathfrak{E} = \sqrt{\sum\_{\mathbf{n}=1}^{N} (\mathbf{I\_n}^{\mathrm{d}} - \mathbf{I\_n})^2} \tag{6}$$

where In = |U(λn)|<sup>2</sup> is the intensity of the target spectrum and I*<sup>n</sup> <sup>d</sup>* is the diffracted intensity spectrum at the considered diffraction angle *ϑd*, both evaluated over the same set of *N* wavelength within the spectral range of interest. Once this error function has been defined, the PMDG programming procedure reduces to the optimization problem of finding the minimum of ℇ with respect to the control parameters (V1, V2, … VM). By setting *K* = *Lγ/d* we can write, Dm =*K Vm* and the new variables (D1, D2, … DM) have the dimension of a length, so each *Dm* value considers the optical path differences, the different waveguides.

This is physically equivalent to introducing a programmable phase-shift offset in the first term of Eq. (5). Then, the actual voltage pattern to apply to the different electrodes of the PMDG is calculated from the Dm values, resulting from the optimization routine, once the technological parameters have been defined.

For the solution of the multivariable optimization problem, several numerical approaches have been proposed and implemented so far, in particular, iterative Fourier Transform phase-retrieval algorithm [12], genetic algorithms [11] or gradient-based multi-variable minimization routines [13]. The Nelder–Mead Simplex Method [14] demonstrates to be extremely effective providing a monotonic and rapid convergence to the minimum of the error function ℇ. Moreover, the numerical implementation of this method is available in the most common scientific computation libraries.

An example of synthetic spectrum created with the numerical method of reference [14] is reported in **Figure 11** where a portion of the COCl2 spectrum has been reconstructed in the hypothesis of a PMDG having *M* = 50 waveguides *W* = 8 μm and pitch *P* = 80 μm. The experimental absorbance spectrum is shown in **Figure 11(a)**, whereas the calculated synthetic one at the optimal diffraction angle *ϑ<sup>d</sup>* of 3.75 degrees is presented in the (b) panel of the same Figure. The (c) panel shows the optimised parameters set Dm calculated with the numerical routine that, once introduced in (2), generates the synthetic spectrum displayed in (b). The agreement between the two spectra is remarkable over the entire wavelength range of interest, confirming both the effectiveness of the PMDG device and of the numerical optimization routine adopted to retrieve the programming pattern.

**Figure 11.**

*(a) Experimental absorbance spectrum of gaseous phosgene (target spectrum T) and (b) PMDG-synthetized spectrum of the same analyte (synthetic spectrum S). (c) Values of the optimised Dm (m = 1. .,50) control parameters.*
