Realisation of Pressure Sensor using one Dimensional Indium Arsenide (InAs) Based Photonic Waveguide in 3 Communication Windows


 Indium arsenide (InAs) based one dimensional photonic crystal waveguide is cautiously considered in three optical communication windows. Here, the emerging transmitted signal from one dimensional photonic structure is determined with the consideration of five types of losses (diffraction loss, reflection loss, absorption loss, propagation loss, polarisation loss). Further, the transmitted signal is obtained with respect to pressure, which ranges from 0 GPa to 5 GPa for different lattice constant of photonic structure (100 nm, 120 nm, 140 nm). Simulation upshots revealed that indium arsenide semiconductor based photonic waveguide shows an excellent outcome for pressure sensor in the three optical windows as well as different waveguide lengths.


Introduction
In recent times, group of III-IV compound semiconductors have exhibited an outstanding performance in the design of optoelectronic devices for their unique optical characteristics with respect to low noise, high stability, and high breakdown voltage [1]. Moreover, Indium Arsenide (InAs) is an excellent material, which shows little unusual direct band gap properties that become widely applied in the construction of different efficient photonic devices. For example, photovoltaic infrared detector, photochemical sensors, fast transistors, and solar cells so on [2]. Moreover, an optical characteristics of such photonic material is useful for band gap investigation [3]. As far as a literature review of the photonic structure is concerned, a good number of research papers are previously published on semiconductor waveguides [4]. Aside this, a few number of articles are found for sensing applications by photonic waveguide structure [5][6][7][8]. For example; reference [5] investigates the sucrose concentration in metamaterial by deploying plane wave expansion technique, while in the reference [6], authors describe the investigation of polymer based optical waveguide pertaining to the temperature. Again in the reference [7][8], authors point out various losses in photonic waveguide with respect to the variety of sensing parameters such as porosity, temperature, concentration etc for realising competent photonic integrated circuit. Experimental demonstration of one dimensional strain sensor and its application have been discussed [9]. Polymer based 1 D photonic crystal have been investigated in the reference [10]. Even though reference [6][7][8][9][10] provides the notion on different sensor, reference [11][12][13][14][15][16][17][18] explains the different pressure sensors and their outcomes, which is indicated in the tabular form ( Aside this, such investigation is made at three optical communication windows to fetch the pressure on the photonic structures. The applied pressure plays a vital role in the photonic crystal waveguide for managing the various optical properties of compound semiconductor material. To compute the transmitted intensity of indium arsenide based waveguide structure, the different type of losses play a crucial role corresponding to different pressure and lattice spacing in the three optical communication windows, which can be used a pressure sensor. Here, three optical communication windows have been considered or each pressure. Focusing on the optical windows, we know that window considers from 800-900 nm with signal loss of 4dB/km. The second optical window is occupied at 1310 nm also known as O-band, which signal loss occurs at 0.5dB/km. The third optical window is considered at 1550 nm also known as C-band, which provides the loss of 0.2dB/km and the 1550 nm wavelength is chosen for long distance applications due to the lowest loss accessible at this wavelength than other.

Structure Analysis
We have proposed a 1-D semiconductor (InAs) based waveguide photonic structure to realise the pressure (from 0 GPa to 5 GPa) sensor with respect to the output transmitted intensity, which is indicated in figure 1(a).  Here we compared different waveguide lengths for 3 optical communication windows such as 850 nm, 1310 nm and 1550 nm. For example, there are 3 different types waveguide has been considered, which are represented in figure 1(b). It is observed that the waveguide length of InAs 150 nm, 180 nm and 210 nm for type-I, type-II and type-III respectively. The width of each layer is chosen as 50 nm, 60 nm and 70 nm for type-I, type-II and type-III respectively. Further, we observed (from figure-1) that the signal of 850 nm, 1310 nm and 1550 nm impinges the aforementioned photonic structure separately, subsequently incident signal attenuates because of suffering from different losses such as diffraction loss, reflection loss, absorption loss, propagation loss, polarisation loss etc. After suffering from these losses, the signals collected at the output end, where transmitted intensity is computed with the term of photo detector.
As far as practical feasibility of proposed photonic crystal is concerned, reference [20][21][22][23][24][25] states the different research with respect to the experimental work. For example; reference [20] provides an idea of fabrication of titanium metal oxide based one dimensional photonic structure for calorimetric sensor which measures the volatile organic compound and relative humidity. Similarly in the reference [21], authors fabricate one dimensional periodic nanostructure to investigate the various chemical components. Further fabrication of erbium chloride silicate nanowire based one dimensional photonic crystal is discussed in the reference [22]. In the reference [23], authors characterize one dimensional multilayer structure through atomic force microscopy, ellipsometry and visible-near IR spectroscopy. Aside these, reference [24] shows a method to fabricate porous silicon (pSi) based onedimensional photonic crystal by photoacoustics for radiometry application. Again in the reference [25], authors use physical vapor oblique angle deposition technique to design TiO2-SiO2 based one dimensional photonic crystal structure. Since the present structure is similar to the reference [20][21][22][23][24][25], the InAs based one dimensional could be fabricated for computing the amount of the pressure.

Mathematical equations
The current research paper treats with different type losses to compute the amount of pressure impacted on the photonic structure. These losses are diffraction loss, reflection loss, absorption loss, propagation loss and polarisation loss, which is discussed here.

The equation for absorption loss can be represented in terms of absorption coefficient as
Where, β1, β2, t1 and t2 denote the absorption coefficient of odd, even layer, the thickness of odd and even layer InAs photonic structure respectively.
In the same way, the reflectance is calculated with the help of Helmholtz equation, which is represented by The result of the equation is Moreover, the electric field intensity is calculated through proper boundary condition. Ultimately the reflectance would be the diffraction loss is articulated as Where n, d and λ denotes the refractive index of material, which varies with pressure, the total thickness of the proposed one dimensional structure, and incident wavelength respectively Again the polarisation loss is written as Where , n and a are the input wavelength, refractive index, and the lattice constant respectively.
At last, the transmitted intensity can be determined relating to the different losses as Transmitted intensity (Tr) =Transmitted efficiency (Teff) × Input signal (Ii) Where transmitted efficiency (Teff) Where A, R, Ldif, Lpro, Lpol are absorption, reflection, diffraction, propagation, and polarisation losses respectively.

Results Discussions
From equation (8) and (9), it is found that transmitted intensity depends on the various losses with respect to three optical windows.

Absorption loss
The absorbance relies on both absorption coefficient and thickness of even and odd layer of 1D InAs based photonic structure. The absorption coefficient of indium arsenide material is found from the literature pertaining to all three communication windows. Putting the values in equation (4), it is found the zero loss with the different waveguide lengths as well as 3 optical windows.

Reflection loss
The reflectance loss of indium arsenide based one dimensional photonic structure with respect to

Polarisation and diffraction
Polarisation and diffraction is calculated for each waveguide length of 150 nm, 180 nm, 210 nm and at all the wavelengths (850 nm, 1310 nm and 1550 nm) of indium arsenide waveguide photonic structure with the help of equations (5) and (6)

Propagation loss
The propagation loss efficiency is calculated using the equation (7), which depends on different parameters such as lattice spacing, input signal and the applied pressure. Using the values of the aforementioned parameters in the equation (7), the deviation of propagation loss efficiency with respect to the pressure is computed for all lengths as well as the input signal. The results are represented in figure 5. shows that propagation loss is very less compared to other loss.

Calculation of transmitted intensity
Ultimately, the transmitted intensity for all input signals would be computed with the help of equation (8)(9). The output upshots relating to all selected wavelengths are represented in figure 6. The pressure is taken x axes and transmitted intensity is taken y axes, which is shown in figure 6.

Conclusions
In this research, the amount of pressure in the indium arsenide photonic materials is computed using one dimensional photonic structure. Here, different type of losses (diffraction loss, reflection loss, absorption loss, propagation loss, polarisation loss) are thoroughly analysed during the computation of transmitted intensities It is realised that amount of pressure in indium arsenide is determined by knowing the amount of transmitted intensities at the output end, which shows that InAs material is a good candidate for realisation of pressure sensor.