To calculate the evanescent field by the gas

To calculate the evanescent field by the gas samples the Beer-Lambert law can be used. The relationship between optical intensity and gas concentration can be determined as: The absorbance of the sample can be defined as: Here, αm is the metalloproteinase coefficient of the gas being detected; l is the length of the PCF; c is the gas concentration. Output light intensities with and without the presence of gas are I and I0 respectively. Relative sensitivity r can be defined as:where ns is the refractive index of gas species considered 1; Re[neff] is the real part of the effective mode index. Here f is the fraction of total power and hole power which can be defined as: Here, Ex, Ey, Hx and Hy are the transverse electric and magnetic field. A circular perfectly matched layer (PML) is used to fulfill the boundary condition which avoids possible reflection at the boundary. By this term confinement loss or leakage loss can be calculated by the imaginary part of the effective refractive index. The confinement loss or leakage loss can be calculated by the following equation:where, K0 is the wavenumber and Im [neff] is the imaginary part of the effective refractive index. The difference between refractive index of x-polarization and y-polarization is called the birefringence which can be defined as: This property leads to periodic power exchange between two orthogonal components. This period is beat length which can be determined by: The single mode response can be determined by the V-parameter which is defined by: Here, nco and ncl are the refractive indexes of core and cladding. V-parameter (Veff) of a PCF must be less than or equal 2.405 to be a single mode fiber. The effective area [33] of a PCF can be determined by the following equation: High optical power density is provided by a small effective area for which the nonlinear effect to be significant. The nonlinear coefficient [34] can be examined by the following: Here, n2 is the nonlinear refractive index. Splice loss occurs during the splicing of the photonic crystal fiber and the single mode fiber. Splice loss can be calculated by the following equation: Here, WSMF and WE-PCF are the mode field diameters of the single mode fiber and the proposed E-PCF respectively. The background material was set pure silica whose refractive index changes with the variation of the wavelength according to the Sellmeier equation. Here, n(λ) is the refractive index of silica which varies with the operating wavelength and B and C are Sellmeier coefficients.
Results and discussion The mode field pattern along the x-polarization and y-polarization of the proposed E-PCF has been shown in Fig. 2. From the figure, it can be demonstrated that the mode field is tightly confined to the core region. So the leakage loss will be very low. Fig. 3 depicts the comparisons of sensitivity and confinement loss of the proposed PCF with prior PCF1 [24], PCF2 [23] and PCF3 [35] respectively. The proposed PCF for optimized parameters shows higher sensitivity and lower confinement loss comparing to prior PCFs. Optimizing the parameters, sensitivity and confinement loss coefficients of 53.07% and 3.21×10dB/m are obtained at 1.33μm wavelength for x-polarized mode respectively. To optimize the different parameters a simple technique has been followed on the proposed E-PCF. To calculate the confinement loss efficiently, proposed structure thickness is fixed at 10% of the fiber radius by PML test. But no significant effect on relative sensitivity has been noticed for the proposed thickness about 1.5μm. By selecting a fine mode of mesh size, the simulation work has been completed using 4.2 version COMSOL Multiphysics. Convergence error, defective modes in PCF with compactly supported perturbations, is very low about 2.71×10%. First, air filling ratio (d/Λ) is varied to 0.447, 0.460 and 0.475μm keeping other parameters constant. From Fig. 4 it is clearly depicted that sensitivity increases as the air filling ratio increases, for example, at 1.33μm wavelength, the sensitivity is 43.71%, 48.23%, 53.07%; the confinement loss is 1.35×10dB/m, 7.37×10dB/m, 3.21×10dB/m and the birefringence is 1.23×10, 5.31×10, 6.9×10 for d/Λ=0.475, 0.460 and 0.447μm respectively. So it is also clearly visualized that the proposed PCF shows higher sensitivity as well as higher birefringence for d/Λ=0.475μm shown in Fig. 6 (a). Simultaneously the higher birefringence and sensitivity makes a fiber as a potential candidate to detect colorless and noxious gasses as well as environment pollution monitoring [13]. Now d/Λ=0.475μm is selected for further investigation process.