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We have demonstrated and analyzed the methane gas sensor based on octagonal cladding and hexagonal hybrid porous core photonic crystal fiber (HPC-PCF) for gas detection purpose. The proposed design of HPC-PCF has been numerically investigated by COMSOL Multiphysics software through utilizing the full vectorial finite element method (FEM). The optical characteristics of HPC-PCF as well as confinement loss, relative sensitivity and refractive index, effective area, nonlinearity and numerical aperture are optimized properly by changing the geometrical parameters as well as air filling ratio, air hole diameter, pitch constant of cladding and porosity of the core. In this simulation work, we have achieved optimum relative sensitivity of 21.2%, and confinement loss of 0.000025 dB/m at 3 μm pitch, 0.7 air filling ratio of the cladding and 29% porosity of the core for 3.5 μm absorption wavelength of CH
_{4} gas. This proposed design of HPC-PCF will keep exclusive contribution for detecting the CH
_{4} gas accurately.

Conventional optical fiber technology provides greater bandwidth services and excellent data accuracy than copper wire in telecommunication systems. An application of optical fiber is fixed due to its geometrical restrictions and it is typically used in telecommunication systems. But we can overcome the application restrictions of optical fiber through re-structuring the geometrical model. One of the re-structuring models of optical fiber is called the photonic crystal fiber (PCF). The PCF having microstructured array air holes regularly spreads across the whole length of the fiber [_{4} gas. For the purely silica material, interaction happens between optical signal and CH_{4} gas at 3.5 µm absorption wavelength of CH_{4} gas. We can use various polymer materials as background materials instead of silica material like Cyclo-Olefin Polymer (COP), polyethylene, polymethyl-methacrylate (PMMA), Cyclic Olefin Copolymer (COC), Teflon and so on. In that case, HPC-PCF will operate in THz frequencies. In fact, the HPC-PCF have many properties like relative sensitivity [_{4} gas than other values. The HPC-PCF can be used successfully as a sensing device through accomplishing the whole fabrication process properly. Most well-known fabrication processes of PCF are 3D-printing, sol-gel, capillary stacking, stack and drilling, extrusion and slurry casting. Among them, extrusion is the most suitable fabrication process for HPC-PCF design. The prime dream of proposed design of HPC-PCF is to improve relative sensitivity and decrease confinement loss at minimum level that will sense CH_{4} gas accurately.

_{4} gas through utilizing the HPC-PCF. The CH_{4} gas sensing system is made up of miscellaneous elements as well as vacuum pump, gas cylinder, gas valve, laser source, optical spectrum analyzer (OSA) and chamber unit. It is seen from _{4} gas sensing mechanism of HPC-PCF is that an interaction occurs between CH_{4} gas and optical signal at the 3.5 µm absorption wavelength peak of CH_{4} gas into the chamber unit. In that case, gas constituents absorb the energy of photon of optical signal and the intensity of optical signal varies with respect to absence of gas. This whole matter is clearly explained by Beer Lambert Law (BLL) in the later part of this manuscript.

_{4} gas. The HPC-PCF shows feature like hollow core PCF and confines the optical signal into the core by utilizing the mechanism of PBG effects. This phenomenon is clearly described in the later section of this manuscript.

The confinement loss is the significant optical characteristic of HPC-PCF. It is dominated by air hole shape, number, background material, thickness of perfectly match layer (PML), wavelength and etc. When optical signal penetrates into core and then goes in cladding region, this matter is known as confinement loss. The confinement loss of HPC-PCF can be determined by following equation

L c = 8.686 k 0 I m [ n e f f ] (1)

where k_{0} is known as wave number for free-space and I m [ n e f f ] is known as imaginary part of the effective mode index. The relative sensitivity means that the interaction between the light and gas components at the precise wavelength of optical signal. Relative sensitivity is integrated with absorption coefficient of the gas of Beer-Lambert law. The Beer Lambert law can be expressed by the following equation

I ( λ ) = I 0 ( λ ) exp ( − r θ m l c ) (2)

where I(λ) and I_{0}(λ) are known as amplitudes of optical signal with and without gas, r is known as relative sensitivity, a_{m} known as absorption coefficient, l_{e} is known as length of channel and is known as absorption wavelength of CH_{4} gas. The relative sensitivity of HPC-PCF can be expressed by the following equation

r = n r n e f f (3)

where n_{r} is identified as refractive index and n_{eff} is identified as effective refractive index. The coefficient f is defined as the optical power available in air holes to total optical power of the HPC-PCF which can be mathematically expressed by the following equation

f = ∫ Hole ( E x H y – E y H x ) d x d y ∫ Total ( E x H y − E y H x ) d x d y (4)

where E_{x}, E_{y}, are known as transverse electric field and H_{y}, H_{y} are known as longitudinal magnetic field respectively. The refractive index is the ratio of length of wavelength of optical signal in the air to the length of wavelength of optical signal in a medium. Mathematically, it can be expressed by the following equation

n = λ 0 λ (5)

where n is the refractive index, λ_{0} is the length of wavelength in air and λ is the length of wavelength in a medium. The porosity is the geometric property of the HPC-PCF. Typically, it is the ratio of the total air hole area of the core and to the total cross sectional area of the core which can be expressed by the following equation

P s = a A × 100 % (6)

where a is the total cross section area of air holes into core area and A is total cross section area of the core respectively. The area which is used by optical signal in the core while propagation in waveguide is known as effective area of HPC-PCF. The effective area of the core of HPC-PCF can be expressed by the following equation

A e f f = [ ∫ F ( x ) x d x ] 2 [ ∫ F 2 ( x ) d x ] 2 (7)

where A_{eff} is identified as effective area of the core and F ( x ) = | E x | 2 is identified as transverse electric field distribution in the core area of HPC-PCF. Nonlinearity is an important feature of HPC-PCF which is inversely proportional to effective area of the core. The nonlinearity of HPC-PCF can be demonstrated by the following equation

N L = 2 π n 2 λ A e f f (8)

where NL is known as nonlinearity, n_{2} is known as refractive index, λ is known as length of wavelength and A_{eff} is known as effective area of the core of HPC-PCF. The higher value of numerical aperture is more important to operate HPC-PCF as a sensor and it can be achieved effortlessly when the refractive index difference between the core and the cladding is large. The numerical aperture of HPC-PCF can be determined by the following equation

N A = 1 1 + π A e f f f 2 c 2 (9)

where f is referred to as frequency of optical signal, c is referred to as velocity of optical signal and A_{eff} is referred to as effective area of the core of HPC-PCF.

from the core, more interaction occurs in core between optical signal and gas elements and this causes higher relative sensitivity.

The characteristics of effective refractive index as a function of wavelength at diverse porosities of the core of HPC-PCF are shown in

pitch of the cladding provides minimum effective area than maximum pitch. This statement is true because geometrically when the pitch of the cladding decreases, area of the core decreases automatically. On the other hand, when the pitch of the cladding increases, area of the core also increases. Note that the effective area is the major part of the total core area. So the lower pitch of the cladding provides the lower effective area than the higher pitch.

In

considered for observing the variations of confinement loss with respect to each porosity value for the 3.5 µm absorption wavelength of CH_{4} gas at 3.0 µm pitch and 0.7 air filling fraction of the cladding. It is seen from _{4} gas. This result is reasonable because minimum porosity of 22% of the core creates maximum refractive index difference between core and the cladding than the maximum porosity of 29%. In that case, minimum optical signal penetrates from the core and goes in cladding region that happens minimum confinement loss. In _{4} gas at 3.0 µm pitch and 0.7 air filling fraction of the cladding. It is observed from

maximum amount of gas. In that case, more interaction happens between gas elements and the light for the same absorption wavelength of CH_{4} gas. So in _{4} gas of HPC-PCF.

We have proposed and analyzed the CH_{4} gas sensor based on octagonal cladding with circular air holes and hexagonal core with rectangular and circular air holes of HPC-PCF. The whole design and simulation work of HPC-PCF have been accomplished by COMSOL Multiphysics software through using full vectorial FEM. In this design of HPC-PCF, 2.80 µm, 2.85 µm, 2.90 µm and 3.0 µm pitches of the cladding and 22%, 24%, 25%, 26%, 28% and 29% porosities of the core are considered for optimizing the HPC-PCF. In the end, we have achieved optimum confinement loss of 0.000025 dB/m and relative sensitivity of 21.2% for 3.0 µm pitch, 0.7 air filling ratio of the cladding and 29% porosity of the core at 3.5 µm absorption wavelength of CH_{4} gas. In addition, we have determined the numerical value of effective refractive index, effective area, nonlinearity and numerical aperture of 1.3725, 52.5 µm^{2}, 0.9 W^{−}^{1}∙m^{−}^{1}, and 0.26 respectively at 3.5 µm absorption wavelength of CH_{4} gas. Note that CH_{4} gas is used in various commercial purposes like generation of electricity, domestic heating and cooking, as an ideal fuel for some modern vehicles and also other applications. Moreover, presence of CH_{4} gas in all the places is not secured for the human beings because it may create serious accident like fire. So it is more essential to detect the presence of CH_{4} gas correctly. The proposed design of HPC-PCF will keep optimistic and innovative role for detecting CH_{4} gas properly which will supportive for global economic in future.

The authors declare no conflicts of interest regarding the publication of this paper.

Sardar, M.R. and Faisal, M. (2019) Methane Gas Sensor Based on Microstructured Highly Sensitive Hybrid Porous Core Photonic Crystal Fiber. Journal of Sensor Technology, 9, 12-26. https://doi.org/10.4236/jst.2019.91002