High Sensitive Methane Sensor With Temperature Compensation Based on Selectively Liquid-Infiltrated Photonic Crystal Fibers

A highly sensitive and temperature-compensated methane sensor based on a liquid-infiltrated photonic crystal fiber (PCF) is proposed. Two bigger holes near the core area are coated with a methane-sensitive compound film, and specific cladding air holes are infiltrated into the liquid material to form new defective channels. The proposed sensor can achieve accurate measurement of methane concentration through temperature compensation. The sensitivity can reach to 20.07 nm/% with a high linearity as the methane concentration is within the range of 0%–3.5% by volume. The proposed methane sensor can not only improve the measurement accuracy, but also reduce the metrical difficulty and simplify the process.


Introduction
Photonic crystal fiber (PCF) [1][2][3] becomes a great sensing platform due to its special light controlling capability and excellent sensing abilities. With the promotion of fabrication techniques, various PCF-based sensors have been developed for different measurements [4,5]. One aspect of particular interest in such applications is the target gas detection. Methane is extremely flammable and explosive, and is often found in the gas mixture. Therefore, it is necessary to explore an effective sensing method for the real-time measurement of methane concentration. Many methane-sensing structures have been proposed, including long period fiber grating (LPFG) [6][7][8], modal interference (MI) [9], surface plasmon resonance (SPR) [10], cryptophane-E infiltrated photonic crystal (PC) micro-cavity [11], and optical absorption spectroscopy technology [12]. Although these configurations have their own advantages, most of them are interference-sensitive not only to the methane concentration but also to the temperature.
The key solution is to eliminate the temperature interference and enhance the measurement precision.
Owing to the distinct advantages of high sensitivity, good physical strength, and low cost, the PCF-based sensors become an excellent candidate of methane measurement [13,14]. However, the temperature cross-sensitivity is still a critical problem to be considered. To solve this problem, the

Theoretical model and parameter optimization
As shown in Fig. 1, the structural parameters of the proposed PCF are described in detail, including the diameters of air holes (d air , d v1 , d v2 , d 1 , and d 2 ), photonic lattice period  , and the gas-sensitive film thickness t. Two smaller holes of the fourth layer with different diameters d V1 [18]. Conversely, two bigger holes near the core ( ) b d are coated with the methane-sensitive film. Especially, another two different holes of the second layer (d 1 and d 2 ) with different diameters are introduced to adjust the coupling intensity of core fundamental mode LP 01 . The finite element method (FEM) and perfectly matched layers (PML) boundary condition are used to calculate the effective indices of electromagnetic modes [19]. The optimized structural parameters of PCF will be obtained in the end of Section 2.
The whole structure takes into account the practical and convenient qualities to manufacture, and the precise fabrication can be ensured through the multi-step "stack-and-draw" method. The collapsing process of silica tubes is carried out in the lathe of modified chemical vapor deposition [20,21]. Capillaries are drawn from high-purity fused silica tubes and stacked layer by layer in a stacking rig, where a capillary is used instead of the solid rod to create a central void in the structure. Moreover, we need to manipulate the pressure in different areas carefully during the whole fiber drawing process. In addition, the precise infiltration of proposed PCF can be achieved through the two-step filling technique [21]. All holes are applied with the ultraviolet (UV)-harden glue through the taped glass tip by carrying a tiny drop of UV-harden glue, except for the ones to be filled. Then, the fiber is connected to a syringe from the other end, and liquid can be pumped into the open holes throughout the whole fiber. Moreover, the uniform thickness methane-sensitive compound film can be coated by a capillary dip-coating technique at a withdrawal speed of 12 cm/min [22]. After coating the dilute solution onto the internal surface of air holes, the 0.4 MPa nitrogen stream is used to polish the inner surface of film. Besides, the fusion-splicing machine is used to achieve the splicing between the single mode fiber (SMF) and PCF [23]. During the splicing procedure, the lead-in SMF and PCF should be first aligned roughly center-to-center in the V-grooves [24]. The background material is pure silica, whose material dispersion is determined by the Sellimeiers equation as shown in [25]. The RI of methane-sensitive film methane n varies with the methane concentration C when the methane gas interacts with the intra-cavity compound thin-film [26,27], and the reaction of methane to gas-sensitive film is reversible which is useful for the repeated test. Moreover, based on the experimental results from [28,29], (2) is selected to describe the relationship between RI of cryptophane-E and gas concentration C. Within the range of 0% to 3.5%, for each 1% increase in methane concentration, the refractive index of gas-sensitive film will decrease by 0.0046. The fiber core and the defective channels can form a balanced directional coupler. At this point, the energy would transfer from the fiber core to defective channel, and a resonant dip would appear in the transmission spectrum. The coupling between the core mode and defect mode ( mode 1 ) results from their interaction via their evanescent fields and the coupling process only happens at specific wavelength. The mode coupling between the core mode and defect mode is analyzed by the coupled-mode theory, and the coupling equations are expressed as (3) [30,31]. In (3), 1 1 | | A represent the transmitted power of the core mode and defect mode, respectively. Then, the normalized optical powers 1 ( ) P Z and 2 ( ) P Z can be obtained as (4). In (4), , and the initial values are set as 1  as the light is injected into the core only. Since the effective RIs are plural, the complete coupling condition could be satisfied when In order to design a reasonable and available PCF sensor, we need to consider the sensitivity and linearity together. The RI sensitivity of the sensitive film is obtained in Fig. 3, and the sensitivity for 1 4362.32 nm / RIU and 4017.6 nm/RIU, respectively. Figure 4 shows the effect of the structure parameters t and d b on the sensitivity and linearity. The sensitivity of the proposed sensor is changing linearly with the varying of structure parameters t or d b , which are summarized in Tables 1 and 2 Fig. 3 Effect of sensitive film RI on the sensitivity.     Fig. 5 Relationship between the gas sensitivity of the sensor and (a) the thickness t of the gas-sensitive film (b) the diameters db of air holes. Table 1 Influence of t on the sensitivity of proposed sensor.  Table 2 Influence of db on the sensitivity of proposed sensor.  Figure 6 represents the polarization-dependent relationships between the loss-peak shifts and main structural parameters, and the influences of each parameter on the spectral responses are summarized in Table 3. It is interesting to note that the variation of P and air d can affect the peak-shifts of mode Based on above conclusions, we need to find some sort of balance among the central wavelength, loss peak intensity, sensitivity, and linearity. After research and repeated comparisons, the optimized structural parameters of the PCF are presented in Table 4. Table 3 Influence of different parameters on the loss peak.

Parameter
Available range (µm) Peak intensity direction     Fig. 6 Loss spectra of the core mode with different values of (a) P, 1 d , and (f) 2 d .

Measurement results and discussion
The experimental setup begins with an optical broadband source (BBS), and the transmitted light enters the PCF via a polarization controller, as shown in Fig. 7. The spectral response of output light can be observed through an optical spectrum analyzer (OSA). Since the optical properties of the x-polarization mode are mainly investigated, a polarization controller (PC) is needed to eliminate the y-polarization mode. The concentration of methane gas can be precisely controlled through two mass flow controllers, and the gases are mixed by the stainless steel helical tube between the controllers and the chamber. The PCF sensor locates in the center of a controllable gas chamber to evaluate the sensing performance of the methane sensor, and the length of the proposed PCF is set to 18 mm. Moreover, the cladding layer of the SMF at the junctions should be partially removed to make the methane gas enter the air holes easier. The two fiber ends are exposed to an intense discharge for a few seconds, and the fibers should be pushed and pulled to form a robust connection. In order to ensure the accuracy of the measurement, the ventilation time is generally set to 10 minutes before each measurement. Then, the methane gas can enter into the cladding air-holes via free diffusion.
For an accurate simulation, the thermal expansion effect and thermo-optic effect both are considered. The thermal-expansion coefficients are taken as . Since the coupling between LP 01 mode and mode D varies with the methane concentration and ambient temperature, the peak-shift of LP 01 mode induced by measured parameters should be investigated at first. Moreover, based on the experimental results from [34], the sensor's response time is about 50 s, and recovery time is 72 s. Considering the lower explosion limit of methane and the linear relationship between the RI of gas-sensitive film and gas concentration, the methane gas concentration between 0% and 3.5% is set as the measurement range. Figure 8(a) indicates the confinement loss spectra of LP 01 mode within the concentration range of 0% to 3.5% on the condition of T = 20 ℃, and there is an obvious blue peak-shift with an increase in C. The case of C = 0 is set as the reference point, and then the methane sensitivities for resonant peaks 1 V  and 2 V  can be calculated directly. Figure 8(b) reveals the relationship between loss-peak shifts and methane concentration. The gas sensitivities of these two peaks are 1 20.07 nm / % k   and 2 18.48 nm / % k   , respectively. Then, we can obtain the temperature sensitivities in the same way. respectively, which can be obtained from Fig. 9(b). The different methane concentration sensitivities and temperature sensitivities are conducive to further multi-parameter discrimination.
According to above results, the loss-peak shifts of  have a good linear relation to the temperature and methane concentration. By the use of matrix demodulation method, the impact of temperature T can be filtered to achieve the accurate measurement of methane concentration C. As it is expressed in (6) and (7), the peak-shifts Based on (8) [32], the sensor resolution of temperature and methane concentration also can be calculated as 4.17 × 10 -1 ℃. ( min 0.2 nm    ) and 3 9.96 10 %   ( min 0.2 nm    ), respectively.  A two-dimensional parameter (C, T) is defined to represent the sampling process due to that the ambient conditions vary randomly in the sensing process. Five sampling points [I (1%, 30 ℃), II (3.3%, 7 ℃), III (2.1%, 50 ℃), IV (2.6%, 45 ℃), and V (1.4%, 59 ℃)] are selected as examples. Based on the loss spectra shown in Fig. 10, the peak-shifts and corresponding results with and without temperature compensation are compared in Table 5. The calculated results show a very good agreement with the theoretical values, and the feasibility and effectiveness of proposed measurement method vary adequately. Especially, the sensor can improve the measurement accuracy by eliminating the temperature cross-sensitivity effect. Table 6 shows the comparison of the sensitivity and detection range of the proposed sensor with some other reported methane sensors. It is obvious that the proposed PCF structure can achieve higher sensitivity.

Conclusions
In conclusion, a high sensitive methane sensor with temperature compensation based on MF-infiltrated PCF is proposed. The methane concentration can be accurately measured just by using a matrix demodulation method to eliminate the cross-sensitivity effect. The methane sensitivity can be up to 20.07 nm/% with a good linearity within the detection range of 0 to 3.5%. The proposed sensor is very suitable for gas measurements owing to its high sensitivity, good linearity, and simple preparation process.