Methane and hydrogen are flammable and potentially explosive gases and it is important to detect methane and hydrogen at the same time in industrial production and other applications. There are several types of electrical sensors to monitor hydrogen and methane but they are not suitable for the industrial environment due to the potential risks of sparks and explosion^[1]. Optical fiber sensors can overcome the shortcomings as they have the advantages of small size, fast response, electrical insulation, corrosion resistance, and electromagnetic interference resistance. At present, several types of optical fiber sensors have been developed for gas sensing^[2-4]. The Fiber Bragg Grating (FBG) sensor has the wavelength multiplexing capability but relatively lower sensitivity^[5], whereas the interferometric optical fiber sensor has better sensitivity but poor stability^[6]. Compared to these sensors, optical fiber sensors based on Surface Plasmon Resonance (SPR) have high sensitivity, low production cost, and remote on-line monitoring capability^[7-10].

The SPR phenomenon which can be described in terms of collective oscillations of the free electron plasma at the interface between the metal and dielectric medium has been applied to refractive index sensing^[11-14]. However the conventional prism-SPR sensor is too bulky. Aiming at the above problem, the miniature SPR sensors composed of optical fibers have been designed. For example, Wei et al.^[15] have proposed a Long-Period Fiber Grating (LPFG) surface plasmon resonance sensor coated with a silver film and graphene monolayer for methane detection, the detection sensitivity is 0.344 nm/%. Liu et al.^[16] have designed a Photonic Crystal Fiber (PCF) SPR sensor with a large side-hole structure. A gold film and Pd-WO₃ and UltraViolet Curable Fluoro-Siloxane (UVCFS) nanofilms incorporated with cryptophane A are used to enhance the sensitivity of hydrogen and methane to achieve a sensitivity of 0.19 nm/% for hydrogen and 1.99 nm/% for methane. Liu et al.^[17] have designed a methane sensor based on the long-period grating in photonic crystal fiber. By taking advantages of the LPFG and PCF-SPR, the methane sensitivity is 6.39 nm/%. However, the researches about SPR sensors with the ability of simultaneous detection of methane and hydrogen are rarely reported.

In this work, a Photonic Quasi-crystal Fiber (PQF) based on SPR is designed to detect methane and hydrogen at the same time. PQF is a kind of microstructured optical fiber which are ordered but not periodic structures that lack translational symmetry but include rotational symmetry. Comparied with PCF, the PQF exhibits similar properties such as endlessly single mode, flattened dispersion^[18-19], high nonlinearity^[20], large effective mode area^[21] , high birefringence and so on. The structure includes two separate sensitive layers, and nano silver films are deposited on the D-shape surface and outside surface of the PQF. The methane and hydrogen sensitive films are coated on the silver films respectively to exploit the SPR effect. Our results show that the sensor has a high sensitivity of 10 nm/% for methane and 0.8 nm/% for hydrogen.

The cross-section of the PQF-SPR sensor is shown in Fig. 1 (Color online). The basic structure is based on the simple six-fold quasi-crystal configuration with a lattice pitch Λ=2.5 μm and air hole diameter d=1.58 μm. To enhance the SPR effect, the three central air holes marked by the dotted line in Fig. 1 are removed to form a larger fiber core and two air holes are added to confine the core mode and reduce the transmission loss. The four top air holes are removed to form the D-shape region as the methane gas channel with a height of h₂=2.17 μm. The sensor can be fabricated by laser etching, 3D printing or pouring^[22-23]. The silver film with a thickness of t₂ = 30 nm can be deposited on the flat surface by Chemical Vapor Deposition (CVD)^[24] or magnetron sputtering^[25]. The polysiloxane nanofilm with cryptophane E can be coated on Ag film as the methane sensitive materials by capillary impregnation coating^[16] to avoid oxidation of silver. The thickness is t_CH₄=500 nm. In the same way, the Ag film and hydrogen sensitive film Pd-WO₃ are coated on the external surface of the PQF. The thicknesses aret₁=30 nm and t_H₂=250 nm. The outer layer is a perfectly matched layer and the background materials in the PQF are silica. The sensor is covered by a Perfectly Matched Layer (PML) with a diameter of 20 μm. As the concentration of hydrogen and methane increases, the refractive indexes of the hydrogen-sensitive film and methane-sensitive film decrease linearly in the range of 0%−3.5%. The functional relationships are described in equations (1) and (2)^{[16, 26]}, where C_H₂ and C_CH₄ represent the concentration of hydrogen and methane respectively.

${n_1}=1.995-0.000\;67\;C\_H_{2}\quad,$ (1)

$ {n_2}=1.448-0.004\;6\;C\_CH_{4}\quad.$ (2)

The dispersion relationship of background material is determined by Eq. (3), where A₁=0.696166300, A₂=0.407942600, A₃=0.897479400, B₁=0.0684043 µm², B₂=0.1162414 µm², B₃=9.896161 µm^{2 [27]}. In addition, the Drude-Lorentz model is used to describe the dielectric constant of silver and expressed in Eq. (4), where ε_∞=2.48 is the high frequency dielectric constant, ɷ_p=1.35×10¹⁶ (rad/s) is the plasma frequency, and ɷ_d=7.62×10¹³(rad/s) is the damping frequency^[28]:

$ {n^2}(\lambda ) = 1 + \frac{{{A_1}{\lambda ^2}}}{{{\lambda ^2} - B_1^2}} + \frac{{{A_2}{\lambda ^2}}}{{{\lambda ^2} - B_2^2}} + \frac{{{A_3}{\lambda ^2}}}{{{\lambda ^2} - B_3^2}}\quad, $ (3)

$ \varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2}}{{\omega (\omega + i{\omega _d})}}\quad. $ (4)

The calculation of confinement loss (CL) is shown in Eq. (5)^[29]:

$ {\alpha _{{\rm{loss}}}} = 8.686 \times \frac{{2{\text{π}} }}{\lambda }{{\rm{Im}}} \left( {{n_{{\rm{eff}}}}} \right) \times 1{0^4}\left( {{\rm{dB}}/{\rm{cm}}} \right)\quad,$ (5)

where Im(n_eff) represents the imaginary part of the effective refractive index of the core mode.

For a hydrogen concentration of 2.5%, the dispersion relationships of the X-polarized core mode and Surface Plasmon Polariton (SPP) mode are calculated and plotted in Fig. 2 (Color online) as red square dots and circular dots, respectively. It is evident that the phase matching condition of SPR is achieved at the cross point when resonance is the strongest. This is verified by the core mode and SPP mode field diagrams for X-polarization in Fig. 2(b). The power of the core mode is transferred to the SPP mode and therefore, the peak of the confinement loss spectra appears at the phase matching point as shown by the black curve in Fig. 2. The peak wavelength is 1848.2 nm. Figs. 2(a) and 2(c) also show the electric field distributions of the X-polarized core mode and SPP mode at 1875 nm. The resonance intensity is weakened as the wavelength is changed. The blue curve represents the confinement loss of Y-polarization. It is evident that the coupling intensity of X-polarization is much larger than that of Y-polarization due to the asymmetry of the structure. Therefore the confinement loss of X-polarization is chosen to analyze hydrogen sensing characteristics. Similarly, the SPR effect induced by the methane is shown in Fig. 3. The Y-polarized mode is adopted to calculate the confinement loss spectrum for methane since the methane-sensitive film is coated on the polished plane in the Y direction^[30-31]. The peak wavelength of the confinement loss spectrum is 1513 nm for a methane concentration of 2.5%. Fig. 3(b) shows the electric field distributions of the Y-polarized core mode and SPP mode at the phase matching point and Figs. 3(a) and 3(c) correspond to wavelength detuning of 1570 nm. The confinement loss spectra of the PQF-SPR sensor exhibit two peaks at different wavelengths for hydrogen and methane and so simultaneous detection of methane and hydrogen can be accomplished.

The SPR sensor is very sensitive to the refractive index of the surrounding environment^[32]. The refractive indexes of the hydrogen-sensitive film and methane-sensitive film change with hydrogen and methane concentrations, and therefore the position and peak intensity of SPR generated by coupling between the Ag film and core mode change accordingly. The sensitivity of the sensor can be determined by the wavelength interrogation method as shown in the following^[33]:

$ S(\lambda ) = \frac{{\Delta {\lambda _{{\rm{peak}}}}}}{{\Delta {C_{{\rm{gas}}}}}}({\rm{nm}}/\% )\quad, $ (6)

where Δλ_peak represents the variation of the resonance wavelength with changing gas concentration and ΔC_gas represents the variation of gas concentration.

From the safety point of view, the performance of the sensor is studied in the concentration range of 0%−3.5% for hydrogen and methane. Ford=1.58 μm, Λ=2.5 μm, t₁=30 nm, t₂=30 nm, h₁=1.5 μm, h₂=2.17 μm, t_H₂=250 nm, and t_CH₄=500 nm, the variations of the confinement loss spectra with hydrogen and methane concentration are shown in Fig. 4 (Color online). With increasing hydrogen concentration, the confinement loss spectra of the X-polarized core mode move slowly to the short wavelength direction as shown in Fig. 4(a). The relationship between the resonance wavelength and hydrogen concentration is displayed in Fig. 5 (Color online). The resonance wavelength decreases linearly in the range of 0%−3.5%. The sensor achieves the highest hydrogen sensitivity of 0.8 nm/% in the range of 0.5%−1% and 3%−3.5%. Meanwhile, the average sensitivity is 0.65 nm/% according to the linear fitting in Eq. (7). In the same way, the confinement loss spectra of different methane concentrations are shown inFig. 4(b). The results show that the methane has higher loss peak, narrower linewidth, and greater wavelength shift than hydrogen. The maximum sensitivity is 10 nm/% for methane concentration ranges of 0%−1% and 2%−2.5% and the average sensitivity is 8.81 nm/% according to Eq. (8). The R-square values (R²) of the linear fitting curves for hydrogen and methane are 0.998 and 0.999, respectively, indicating that the relationship between the refractive index and gas concentration can be fitted well.

$ {y_1} = - 0.01 - 0.65{x_1}\quad,$ (7)

$ {y_2} = - 0.58 - 8.81{x_2} \quad. $ (8)

The performance of the sensor can be optimized by changing the structural parameters. For a hydrogen concentration of 3%, the CL spectra for different air hole diameters d are shown in Fig. 6(a) (Color online). The resonance peak blue-shifts with increasing of air hole diameters. A larger d changes the effective refractive index of the core mode and shifts the phase matching point^[34]. In order to optimize d, Fig. 6(b) (Color online) shows the relationship between the resonance wavelength and hydrogen concentration for different air hole diameters d, and the results exhibit a similar monotonic trend. The average sensitivity of the sensor is calculated by linear fitting and d=1.58 μm is the optimal air hole diameter to attain the maximum average hydrogen sensitivity.

By using the same structural parameters, the sensitivity of the sensor for methane is analyzed as shown in Fig. 7(a) (Color online). The loss spectra blue-shifts and the resonance peaks decrease greatly with increasing air hole diameter d for methane concentrations of 2% and 2.5% because the Y-polarized core mode is better confined by a bigger air hole and energy leakage is less^[34-35]. Fig. 7(b) shows the variation trend of the sensor with different air hole diameters as the methane concentration is changed from 0% to 3.5%. The slope of the linear fitting represents the average sensitivity of the sensor. It can be seen that the maximum sensitivity is obtained at d=1.58 μm and therefore d=1.58 μm is selected as the optimal air hole diameter.

The thickness of the metal film is optimized. When the silver film thickness is changed from 28 nm to 32 nm, the confinement loss spectra for C_H₂=3% is shown in Fig. 8(a) (Color online). The confinement loss spectra move to a longer wavelength with increasing Ag film thickness because a thicker silver film requires a longer wavelength to excite surface plasmon resonance^[36]. At the same time, increasing the thickness of the silver film enhances the resonance between the core mode and SPP mode and subsequently the resonance peak. Fig. 8(b) (Color online) shows the relationship between the resonance wavelength and hydrogen concentration for different silver film thicknesses. The slope of the curve indicates the average sensitivity which is calculated by linear fitting. The maximum average sensitivity is obtained when t₁=30 nm. The impact of the silver film thickness on the methane confinement loss spectra is analyzed and shown in Fig. 9(a) (Color online). For methane concentrations of 2% and 2.5%, the spectra exhibit a significant blue-shift with increasing silver film thicknesst₂. As the thickness is increased, the effective refractive index of the SPP mode decreases, but the effective refractive index of the core mode changes little, so that the phase matching point moves to a shorter wavelength^[16]. At the same time, when the silver film thickness is large, the evanescent wave excited by evanescent field has more difficulty crossing the surface of the metal, resulting in the weakened SPR response^[37]. Fig. 9(b) shows the average sensitivity of the sensor for different silver film thicknesses when the methane concentration is changed from 0% to 3.5%. The maximum sensitivity is observed for t₂=30 nm and hence, t₂=30 nm is the optimal parameter.

Finally the influence of the methane channel size on the sensor performance is analyzed and shown in Fig. 10 (Color online). When the height h₂ is increased from 1.97 μm to 2.37 μm, the confinement loss spectra move to a longer wavelength and the loss peak increases, because the height h₂ which determines the distance between the core and plasmonic materials influences the coupling efficiency of the core mode and SPP mode^[34]. When the h₂ is increased, the distance between the silver film and fiber core is shorter so the resonance is stronger and loss peak is larger. Fig. 10 (b) shows the average sensitivity for different h₂ and the sensitivity reaches the maximum for h₂=2.17 μm and therefore, h₂=2.17 μm is the optimal channel height.

A high-sensitivity methane and hydrogen sensor based on PQF-SPR is designed and analyzed. The two areas coated with Pd-WO₃ and cryptophane E doped polysiloxane are designed to detect hydrogen and methane, respectively. The sensor can be operated at different wavelengths to detect the two gases at the same time. The properties of the sensor is investigated by the finite element method and the numerical analysis result shows that the sensor has a maximum sensitivity of 0.8 nm/% and average sensitivity of 0.65 nm/% for hydrogen and maximum sensitivity of 10 nm/% and average sensitivity of 8.81 nm/% for methane. The sensor shows higher sensitivity in the gas concentration range between 0% and 3.5% and has great potential in gas detection. Moreover, the sensor structure and method can be further extended to detection of multiple gases and other fields.