D-Shaped Tellurite Photonic Crystal Fiber Hydrogen and Methane Sensor Based on Four-Wave Mixing With SPR Effect

A new D-shaped tellurite photonic crystal fiber sensor based on the four-wave mixing (FWM) effect with the surface plasmon resonance (SPR) effect is designed and optimized. The substrate of the D-shaped photonic crystal fiber (D-PCF) is tellurite glass, and the polished surface is plated with the gold film and hydrogen gas-sensitive film. An air hole of the inner cladding, which is plated with the gold film and methane gas-sensitive film, is selected as the second sensing channel to simultaneously measure the concentration of hydrogen and methane. Based on the four-wave mixing, the wavelength shifts of the Stokes and anti-Stokes spectra resulting from the variation of the gas concentration can be used to accurately detect the concentrations of methane and hydrogen. Meanwhile, it is found that the SPR effect can increase the wavelength shifts, which means the sensitivity of methane and hydrogen augment. After parameter optimization, the maximum sensitivities of methane and hydrogen are 4.03 nm/% and −14.19 nm/%, respectively. Both the linearities are up to 99.9%. The resolution of methane is 1.25×10−2% and hydrogen is 7.14×10−3%. Moreover, the fiber length of this sensor is only 20 mm, which is conducive to the construction of a compact or ultra-compact embedded FWM fiber sensor.


Introduction
Based on the porous structure of photonic crystal fibers, surface plasmon resonance (SPR) produced by filling metal rods or coating metal films has recently become a hot spot in the field of optical fiber sensors. In particular, researches on the SPR coated with the metal film on the polished surface of the D-shaped photonic crystal fiber (D-PCF) are more attractive, including the refractive index [1], methane [2], temperature [3], magnetic field [4], strain, [5] and biochemistry [6] sensors. Most of the above studies are conducted by the loss spectrum which has some disadvantages. It can only provide one degree of freedom, which needs to be combined with other methods or special PCF structures, such as the Sagnac interference [3], directional coupling [7], or side-hole structure [8] to achieve dual-parameter sensing. At present, the detection of the gas concentration is often limited by detecting the sensitivity and cross-sensitivity. An even greater obstacle is the inability to accurately detect specific gases in mixtures of two or more gases. The four-wave mixing (FWM) effect can solve this problem. The FWM process is accompanied by the annihilation of two photons, resulting in two new photons. Thus, two gain peaks, Stokes and anti-Stokes, are formed, and the Stokes and anti-Stokes peak shifts can provide two independent sensing channels to achieve dual-parameter sensing by a sensitivity demodulation matrix. Since the FWM is very sensitive to optical fiber dispersion, the method combined with the SPR effect can obtain high sensitivity. In 2018, Nallusamy et al. [9] designed a D-shaped PCF-SPR sensor to simultaneously measure the temperature and salinity of seawater by using the FWM effect. The salinity sensitivity and temperature sensitivity are 1.6 nm/% (kg/kg) and 12.31 nm/℃, respectively. Although gas-sensing has not yet been reported, the FWM effect combined with the SPR effect has good application prospects in the multi-gas detection field.
Most PCF sensors use silica as the substrate, and the transmission window of the quartz fiber is 0.38 μm -2.3 μm. When the wavelength of the transmitted light wave exceeds 2.3 μm, the transmission loss will increase sharply [10]. The silica has a lower nonlinear coefficient, which limits its application in near-infrared and mid-infrared areas. Therefore, tellurite glass has attracted wide attention due to its wider infrared transmission range, greater nonlinear refractive index, insulation constant, damage threshold, and better third-order nonlinear optical performance [11,12]. The nonlinear coefficient of the tellurite PCF is more than ten times that of the silicon substrate, which makes it easier to meet the phase matching conditions to generate the highly efficient FWM. In 2020, Sun et al. [13] realized temperature sensing by using the FWM in the tellurite photonic crystal fiber, and the temperature sensitivity of the sensor was 0.7 nm/℃ at the pumped wavelength of 3 550 nm. In the following year, Chen et al. [14] realized FWM temperature sensing in the chalcogenide PCF, and the sensitivity was as high as 2.32 nm/℃ in the range of -80 ℃ to 45 ℃, with a pump wavelength of 8 510 nm.
However, there are few reports in the field of gas sensing, especially in hydrogen sensing. At present, the main methods are Bragg grating and Saganc interference, which are complex and have low sensitivity [15,16,20]. In conclusion, as both methane and hydrogen are flammable and explosive gases, it is essential to detect their concentrations. Therefore, it is necessary to design a sensing device that can detect the concentrations of methane and hydrogen simultaneously to achieve higher sensitivity and better accuracy.
In this paper, a new D-shaped PCF-SPR sensor based on the FWM effect is proposed and optimized. Here, we adopt tellurite glass as the substrate and plate the gold film and hydrogen-sensitive film on the polished surface of the D-PCF. Another air hole is selected to be coated with the gold film and methane-sensitive film as the second sensing channel to realize the simultaneous measurement of hydrogen and methane concentrations in mixed gas. The characteristics of the sensor are numerically investigated by using the full vector finite element method under the anisotropic boundary conditions of the perfectly matched layer (PML). When the gas mixture passes through, the refractive index of the gas-sensitive film will change. This will affect the dispersion and nonlinear coefficient of the PCF propagation mode and eventually lead to the shift of the gain peaks of the Stokes spectrum and anti-Stokes spectrum. It is found that the SPR effect enhances the gain peak shifts, which increases the sensitivity of the sensor. After parameter optimization, the final sensitivity of methane can reach 4.03 nm/% and that of hydrogen is as high as -14.19 nm/%. Moreover, the fiber length of this sensor is only 20 mm, which is conducive to the construction of compact or ultra-compact embedded FWM fiber sensors. Meanwhile, it is also applicable Hai LIU et  to the study of the concentration of other mixed gases, which has a wide application prospect.

Basic theory
The FWM is caused by the third-order nonlinear polarizability (3) χ of the medium. Degenerate four-wave mixing (DFWM) is a special form of the FWM, in which two photons at the same frequency annihilate to produce two new photons, namely Stokes photon and anti-Stokes photon. To understand the sensing mechanism of the DFWM, the Raman effect, self-steepening effect, and linear loss can be ignored to obtain the following modified nonlinear Schrödinger equation (MNLSE), as shown in (1) [17], where A is the normalized light pulse amplitude, z is the propagation distance, t is time, n β is the nth order propagation constant, and γ is the nonlinear coefficient. Here, 2 n is the nonlinear refractive index of the fiber substrate materials, and eff A is the effective mode field area at the pump wavelength( 0 λ ).
Only the phase mismatch 0 κ = can produce the significant FWM effect, namely phase-matching. According to the energy and momentum conservation, the phase-matching condition of the FWM is defined as (4) [18], where and fourth-order( 4 β ) propagation constants are the most important factors that affect the FWM, thus, the other higher-order propagation constants can be ignored.
Considering the loss of light waves in the propagation process, the influence of the loss on the gain needs to be considered, so the gain formula is shown as (5) [19]: where α is the limit loss, 0 P is the peak power of the pump, L is the length of the optical fiber, g is the gain coefficient, and In conclusion, the change of the gas concentration will affect the effective refractive index ( eff n ) of the PCF, making the parameters γ , 2 β , and 4 β vary, and finally leading to the shift of the Stokes and anti-Stokes peaks. Therefore, the concentration of the mixed gas can be detected by establishing a direct relationship between the peak shift of Stokes and anti-Stokes spectra and the concentration of gas.

Sensing mechanism and modeling
The cross-section diagram of the proposed D-shaped PCF-SPR sensor is shown in Fig. 1(a). The PCF is microprocessed by the laser etching and optical fiber polishing technology to remove part of the fiber cladding of the cylindrical PCF. The substrate material is tellurite glass, the gold film and hydrogen gas-sensitive film are plated on the polished surface of D-PCF, and another inner cladding air hole is selected to be plated with the gold film and methane gas-sensitive film. Metal films mostly adopt the high-pressure chemical vapor deposition technology (CVD). The specific process is to make gaseous or vapor metal plasma react chemically by means of high pressure heating and deposit the atomic state on the inner side of air holes and polished surface, thus forming metal coating films. The material of the hydrogen-sensitive film is Pd-WO 3 and is coated on the D-shaped polished surface by the sol-gel scheme [20]. Meanwhile, the methane-sensitive film is made of cryptophane-A and UV(ultra-violet)-cured fluorosiloxane (UVCFS), using the capillary dip-coating technique coated on the metal film surface inside an air hole [21]. However, the plating of the nano-level metal and sensing film in the micron-level air hole of the PCF requires a high technological level. The air hole distance is 8 m  Figure 1(b) shows the experimental setup for the FWM-based D-shaped PCF-SPR sensors. The output polarization state of the pump light is selected by an optical polarization controller (PC) and coupled into the single-mode fiber. The signal light modulated by the PCF is output to the optical spectrum analyzer (OSA) through the multimode fiber (MMF) and the wave pass filter (PF). The MMF combined with a wave pass filter can filter out the residual laser light excited by the pump light source, that is, the background spectrum of the FWM is reduced, and only the FWM signal light is collected [18,23].
The substrate is made of tellurite glass In addition, the thermal optical coefficient of tellurite glass is -6 orders of magnitude, so the quantitative change in the refractive index of the tellurite glass with the temperature can be ignored when calculating the effective refractive index [13]. Besides, the refractive indexes (RIs) of methane and hydrogen gas-sensitive films are shown in (9) -(10) [8]. The RIs of them are negatively correlated with the concentration in the concentration range of 0% -3%. The dispersion of gold is described by the Drude-Lorentz model, as shown in (11). Here, Au ε is the permittivity of the gold, 9.75 ε ∞ = is the permittivity at infinite frequency, 16 1.36 10 rad/s p ω = × is the plasma frequency, and 14 1.45 10 rad/s τ ε = × is the collision frequency.

Simulation analysis and parameter optimization
In this section, the characteristics of the sensor are numerically analyzed by using the full vector finite element method under the anisotropic boundary condition of a perfectly matched layer (PML). We adopt the COMSOL software to simulate the model and analyze the influence of structural parameters on the sensor to determine the optimal structural parameters.
To achieve the efficient four-wave mixing modulation, the optical fiber is required to be equipped with a zero-dispersion wavelength (ZDW) and the dispersion wavelength is as flat as possible. The dispersion curves are influenced by both the thickness of the gold film and the depth of polishing. Next, we will investigate the influence of different gold film thicknesses and polishing depths on the dispersion and select the optimal parameters. The initial parameters of the PCF sensor are selected a s 8 m ). Thirdly, we choose the constant thickness of the gold film and the polishing depth increased from 9.4μm to 9.8 μm. The impact on the ZDW is also modest. It can be seen that the ZDW is Under the phase-matching condition, the DFWM can generate Stokes and anti-Stokes sidebands around the pump wavelength with the variation in RI of the measured object. This frequency shift increases with the influence of negative fourthorder dispersion (FOD) in the normal dispersion region [23], namely 2 0 β > and 4 0 β < . Finally, we select 1 798 nm as the pump wavelength and the peak pump power is 5 kW. It is found that with the shortening of the fiber length, the obtained sensitivity is basically unchanged, which is conducive to the construction of compact or ultra-compact embedded FWM sensors. Thus, 20 mm is selected as the fiber length.
Next, the effects of two gas-sensitive film thicknesses on the sensitivity of methane and hydrogen are investigated. Firstly, we keep the methane gas-sensitive film thickness constant at 260 nm, making the hydrogen gas-sensitive film thickness vary from 260 nm to 300 nm with a step length of 20 nm. Then, we change the hydrogen concentration from 0% to 3% with the methane concentration constant at 0%. Figure 3(a) shows the movement of gain peaks corresponding to different hydrogen gas-sensitive film thicknesses when the hydrogen concentration increases from 0% to 2%. It can be seen that the gain peak value decreases with the augment of the hydrogen gas-sensitive film thickness, while the gain peak value basically remains unchanged with the variation of the hydrogen concentration. In order to observe the peak deviation more intuitively, Figures 4(a) and 4(b) illustrate the specific wavelength shifts of the anti-Stokes and Stokes peaks, respectively. It is obviously shown that each group of the Stokes peaks moves to the short-wave direction, while that of the anti-Stokes peaks moves to the long-wave direction with an increase in the hydrogen gas-sensitive film thickness when the methane gas-sensitive film thickness and the hydrogen concentration are constant. When the hydrogen volume fraction is varied by 0.5%, the anti-Stokes peaks redshift, and the Stokes peaks blueshift, both of the gain peak values decline. Their peak offsets will decrease, but the linearities will augment. Under the same conditions, the gain peak curves with the variations of the methane concentration can be obtained by keeping the hydrogen concentration constant at 0% and changing the methane concentration from 0% to 3.5%. Figure 3(b) shows the gain peak curves of the methane concentration at 0% -2%. The peak value decreases with an increase in the hydrogen gas-sensitive film thickness, and the methane concentration also has little effect on the peak value. It can be clearly seen from Figs. 4(c) and 4(d) that each group of the Stokes peaks moves to the short-wave direction, while that of the anti-Stokes peaks moves to the long-wave direction with the augment of the hydrogen gas-sensitive film thickness when the methane gas-sensitive film thickness and methane concentration are constant, which is consistent with those in Fig. 3(a). However, the difference is that anti-Stokes peaks have the blue-shift and the Stokes peaks have the red-shift when the methane volume fraction is varied by 0.5%. Although the peak offsets are reduced, the linearities remain basically unchanged. Considering the sensitivity and linearity comprehensively, we finally choose the hydrogen gas-sensitive film thickness as 280 nm.
Then, the influences of the methane gas-sensitive film thickness on the sensitivity have been studied. The thickness of the hydrogen gas-sensitive film is kept at 280 nm, and the methane gassensitive film thickness is changed from 260 nm to 300 nm with a step length of 20 nm. Firstly, we research the effects on the hydrogen sensitivity. The variations of the Stokes and anti-Stokes gain peaks under different hydrogen concentrations (0% -2%) are plotted in Fig. 5(a). We can see that the gain peak values are almost constant while the wavelength positions are changed. It can be seen from Figs. 6(a) and 6(b) that the anti-Stokes gain peaks of each group move to the long-wave direction, and the Stokes gain peaks move to the short-wave direction as the methane gas-sensitive film thickness increases when the hydrogen concentration is constant. The Stokes peaks blueshifted, but the anti-Stokes peaks are redshifted with increasing the hydrogen concentration. The offsets of both all decrease and the linearities also go down. The conclusions what we obtain here are also consistent with those in Fig. 3(a), except for the linearity. Secondly, we study the effects on the sensitivity of methane under the same conditions as those in Fig. 5(a), which is shown in Fig. 5(b). The methane gas-sensitive film thickness and the methane concentration have little effect on the gain peak value, but only the peak wavelengths are changed. The wavelength shifts are illustrated in Figs. 6(c) and 6(d). We find that with the augment of the methane gas-sensitive film thickness, the movement direction of the anti-Stokes and Stokes gain peaks of each group is the same as that in Fig. 5(a) when the methane concentration is constant. However, the movements of the Stokes and anti-Stokes peaks are just opposite to those in Fig. 5(a)  The specific sensitivities vary with the gas-sensitive film thicknesses are shown in Fig. 7. The sensitivities here are just the Stokes sensitivities of methane and hydrogen. It can be concluded that the sensitivity decreases with an increase in the gas-sensitive film thickness. The reason is that the coupling between the evanescent waves of core guiding-light and the external analyte is reduced, which weakens the SPR effect and thus lowers the peak offset of the FWM. The overall sensitivity variations are listed in Table 1. Taking the above factors into consideration, the numerical values, as shown in Table 2, are selected as the optimal structural parameters of the sensor structure.   According to the formula in Section 2, we know that the variations of 2 β , 4 β , and γ will affect the FWM gain curve. The curves of these parameters with the variation of the gas concentration are shown in Figs to 0.024 572 047 W −1 ⋅m −1 , respectively. Through these parameters, we obtain the gain curves of the FWM, as shown in Fig. 9(a). As can be seen, the Stokes peak has a red-shift and the anti-Stokes peak has a blue-shift with the augment of the methane concentration. The specific peak wavelength movements are described in Fig. 10(a). The Stokes and anti-Stokes lines shift from 2 019 nm to 2 031.1 nm and from 1 620.6 nm to 1 612.9 nm, respectively. Figure 10 Figure 9(b) shows the obtained Stokes and anti-Stokes gain curves. In contrast to Fig. 9(a), as the concentration of hydrogen increases, the Stokes peak has a blue-shift from 2 019 nm to 1 976.5 nm and the anti-Stokes peak has a red-shift from 1 620.6 nm to 1 648.8 nm. The sensitivities of hydrogen are 2 14.186 nm / % k = − and 4 9.414 nm / % k = , respectively. Their linearity can also reach up to 99.9%.

Photonic Sensors
In addition, Fig. 10 shows that the variations of the gas concentration and the wavelength shifts of the Stokes and anti-Stokes gain peaks are linear. Hence, the variations of methane and hydrogen concentrations can be measured simultaneously by using a 2×2 sensitivity matrix [24], where We can define a two-dimensional parameter ( ) 4 2 CH H / %, / % C C to represent the gas mixture.
Here, we select ( ) 0.6%, 1.5% as the initial state and ( ) 1.8%, 2.5% as the final state to verify the feasibility of the proposed measurement method. Figure 11 shows the FWM gain spectra of the initial and final states. The Stokes peak blueshifts and the anti-Stokes peak redshifts with increasing methane and hydrogen concentrations. From Fig. 11, we can obtain In addition, the resolution of the dual-parameter sensor proposed in this paper can be defined as (13) [25], where C Δ demonstrates the variation of the methane or hydrogen concentration, min λ Δ is the minimum spectral resolution of 0.1 nm, and peak Δλ is the resonance wavelength shift. When the concentration of methane or hydrogen changes by 0.05%, the calculated methane and hydrogen resolutions are (13) Table 3 shows some sensors based on the photonic crystal fiber published in recent years. By comparison, the D-shaped PCF-SPR sensor proposed in this paper has obvious advantages in terms of both the sensitivity and linearity. Meanwhile, this is a new study of FWM gas sensing combined with the SPR effect in the non-silicon D-PCF, expanding the gas detection method.

Conclusions
Many traditional D-PCF sensors adopt the loss spectrum analysis method, which needs to be combined with other methods (coupling or interference method) to realize double-parameter detection. Since the transmission loss of the quartz fiber is larger in the near infrared region, we propose a tellurite PCF-SPR methane and hydrogen sensor based on the FWM effect. We use tellurite glass as the substrate, and plate the gold film and hydrogen-sensitive film onto the polished surface of the D-PCF. Then, we select another air hole of the inner cladding to be coated with the gold film and methane-sensitive film to form the second sensing channel. The peak shifts of the Stokes and anti-Stokes spectra caused by the variation of the gas concentration can be measured by the FWM effect, and the concentration of methane and hydrogen in the mixed gas can be accurately measured. It is found that the SPR effect can increase the peak shifts of the Stokes and anti-Stokes spectra and enhance the gas sensitivities. In addition, the peak displacements of the Stokes and anti-Stokes spectra are basically unchanged as the fiber length shortens, which is conducive to the construction of compact or ultra-compact embedded FWM sensors.