A highly sensitive dual-core D-Shape photonic crystal �ber based on surface plasmon resonance for methane sensing

This paper presents a gas sensor that uses surface plasmon resonance (SPR) technology and a novel D-type photonic crystal �ber (PCF) structure to detect methane. The sensor's double-sided, side-polished gas holes are the key components for achieving large-area contact with external methane gas. The coating material chosen to stimulate the SPR effect was a gold nanolayer. To increase the sensitivity of methane gas detection, the researchers used polysiloxane-doped cryptane E as a coating material. The study analyzed the sensor characteristics using �nite element analysis (FEA) and numerical analysis to examine the effect of optical structure parameters on the sensor performance. The numerical results demonstrate that the sensor has a sensitivity of 11.52 nm/% and a FOM value of 0.409 when measuring methane gas in the concentration range of 0–3.5%. The curve �tted shows excellent linearity. The sensor is a promising technology for the future development of gas leakage detection due to its low cost, simplicity, and real-time detection capability.


Introduction
Accurately detecting methane gas leaks and determining their concentration is critical to both the mining industry and environmental monitoring.However, due to the ammable and explosive nature of methane, traditional electrical methods are not always feasible [1].Fiber optic sensors have been developed for methane detection due to their unique properties, including fast response time, small size, resistance to electromagnetic interference, exible structural design and the ability to be monitored remotely in real time [2,3].In addition, a variety of ber optic sensors based on different optical principles, such as long period ber grating sensors and interferometric ber optic sensors, have been proposed for methane gas detection [4,5].Among them, long period ber grating sensors have attracted much attention due to their exible long period ber grating structure and excellent sensing performance.For example, Yang et al. designed and applied a novel long-period ber grating (LPFG) thin-lm methane sensor with a sensitivity of 0.30 nm/% and a detection limit as low as 0.2% [6].There is also a class of sensors based on the principle of light interference, which detects environmental changes by measuring the phase change of light waves.Wang et al. investigated a modi ed D-type PCF methane sensor based on Sagnac interference, which had an average gas sensitivity as high as 36.64 nm/% over a detection range of 0-3.5% [7].However, the sensitivity of these two types of ber optic sensors can be affected by environmental factors such as temperature variations, light intensity variations leading to measurement instability and errors.
Surface plasmon resonance (SPR) ber optic sensors make use of the surface plasmon resonance phenomenon on metal surfaces to detect the resonance angle changes caused by the substance to be measured in the sensitive region in real time by monitoring the interaction between the incident light and the metal surface, thus realizing highly sensitive real-time monitoring of biomolecular interactions, an effect that has been widely used to monitor refractive indices, gas concentrations and other sensing parameters.A novel D-type telluric crystal photonic crystal ber optic sensor based on the four-wave mixing (FWM) effect of surface plasmon resonance (SPR) for methane gas concentration measurement was investigated by Hai Liu et al. [8].The maximum sensitivities for methane and hydrogen were 4.03 nm/%, respectively, and the linearity was 99.9% for both.The resolution was 1.25 × 10 − 2 per cent for methane and 7.14 × 10 − 3 per cent for hydrogen [9].Yui et al. developed a PCF-SPR sensor for SiO 2 gas, which consists of a large air hole in the optical ber as the sensing channel.The sensitivity of this sensor for SiO 2 was 1.99 nm/% [10].Wei et al. designed a D-type PCF-SPR sensor using gold nanorods to excite the SPR in methane detection, which was able to detect an average wavelength sensitivity of 4.26 nm/% at a higher wavelength range of 1.8 to 2.3 µm wavelength [11].Ranju Sardar et al. found out a hollow core photonic crystal ber (HC-PCF) based gas sensor for monitoring carbon dioxide (CO 2 ).This optimal design provides the relative sensitivity of 93.5% with a con nement loss of 0.004 dB/m at λ = 2.65 µm the absorption wavelength of CO 2 [12].Bikash Kumar Paul et al. presented a novel shape photonic crystal ber based on gas sensor for the rst time.Numerical simulations evidences that the sensor shows the sensitivity responses of 64.69% and con nement loss of 4.38 × 10 − 6 dB/cm at the transmission wavelength k = 1.55 mm [13].Overall, the proposed methane sensor demonstrates higher gas sensitivity and lower cross-sensitivity effect, and provides a new design idea for the methane gas monitoring.
A well-designed PCF structure can enhance the coupling between the core mode and the surface plasmon polariton (SPP) mode, thus improving the sensing performance of PCF-SPR sensors.It is important to note that the plasmonic material plays a crucial role in determining the properties of these sensors [14].
Furthermore, various PCF-SPR structures, including dual-core and triple-core PCFs, dual-slot PCFs, and Vshaped PCFs, have been studied.Xianli Li et al. have designed a dual-resonant, peaked SMF SPR gas sensor with a V-shaped slot for the highly sensitive detection of methane.The SPR sensor can simultaneously operate on two transmission bands with maximum wavelength sensitivities of 12 nm/% and 8 nm/%.The corresponding resolutions are 0.0083% and 0.013%, respectively [15].The detectable refractive index range and sensitivity of the sensor are determined by the plasmonic material.Compound lms such as AuTiO 2 , AuMgF 2 and AuTaO 5 have recently been used as plasmonic materials.Ai Hosoki et al. have developed a novel hydrogen sensor based on ber optic surface plasmon resonance (SPR) technology.The cylindrical cladding surface is uniformly coated with AuTaO 5 and palladium (Pd).The SPR sensor showed a change in transmission loss of 0.23% and a response time of 15 seconds for 4% hydrogen when using 25 nm Au, 60 nm AuTaO 5 , and 3 nm Pd multilayer lms [16].However, the ber optic gas sensors described above generally suffer from low wavelength sensitivity or relatively narrow detection limits.Therefore, it is di cult to detect gas concentration in complex environments.
In this study, a new dual-core D-shaped photonic crystal ber (PCF) for methane sensing was designed.It is a special PCF structure with rotational symmetry, which is coated with a gold lm and polysiloxanedoped cryptane E on its attened D-shaped surface.As a result, the SPR effect is enhanced and the sensing performance is improved.The optimal structure and materials resulted in an average wavelength sensitivity of 11.52 nm/%, almost double the previously reported value.

Geometric construction
The cross-section of the proposed double approved D-shaped PCF-SPR sensor is shown in Fig. 1.The PCF-SPR sensor consists of two layers of equally spaced stomata, with the center being a dual-core structure split by three small stomata to form two symmetric cores.The air holes on the left and right sides are lled with a gold lm with a thickness of t 1 and t 2 represents the thickness of the methane gas sensitive lm.The methane gas-sensitive lms were selected from polysiloxane-doped cryptane E. The radius of the silica cladding is denoted by r, and the polishing depth is denoted by h.The thickness is denoted by t 2 .The spacing between pores is denoted by p, and the thickness of the perfect match layer is 1 µm.The parameters initially chosen were t 1 = 30 nm, t 2 = 1µm, d 1 = 1.2 µm, d 2 = 1.5 µm, h = 7.5 µm.The PCF has a six-fold quasicrystalline structure consisting of square triangles and squares.
The PCF preforms can be fabricated by laser punching or 3D printing, and at d-shaped planes can be fabricated by side polishing methods.The distance between the polished surface and the center of the PQF is h.Gold (Au) is a plasma medium that can be easily plated on the polished surface by magnetron sputtering or chemical vapour deposition (CVD).Finally, polysiloxane-doped cryptane E methane-sensitive lm is coated on the outer surface of the Au lm using a capillary dip coating technique.The thicknesses of the Au lm and the methane-sensitive lm are t 1 and t 2 , and the outermost layer is a perfect matching layer (PML).

Parameters
The PCF-SPR can be fabricated by the stacked stretching method and the double stretching method.A gold lm is deposited on the inner wall of the anti-resonator tube by high-pressure chemical deposition.
Polysiloxane-doped cryptane E can be fabricated by the capillary dip coating technique.In addition, coating can be achieved by sol-gel schemes.
The refractive index of polysiloxane-doped cryptane E at room temperature versus methane concentration C_CH 4 can be determined by the following equation [19]: 3 The response time of the sensor is determined by the methane-sensitive material, which has an adsorption time of 90 s and an analysis time of 300 s.The performance of the sensor is measured by the con nement loss, as shown in Eq. [20]: where Im(n eff ) is the imaginary part of the effective refractive index of the core mode.

Simulated experimental setup
Based on the description of the above principles and equations, we designed the experimental setup shown in Fig. 2. The complete optical system consists of a light source device, a spectral detection device and a transmission optical path.The broadband light source (BBS) is selected for the light source device.The optical signal is processed by the Optical Spectrum Analyzer (OSA), which quanti es and displays a graph of the optical light source in a given wavelength range.The ber optic coupler, also known as the splitter, splits the optical signal from one optical ber into a number of optical ber components.As a link, the transmission light path passes through a single mode ber (SMF), a solid core anti-resonance ber (PCF-SPR) and another SMF, and the nal optical signal is output.
The Variable Optical Attenuator (VOA) is an important passive optical component in ber optic communications, allowing real-time control of the signal by attenuating the transmitted optical power.
The SMF and PCF with bare ber adapters are mounted on two six-axis optical stages with a pitch of 40 µm.Experiments have shown that the process can be carried out on the PCF-SPR.The sensors are released into a gas chamber and the concentration of a mixture of nitrogen and methane entering the chamber is Mass Flow Control (MFC).
3 Modeling and analysis index for the x-polarized core mode and the SPP mode, respectively.At the intersection point, the phase matching condition of SPR is satis ed and the energy of the core mode is coupled to the SPP mode.The physical process is re ected in the electric eld distribution in Fig. 3x-polarized mode loss reaches its maximum value [21].

Principle of the sensor
Figure 3 shows the electric eld distribution of the core mode at 2.34 µm; at the detuning point, the core conduction mode and the SPP mode clearly show a weak coupling.As a result, the loss spectrum shows a single peak [22].The effective refractive index of the SPP mode varies with the external refractive index, and the displacement of the crossing point produces a corresponding shift in the loss spectrum.

Sensor performance
It is crucial for us to judge the performance of a sensor.Figure 4(a) shows the con nement loss spectra of the sensor at different methane concentrations.According to Eq. ( 3), the refractive index of the methane-sensitive lm decreases with increasing methane concentration; therefore, the effective refractive index of the SPP mode decreases, while the change in the nuclear mode is small.
As a result, the phase matching point is shifted to shorter wavelengths, limiting the spectral blue shift of the loss.At the same time, as the methane concentration increases, the effective refractive index difference between the core and SPP modes decreases, increasing the evanescent eld and leading to stronger coupling.The performance of the sensor can be evaluated in terms of wavelength sensitivity as follows [21]: where C_CH 4 denotes the change in methane concentration and λ is the corresponding wavelength shift.
The relationship between resonance wavelength and methane concentration was monotonically decreasing as shown in Fig. 4(b), and the average sensitivity of the linear t for resonance wavelength was 11.52 nm/%.

Gold lm thickness
Fiber cladding diameter, metal lm layer thickness, metal type and sensing region length all have an impact on the sensor performance.When the diameter of the ber core is xed as D core = 10 µm, the diameter of the cladding D cladding = 20 nm, and the length of the sensing area L = 0.1 mm, the sensing model is simulated and analyzed for the gold lm thickness t 1 = 30 nm, 35 nm, 40 nm, 45 nm, and 50 nm in turn.
It can be seen from the change of the loss spectrum in Fig. 5(a)that the position of the resonance peak of the loss spectrum blue shifts with the increase of t 1 from 30 to 50 nm, and the loss intensity decreases continuously, and the resonance effect of the sensor is weakened.From Fig. 5(b), it can be seen that the sensitivity of the sensor is optimal among the ve parameters at a gold lm thickness of t 1 of 40 nm.

Cladding aperture d 1
The effect of small stomata d 1 in the cladding is also critical to the performance of the sensor.Fixed methane gas concentrations of 2.0% and 2.5% were used to classify stomatal diameters d 1 as 1.0, 1.2 and 1.4 µm.As shown in Fig. 6(a), we nd that the loss curves shift towards shorter wavelengths as the gas concentration increases, and then redshift to the right as the stomatal diameter increases.This is due to the fact that the size of the small gas pores affects the loss of nuclear energy in the electric eld. Figure 6(b) shows the curve of the resonance wavelength at different concentrations from 0-3.5%.The sensitivity can be calculated separately from Eq. ( 5) and the maximum sensitivity is 10.21 nm/% at a stomatal d 1 of 1.0 µm.From this it can be deduced that the optimum size for three different stomatal diameters is d 1 = 1.0 µm.

Gas-sensitive lm thickness
Figure 8(a) shows the loss spectra of different cladding hole radii at methane concentrations of 2.0% and 2.5%.When the methane concentration is constant and the cladding hole diameter increases, the loss spectra are blue-shifted and the peaks become larger and larger.The reason for the above phenomenon is that the cladding holes have a large binding effect on the energy of the core mode, preventing the coupling between the core mode and the metal lm [24].Considering d 1 = 1.0 µm, the loss peak is not strong and the full width at half maximum (FWHM) is wider.
A wider FWHM reduces the resolution of the sensing detection.Therefore, the optimal radius is only 1.0 µm [25].The design is not suitable for gas sensing when t 2 = 0.8 µm.Too thin a gas-sensitive lm would cause severe energy leakage and increase losses.In conclusion, 1 µm is the optimum gas-sensitive lm thickness.

Analysis of results
The sensing performance of the proposed SPR ber-optic methane sensor was compared with some reported ber-optic methane sensors, as shown in Table 1.The rst two sensors are based on SPR [26].
Although they can measure two gases, they are not very sensitive.In the LPFG structure, gas sensing using gratings has a fast response time, but its sensitivity is not high.
In the Sagnac interferometer, the interferometric ber-optic methane sensor has the advantage of accurate measurement and high sensitivity.Its disadvantage is that it is strongly affected by temperature, humidity and air pressure and cannot meet the requirements of distributed sensing [27].
Page 9/16 In this paper, a dual-core D-type PCF methane gas sensor based on SPR is designed.A gold lm is deposited on the polishing groove of the optical ber to stimulate the SPR effect.A methane sensitive lm is deposited on the ber polishing groove.The effects of different optical ber parameters on the sensor performance were analyzed.The sensitivities of the sensors were up to 11.52 nm/% at methane gas concentrations ranging from 0-3.5%.The linear ts were all up to 99.8%.The best sensor performance was achieved when t 1 = 30 nm, t 2 = 1 µm, d 1 = 1.2 µm, d 2 = 1.5 µm and h = 7.5 µm.Compared with existing reports, our proposed D-type PCF methane gas sensor is more sensitive and easier to contact with methane gas.Therefore, our designed sensor can be used in methane gas leak detection, coal mining and oil extraction.The sensor is a good example of a D-type PCF gas sensor based on SPR. in revising and re ning the nal paper.Shubo Jiang: is the main sponsor and project leader of this research project.She was responsible for the design of the entire project, the development of the experimental protocol, and the writing of the nal report.She was also responsible for the preliminary analysis and interpretation of the experimental data.In addition, she undertook the task of funding application and management.

λ
The dispersion relation and loss spectrum of the PCF-SPR sensor with parameters r = 8 µm, d 1 = 1.2 µm, d 2 = 1.5 µm, d 3 = 1.8 µm, h = 7.5 µm, t 1 = 30 nm, and t 2 = 1 µm for a methane concentration of 3% are shown in Fig.3.The red solid line and the black solid line indicate the real part of the effective refractive

Figure 7 (
Figure7(a) shows the loss pro les of stomatal d 2 for different claddings at methane concentrations of 2.0% and 2.5%.The loss curves are a red-shifted phenomenon with increasing stomatal d 2 at the same concentration and the resonance wavelengths of the d 2 stomata at 2.0% concentration are 2203 nm, 2336 nm, and 2435 nm, respectively, and the loss also increases with increasing stomata.The curves are shifted to the left at both concentrations.

Figure 7 (
Figure 7(b) shows the tted curves of sensitivity at different stomatal diameters d 2 .The lines of the three tted curves are y 1 = − 10.42x + 2531.64,y 2 = -8.52x+ 2336.89 and y 3 = − 9.14x + 2152.8.The slope of thetted curves for sensitivity at d 2 of 1.5 µm is -8.52 nm/%, which tells us that at d 2 of 1.6 µm is when the sensitivity is maximum, so that d 2 = 1.6 µm is the optimum size[23].
Figure 8(b) shows the numerical tting results of the resonance wavelength versus methane gas concentration.The tted functional relationships are y 1 = − 8.82x + 2318.45,y 2 = -9.07x+ 2314.18, and y 3 = -11.54x+ 2286.68,respectively.as the radius of the cladding pores increases, the sensitivity of the designed sensor increases.

Figures
Figures

Figure 1 Model
Figure 1

Table 1
Comparison of ber optic methane gas sensors