High-sensitivity temperature sensor based on photonic crystal ber fully coated with gold and PDMS lms

This paper presented a high-sensitivity temperature sensor based on photonic crystal fiber fully coated with gold and PDMS films. For the convenience of production, gold film is coated outside the fiber cladding, and it is used to excite the surface plasmon resonance (SPR) effect. In addition, the temperature response has been effectively improved by depositing poly-dimethylsiloxane (PDMS) layer outside the gold film. This fully coated structure on the outside of PCF enables temperature-sensitive medium to be in direct contact with the environment, which reduces the difficulty of internal coating and filling. The influences of the parameters on the sensing characteristics are investigated by using the finite element method (FEM). Simulation results show that the average temperature sensitivity is up to 9.287nm/°C in the range of -20°C-40°C. Moreover, compared with other designs, the optimized process of structure in this study provides an effective method, which shows a wide application prospect to overcome the difficulty of filling liquid in the air holes.


Introduction
Photonic crystal fibers (PCFs), also known as microstructured fibers that have various air holes extending along the fiber in its cross section [1][2][3]. PCFs have been extensively applied to sensors [4], filters [5], lasers [6], and other optical devices due to the flexible structural design and many distinctive characteristics [2]. Since the distinguished performance of surface plasmon resonance (SPR) technology in the sensing domain, SPR technology has been combined with PCFs to increase the function of this fiber [7]. Compared to conventional fiber sensors, SPR-PCF sensors are obviously optimized in terms of cross-sensitivity and coupling loss. In addition, it has qualities of wide operating wavelength range, high sensitivity, and multi-parameter measurement [8][9][10].
Owing to surface plasmon polaritons are sensitive to the external environment and easily changing transmission constants of sensor, SPR-PCF sensors have aroused tremendous interest in temperature measurement, medical diagnostics and more [10].
Temperature measurement plays an indispensable role in industrial production, environmental monitoring and other fields.
At present, electrical temperature sensor has been developed and matured. But as technology advances, fiber temperature sensor based on combination of fiber and metal has attracted people's attention. Fiber temperature sensors have gradually substituted electrical temperature sensors because of its preponderance of long-distance transmission and design flexibility. In 2014, Yang et al. [11] proposed and experimentally demonstrated a PCF temperature sensor based on SPR, which achieves temperature sensing by filling PCF with silver nanowires and liquid. Experimental results show that the sensitivity was -2.08nm/°C, whereas the operation procedure for filling in PCF was cumbersome. In 2015, Zhao et al. [12] presented a PCF-SPR sensor for temperature detection by using a temperature-sensitive liquid as an intermediate and combined with fiber SPR structure. The sensing element is fabricated by packaging a silver-coated fiber probe into a capillary filled with thermosensitive anhydrous ethanol. This proposed sensor achieves the sensitivity of 1.5745nm/°C between 35-70°C. In 2016, Luan et al. [13] presented a SPR sensor, which can simultaneously realize refractive index (RI) and temperature sensing in an exposed-core microstructured fiber. Two orthogonal passageways coated with silver layers are designed in cladding air holes, one of which is filled with thermosensitive liquid to distinguish the variation of analyte RI and temperature.
The corresponding sensitivity was 6.18nm/℃ as the temperature changed from 26 to 43°C. The same year, Lu et al. [14] accomplished sensing by filling liquid crystals into a hollow-core fiber which was coated with a gold film on the inner wall. The sensitivity was 4.72nm/°C in the range of 20 to 34.5°C. Subsequently, Zhu et al. [15] proposed a novel PCF sensor by combining SPR principle with defect coupling mechanism. Two air holes are determined in cladding, metal films are deposited on one of inner surfaces while the diameter of the other air hole is changed. Magnetic fluid material is filled in these two air holes. By analyzing the relationship between RI of magnetic fluid with its temperature and magnetic field, simultaneous sensing of temperature and magnetic field are realized. Liu [16] presented a new core-cladding symmetrical structure PCF in 2019, which fills all air holes of a group of core-cladding with ethanol. Temperature measurement is achieved due to RI of ethanol changes with temperature.
Simulation results show that the sensitivity of 1cm fiber meets 3.21nm/℃ in the area from 20 to 25℃. According to previous studies, most existing fiber temperature sensors selected to be filled with temperature-sensitive materials in PCF. Since infiltrating liquid into air holes or coating metal on the inner wall is comparatively inconvenient in practical approach, fabrication of sensors described above is rather complicated. In addition, filling media are mainly alcohol, benzene or liquid crystal. These materials respond significantly to changes in temperature but poisonous and volatility, which is not conducive to preservation and recycle of sensors. In order to surmount the above problems, this study chooses to wrap the double-layer membrane immediately outside PCF, which reduces complexity of the structure and is more sensitive to external surroundings.
This paper numerically reports a high-sensitivity temperature sensor by using commercial software COMSOL Multiphysics, finite element method (FEM), with anisotropic perfectly matched layers (PML). First of all, SPR material gold is deposited outside PCF cladding with chemical vapor deposition (CVD), owing to its chemical stability and is less likely to be oxidized in presence of temperature sensing medium.
Then, PDMS is wrapped outside the gold film through the curing process, which makes it in direct contact with the environment to be measured and reduce the manufacturing difficulty. By optimizing the parameters, results show that the identification ability of sensor for temperature changes is improved effectively. It's found that the average sensitivity of sensor is 9.287nm/°C, and the maximum can reach 13nm/°C. Finally, the influences of diameters d1, Λ, t1 and t2 on resonance wavelength, loss value and sensitivity are analyzed. Owing to the simple structure and stable performance, the proposed sensor has a chance of actually being manufactured with current technology. The two-dimensional cross-sectional of the proposed PCF is depicted in Fig. 1(a). It consists of twelve air holes arranged in a hexagonal grid. In order to promote the surface plasmons propagate effectively on metal dielectric surface, air holes with two different diameters are designed. The large air holes are placed on both sides parallel to the fiber core while the small air holes are arranged on the upper and lower sides. Consequently, evanescent wave is transferred to gold film through passageways as shown by arrows in Fig. 1(a), which passageways radius is r=7.5µm. The diameters of air holes are represented by d1 and d2, where d1=1.2μm, d2=3μm; Ʌ represents the horizontal distance between adjacent small air holes, which was determined to be 2.5µm; A gold layer with diameter of t1=35nm is used as plasmonic material, which is deposited outside the PCF cladding by CVD method; Symbol t2 expresses the thickness of sensing medium PDMS, which is wrapped on top of the gold surface and it is considered to be t2=1.1µm; The proposed PCF is practically realizable through stack-and-draw fabrication means because of its simple structure. By commercial software COMSOL Multiphysics to investigate sensing properties of the proposed PCF. Fig. 1(b) indicates the meshing of the calculation region for optimized structure. To guarantee the computational accuracy, PML and scattering boundary condition are increased.

Structural design and theoretical analysis
Pure silica is the background material of PCF whose dispersion coefficient is calculated by the Sellmeier equation Here, n is the refractive index of fused silica, which is decided by incident light wavelength  in vacuum. B1, C1, B2, C2, B3, C3 are known as Sellmeier constants.
The dielectric constant of gold is described by the Drude-Lorentz formula [18] : where εm expresses the permittivity of gold, and ε∞=5.9673 is the permittivity at high frequency. ω=2c/ indicates angular frequency of guided light where c is the velocity of light, ωD=2×2113.6 THz refers to plasmon frequency, and D =2×15.92 THz represents the damping frequency. ∆ε=1.09 can be interpreted as a weighting factor, ΩL=2×650.07 THz and ГL=2×104.86 THz are frequency and spectral width of the Lorentz oscillator, respectively.
PDMS is silicone material with unique optical properties extensively applied to optical field, which has excellent qualities of wide operating range, non-toxic and chemically stable [19]. It has high thermo-optic coefficients and is sensitive to where the units of α are dB/cm.  is wavelength in vacuum and Im(neff) represents virtual part of the effective refractive index.
The capability of sensor can also be reflected by sensitivity, which can be calculated by wavelength interrogation method as follows [24] : Here, ∆λpeak represents the distance of resonance peak shift and ∆T indicates the amount of temperature change.
As shown in Fig. 2, experimental setup for realize temperature sensing mainly includes the following three parts: broadband light source (BBS), temperature control chamber and optical spectral analyzer (OSA). BBS is used to transmit light into single mode fiber (SMF) and couple with PCF-SPR sensor.
Then the sensor responds to temperature by changing the temperature of surroundings with temperature control chamber.
Finally, transmission spectrum is tracked and displayed by OSA.
Temperature changes will lead to variations in RIs of PDMS.
Since different RIs will change the phase matching condition of fundamental mode and SPR mode result in loss peak shift. Therefore, temperature measurement is achieved by analyzing the relationship between temperature variation and resonance wavelengths drift.

Results and discussions
A. Influences of different parameters on sensing characteristics In this segment, the influences of structural parameters d1, Ʌ, t1, and t2 on loss values, sensitivity and resonance wavelengths are discussed.   Fig. 3(b). It can be seen from Fig. 3(b) that when d1 is fixed, resonance wavelength blue-shifts with increase of temperature. Average sensitivity is obtained about 8.291nm/°C, 8.807nm/°C, 9.568nm/°C, 10.354nm/°C, 11.507nm/°C, respectively, with the d1 increased from 0.8µm to 1.6µm.
Increasing d1 is instrumental in improving sensitivity, while half-peak width tends to wider and the shape of spectrum is too smooth. Therefore, d1=1.2µm is the optimal value by considering the confinement loss and wavelength sensitivity.   Fig. 4(b). The maximum wavelength sensitivity of 10.781nm/°C is obtained at Ʌ=2.3µm, while the corresponding confinement loss is not conducive to practical application. All in all, by considering the peak loss and sensitivity Ʌ is determined to be 2.5µm. As observed in Fig. 5(a), the confinement loss depends on operable wavelength by changing t1. The confinement loss decreases and the resonance wavelength red-shifts as t1 increases. Since the effective refractive index of fiber core remains invariant, while the effective refractive index of SPP mode varies with t1, which results in the shift of coupling position between two modes. The thickness of metal film will influence the decay rate of evanescent wave and spp mode.
Thicker gold layer is responsible for loss value decreases and half-peak width increases. With the increase of gold layer, the energy of evanescent field decreases and confinement loss increases. The thickness of the gold layer also affects sensitivity of sensor, as depicted in Fig. 5(b). As seen in Fig. 5(b), sensitivity increases from 10.452 to 11.093nm/℃ with the gold layer increases from 32nm to 38nm. Taking into account sensitivity and confinement loss, t1=35nm is determined as the optimum gold layer thickness of the sensor. The effect of varying sensor parameter t2 on loss spectrum and sensitivity is illustrated in Fig. 6. Fig. 6(a) indicates that confinement loss increases significantly and blue-shifts as t2 increases. In addition, the half-peak width greatly decreases and the spectral appears sharper. That is because the RIs of PDMS decreases with increase of temperature, which leads to the variation of phase matching wavelength. According to Fig. 6(b), sensitivities decreased from 11.094 to 10.116nm/℃, when the t2 increased from 1.0µm to 1.4µm. In order to improve the sensing performance and meet practical applications, t2 = 1.1µm was chosen as the optimum PDMS layer thickness. Finally the influence of each parameter on sensor performance is summarized, which is illustrated in Table 1.  Fig. 7(b). The equation of the linear fitting is determined as y=1168.28-9.287x, where y and x represent the resonance wavelength and temperature, respectively. The slope K represents the average sensitivity of the sensor from -20°C to 40°C, which is 9.287nm/℃. Linearity R 2 is equal to 0.99114. The maximum sensitivity of the sensor reaches 13nm/℃ in the range of -10℃ ~ 0℃.   (6) where ∆T refers to the temperature variation. The minimum detection accuracy of the spectrometer is ∆min, which is generally taken as 0.1nm. ∆peak expresses the wavelength shift.
The proposed sensor is capable of detecting extremely small temperature changes with an accuracy of 0.01077°C. A detailed comparison of the performance of our work with previous studies based on sensing range and wavelength sensitivity, which is illustrated in Table 3.  Disclosures The authors declare no conflicts of interest.
Ethical Approval Approval was obtained from the ethics committee of YanShan University. The procedures used in this study adhere to the tenets of the Declaration of Helsinki.

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