Simultaneous measurement of temperature and refractive index based on an SPR Silicon core fiber sensor with a fused silica grating design

This paper proposed a fiber sensor based on a Silicon core fiber incorporated with a fused silica grating design. The proposed structure has a high sensitivity in refractive index and temperature variation through theoretical calculation and finite element method simulation. The sensitivities of the refractive index in different polarization directions are 1838.7 and 1949.8 nm/RIU, respectively, within the index range from 1.28 to 1.38 RIU. The temperature range within 15–40 °C has the sensitivity up to 1.6 nm/°C by using ethanol analyte. The proposed fiber sensor can provide a method or a solution for intelligent sensing systems.


Introduction
The sensing application based on the elements of optical fibers has many advantages including the high sensitivity, miniaturization, electromagnetic wave immunity, real-time and remote sensing capability (Addanki et al. 2018;Qian et al. 2018). In these decades, the most popular fiber sensing device included fiber Bragg gratings (FBGs) (Massaroni et al. 2021) and long-period fiber gratings (LPFGs) (Xu et al. 2020) because they were stable and the mature fabricated methods. However, the sensitivity of refractive index (RI) and temperature with fiber gratings were lower than others novel technologies because of intrinsic fiber structure and materials as well as detection mechanisms. Currently one popular fiber sensor consisted of a fiber-based interferometer. There were various types of fiber-based interferometer, such as Mach-Zehnder interferometers (MZI) (Zuo et al. 2021), Michelson interferometers (MI) , Fabry-Perot interferometers (FPI) (Cui et al. 2020), Sagnac interferometers (SI) (Moan et al. 2020), and multiple modes interferometers (MMI) (Lian et al. 2020). Moreover, their sensitivities can be improved via the loss of novel designs owning to their various structures. The primary mechanism of our proposed sensing method is based on the surface plasmon resonance (SPR) (Amendola et al. 2017) in which the surface plasmon polaritons (SPPs) to be excited are electromagnetic waves propagating at the interface between the dielectric and metal layers. In these years, the SPR based refractive index fiber sensor becomes more attractive because of its ultra-high sensitivity than most popular fiber sensors (Zhang et al. 2019;Fan 2019). C. Liu et al. (2020) proposed an ultra-high sensitivity in refractive index sensing up to 35,000 nm/ RIU within 1.26 to 1.38 analyte range, and the sensor was composed of a photonics crystal fiber with indium tin oxide coating film. In 2020, we have demonstrated an SPR sensor incorporated with silicon core fiber with a more comprehensive RI sensing range from 1.25 to 1.6, and the operating wavelength band could extend to 2 µm (Yu et al. 2020). Up to now, there were some research teams have designed the SPR based sensor which was applied for temperature sensing. Han (2021) proposed a using a liquid-filled hollow-core negative-curvature fiber incorporated SPR phenomenon, and the temperature sensitivity was 2.86 nm/°C in the range of 20-40 °C. However, it is necessary to detect the refractive index with temperature simultaneously because of the RI of material changes with the response to temperature variation. For example, the RI of ethanol in 20 and 25 °C were 1.364769 and 1.362852, respectively (Jimenez Rioboo et al. 2009). There is a relationship parameter between the temperature and refractive index to be called as a thermo-optics coefficient (TOC) (Ge et al. 2013). Therefore, the RI measurement without considering the thermal effect may cause the analyte to be misjudged. In 2017, we proposed a complex sensor combined with an FBG and LFPG for RI and temperature detection (Yu et al. 2017). However, the sensitivity of RI and temperature were only 36.808 nm/RIU and 0.3472 nm/°C, respectively. Zhang et al. (2020) proposed a sensor based on a hybrid SPR multimode interference fiber sensor with the RI sensitivity of 2061.6 nm/RIU and temperature sensitivity of 0.038 nm/°C.
In this paper, we theoretically analyzed the performance of an SPR sensor that could detect and analyze both the RI and temperature for an unknown liquid. Our design was based on a silicon core fiber incorporated with a fused silica grating, and the sensitivity of our proposed sensor in RI sensing could reach to 1838.7 nm/RIU and 1949.8 nm/RIU for different polarization directions in the range between 1.28 and 1.38. The temperature sensitivity of 1.6 nm/°C is obtained in the range from 15 to 40 °C, respectively, and regarded to the effect of the structure thermal expansion and TOC for the ethanol analyte. It is higher than that of previous publications (Osifeso et al. 2020;Zhu and Li 2020), which is contributed to the higher thermal expansion and TOC of silicon material used as transmission core. A detailed description of the sensor design and numerical modeling analysis are given in the next section, followed by an interpretation of the influences of several structural variables on the sensor performance. Figure 1a illustrates the cross-sectional view of the proposed grating-assisted surface plasmon resonance sensor, which is designed by a silicon core fiber. The radii both of the silicon core and fused silica cladding of the proposed SCF sensor in the original setting is 0.5 µm (r c ) and 5 µm(r cl ), respectively. The refractive index of the silicon and fused silica can be obtained by Sellmeier equation as shown in Eq. (1) and (2), respectively (Salzberg and Villa 1957):

Model design and analysis
and (Han et al. 2021) Here T is the temperature in °C, and λ is the free-space wavelength in µm. In addition, the gold film is used as the dielectric interference for SPR, and the dielectric constant ε of gold can be described by the Drude model and written as follows (Peng et al. 2012): where ω c is the collision frequency, ω p is the plasma frequency, and ε ∞ is the absorption peaks at high frequency (ω ≫ ω c ). In our simulation case with gold, the parameters ω c , ω p and ε ∞ were 1.45 × 10 14 Hz, 1.3659 × 10 16 Hz and 9.75, respectively, which were fitted well into the experimental data in ref. (Johnson and Christy 1972). The plasma frequency is related to the temperature due to the thermal expansion, which can be written as (Lin et al. 2009) where T 0 is the room temperature (25 °C), ω p0 is the plasma frequency at T 0 , α v is the thermal volume expansion coefficient of metal. T is the real-time temperature, and our initial (2) n 2 ( , T) = 1.31552 + 6.90754 × 10 −6 ⋅ T + 0.788404 + 23.5835 × 10 −6 ⋅ T 2 2 − 0.0110199 + 0.584758 × 10 −6 ⋅ T setting was 25 °C. In addition, we set two ways to make sure the outcome of a convergence test. Firstly, a perfect matching layer (PML) with 1 µm thickness is added to the outer computational region surrounding the analyte. Secondly the scattering boundary conditions at the outer boundary of PML are set. The meshing is a vital parameter to precisely investigate the simulated mode profile, and Fig. 1b shows our proposed sensor structure in the meshing map. The whole section of our proposed structure is divided into many triangular domains. The maximum triangular sizes in each area are 0.05 µm (silicon core), 0.06 µm (fused silica) cladding, 0.03 µm (Au coating film), 0.3 µm (analyte), and 2 µm (PML), respectively. The proposed sensor mesh consists of 125,380 domain elements, 5488 boundary elements, and the total number of mesh elements of 862,081. Higher number mesh elements are better for the numerical simulation, which indicates the computational area is divided into the small region to get the result more accurate. The fabrication process of the proposed fiber sensor is shown in Fig. 2. First, we need to prepare a silicon core and fused silica cladding fiber. Up to now, there are two fabrication methods for silicon core fiber including the research team fabricated semiconductor material-based core fiber by using the chemical vapor deposition method (CVD) in 2006 (Sazio et al. 2006) and Ballato et al. fabricated the first silicon core fiber by using a high-speed and high-volume-fiber drawn technique which is called the molten core (MC) method in 2008 (Ballato et al. 2008). So far, the applications of SCF are already becoming more and more popular and useful, such as nonlinear optics effect ) and in-line Schottky photodetectors (Lu et al. 2021) etc. In the second step, the D-shaped side polishing can be achieved using a micrometer-level metal V-shaped groove (Chen et al.

Fig. 2
Steps in the fabrication process.
Step 1: Prepare one silicon core fiber.
Step 2: D-shaped side polished on silicon core fiber.
Step 4: Ultra-thin Au coating on fused silica grating 2014) and combining a grinding wheel with abrasive paper (Luo et al. 2021) in which the depth of D shaped is taken with 0.5 µm above the core, which the mentioned methods could achieve. The third process is the fused silica to be etched periodically. In our simulation, the original design of the grating period (Λ) and depth of grating (D G ) are 1.3 µm and 0.25 µm, respectively. So far, there are many methods and techniques to fabricate the fused silica-based grating period with around 1-µm and to be lower than 100 nm surface quality by using the dry etching and laser-assisted etching (Kotz et al. 2019). In 2007, the authors demonstrated the dry etching technique to achieve the fused silica etching with period 0.89 µm and depth 2 µm (Wang et al. 2007). The final process is to achieve the ultra-thin gold film coating. In our article, the proposed fiber sensor achieved only 2 nm ultra-thin Au film coating. Although it was very challenging to fabricate a metal thin film of only 2 nm thick, the low-pressure chemical vapor deposition (LPCVD) method is still used technique (Luhmann et al. 2020).

Results and discussion
Theoretically, the resonance coupling between core modes and SPP modes can be occurred if the fundamental part of effective RIs [Re(n eff )] is matched. In addition, the resonance is also characterized by a prominent peak of the core mode loss spectrum, which indicates the most significant energy transfer from the core mode to the SPP mode. Figure 3a shows the n eff of the core mode and the surface plasmon polariton (SPP) mode with X-and Y-polarization direction when the analyte is Ethanol (C 2 H 5 OH). The confinement loss can be calculated from the imaginary part [Im(n eff )] of the effective RI by using Eq. (5) (Hassani and Skorobogatiy 2007) λ is the free-space wavelength of incident light in µm. The confinement loss curve is shown in Fig. 3a with red solid and dash lines, and the green and blue line with solid and dash represent the dispersion relationship which were the real part of RI of core mode (5) dB ∕ cm = 8.686 × 2 ⋅ Im n eff × 10 4 Fig. 3 a Dispersion relationship and confinement losses of the core mode and SPPs mode for an analyte refractive index of Ethanol. Calculated electric field distributions and effective refractive indices of (b) X-polarization direction core mode, b Y-polarization direction core mode, c X-polarization direction SPP mode, and d Y-polarization direction SPP mode at the 2.3-µm operating wavelength. (The white arrows represent the direction of the electric field) and SPP mode in different polarization direction, respectively. The resonance peaks of Xand Y-polarization direction are located at 2301.6 and 2298.6 nm, respectively, where the fundamental part of the n eff of the core modes and that of the SPP modes in corresponded polarization direction are matched. The peaks are the excited resonance wavelength due to the energy to be transferred into the SPP mode from the core mode. The electric field distributions of the modes with 2.3 µm operating wavelength are shown in Fig. 3b-e. In Fig. 3b and c, display the core modes at resonance wavelength for X-and Y-polarization direction, respectively, where some of the electromagnetic (EM) fields were leaked out and interact effectively with the plasmonic metal and analytes. On the other hand, Fig. 3d and e depict the SPP mode in which EM fields interact mostly around plasmonic metal. In addition, the white arrows in Fig. 3b and c represent the direction of the electric field because the arrow direction of Y-polarization points to the sensing medium directly and the confinement loss of Y-polarization is more significant than that of X-polarization. However, the difference of confinement loss between X-and Y-polarization in our proposed design was still acceptable for sensing application. At the resonance wavelength of 2.3 µm, the core mode and SPP mode are mixed, which implies that a portion of core mode energy is penetrated in the SPP mode. When the refractive index of analyte (n a ) is varied, the Re (n eff ) of core mode and SPP mode would also is varied to cause the shift of the resonance wavelength. According to the phenomenon, the n a variation can be detected by measuring both the X-and Y-polarization resonance peak shifts. Figure 4 represents the confinement loss versus the wavelength in X-and Y-polarization directions of the proposed sensor with different analytes. To confirm the theoretical simulation results close to the reality, five different liquid models are used for the refractive index sensing simulation including the water (Hale and Querry, 1973) (Hale and Querry 1973), Methanol, Ethanol, Propanol and Octane (Myersm et al. 2018). From the loss curve of X-polarization direction in Fig. 4a  (1.379@2.37 µm). The loss around the resonance peak wavelength of the Y-polarization direction is about 4.73 to 5.05 times higher than that of X-polarization, which still could be acceptable for sensing applications. According to the results, the relationships of n a between resonance peak of the X-and Y-polarization can be written as where λ x and λ y are the resonance peak of the X-and Y-polarization direction, respectively. Sensitivity is also a vital issue with measuring sensor's performance. It can be calculated by using the following formula.  where Δλ peak is the wavelength peak shift, and Δn a is the variation of the analyte's refractive index. In the proposed fiber sensor, the spectral sensitivities are 1838.7 and 1949.8 nm/ RIU of X-and Y-polarization direction. The relation gives the resolution of the proposed sensor.  where Δn a is the variation in the RI of the analyte, Δλ min is the minimum spectral resolution, and Δλ peak is the resonance peak shift. As we take the Δλ min of 0.1 nm, the calculated resolution of the proposed in X-and Y-polarization direction are 5.3935 × 10 -5 and 5.1718 × 10 -5 RIU, respectively, which can be employed in the capability of the proposed sensor for detecting a slight change in RI of the analyte. In addition, we have replaced the gold coating film with silver. According to our simulation records, the best performance of sensitivity in refractive index was only around 1.2 µm/RIU. Therefore, we did not consider using the silver coating film in the rest research parts. Figure 5 shows the resonance wavelength shift versus refractive index with different materials of analytes and r c . We can see that as r c is decreased to 0.45 µm, the sensitivity would be increased up to 2.5 µm/RIU. However, the smaller r c has a lower guiding ability which means more energy to be leaked. As shown in the inset of Fig. 5, the loss spectrum with r c of 0.45 µm becomes worse when the n a is increased up to around 1.36 (> 21 nm). The worse shape of the loss spectrum would cause the misjudgment during detection. By referring to our previous research results, the thickness of coating film (2 nm) and D-shaped depth (0.5 µm) (Yu et al. 2020), the Λ of 1.3 µm and D G of 0.25 µm are designed in this part. In addition, in our simulation records, there is not noticeable difference when the cladding radius of fused silica is increased up to 62.5 µm. Therefore, the r cl of 5 µm is set for reducing the simulation cycles. Figure 6a and b show the proposed fiber sensor's loss spectrum with different temperatures in X-and Y-polarized directions for Ethanol analyte (n a ). The simulation results show that the resonant wavelength is shifted toward a shorter wavelength and the peaking loss is decreased as the temperature increases. In X-polarized cased, when the temperatures is varied from 15 °C and 35 °C, the peaking losses at resonant wavelengths of 2.305, 2.3182, and 2.2846 µm are 34.25, 32.76, and 35.97 dB/cm, respectively. The main factor to cause the wavelength shift and variation of peaking loss is the TOC of each material, in which a temperature variation is usually accompanied by an appreciable modification of the refractive index n due to the TOC. Here, the TOC of Ethanol is − 3.94 × 10 -4 /°C (Osifeso et al. 2020). For Au and fused silica, it can be respectively calculated by using Eq. (2) and (4) and TOC of Si can be obtained from ref. (Frey et al. 2006). In addition, the structure of device is affected from temperature varied. In general, the volume will be expanded as temperature increased or shrinked as temperature decreased. The linear thermal-expansion coefficients of silicon, fused silica, and gold are 2.6 × 10 -6 , 0.4 × 10 -6 , and 14 × 10 -6 , respectively. The thermal expansion of the analyte can be neglected because it is a liquid in our proposed application. In order to explain the mechanics issue which induced from thermal effect, we used the concept of von Mises stress which could provide the information of external force applied on the device, e.g. temperature or pressure (Urban et al. 2010;Osunluk et al. 2020). The Fig. 6c and d show the distribution of von Mises stress for the temperature to be increased from 25 °C to 35 °C and is decreased from 25 °C to 15 °C, respectively. The von Mises stress at the central point of silicon core is 2.25 × 10 6 N/m 2 . As the temperature sensitivity is a critical parameter of a temperature sensor, it can be given by Osifeso et al. (2020) where Δλ peak is the resonant wavelength shift and ΔT is the temperature variation. For the above given parameters, as the temperature is varied from 15 to 40 °C, the sensitivities in X-and Y-polarization direction are 1.601 and 1.622 nm/°C, respectively. Figure 7 shows the S T distribution when the Λ and D G are changed from 1.1 to 1.5 µm and 150 to 350 nm, respectively. From this figure, we can see that the period of 1.3 µm and depth of 250 nm for the grating has the best performance in S T . Both of X-and Y-polarization directions of S T values can reach up to 1.6 nm/°C. It is worth mentioning that the sensitivity is higher than those of most previous publications for sensing the Ethanol analyte.
In order to confirm the temperature sensing performance, both the methanol and propanol liquids with the TOC of 4.3 × 10 -4 and 4.0 × 10 -4 /°C (Bauld et al. 2018) respectively are tested. Figure 8 (a) and (b) illustrate the temperature sensing performance in polynomial fitting curves with the different polarization directions and analytes in the temperature range from 15 °C to 40 °C. The R-squared of the fitting curve is around 0.994. The S T of methanol in both X-and Y-polarization are 1.616 and 1.64 nm/°C, and for the propanol the S T values are 1.608 and 1.628 nm/°C, respectively. Thus the higher the TOC, the higher the S T for a testing liquid. It needs to mention is that there are overlap sections about 5 nm wide in the lower temperature of ethanol and in the higher temperature of propanol. However, the temperature difference in this section is more than 18 °C for improving the misjudgment.
According to the results, the relationship between temperature and resonant wavelength in the different analytes and polarization directions could be written as the T is the environmental temperature in the range from 15 °C to 40 °C for the most common temperature in interior space in the world. The resolution of temperature measurement is also an important performance when this sensor detected the temperature tiny variation, and it can be expressed as where ΔT is the temperature difference, and Δλ min and Δλ peak are the same as those of Eq. (8). By using Δλ min = 0.1 nm, the resolution was around 0.06 °C in three different liquids. For neglecting the TOC and the ethanol analyte, Eqs. (6), (10), and (11) are combined to obtain an equation for theoretically calculating both the RI and temperature simultaneously. It can be derived as where Δn is the variation of the RI and ΔT is the variation of the temperature, and the η nx , η Tx , η ny and η Ty are the sensitivity both of refractive index and temperature in X-and Y-polarization directions, respectively. Meanwhile, the theoretical wavelength shift caused by the variation of RI or temperature can be calculated by using Eq. (13). For the given values both of RI and temperature sensitivities, inverse matrices of Eq. (13) can be derived as For relating to the issue of TOC compensation, Y. Zhang had already discussed and mentioned in Osunluk et al. (2020). There are two advantages of using our proposed fiber sensor. Firstly, from measuring two resonant peak wavelengths in the different polarization directions, the temperature and unknown liquid by referring to Fig. 8 the unknown liquid can be confirmed. Secondly the temperature is varied to obtain the fitting curve of resonant wavelengths in different temperatures for calculating the unknown TOC. Finally, the performance comparison between the proposed fiber sensor and the previously reported literatures is indicated in Table 1, including the applied wavelength, sensitivities and ranges of refractive index and temperature sensing.

Conclusion
An SPR fiber sensor based on an SCF and fused silica grating design is proposed in this paper. The sensitivity of RI of liquids is firstly analyzed in the index range between 1.28 to 1.38. For the ethanol, the index sensitivities are 1838.7 and 1949.8 nm/RIU in two different polarizations respectively. Secondly, the temperature measurement is theoretically calculated to analyze the thermal influence on the performance of our proposed fiber sensor. Considering the thermal expansion of structure and the TOC of the analyte, the temperature sensitivity of 1.6 nm/°C can be obtained. In addition, we derive a relationship equation between the resonant wavelength peak shift, temperature, and RI variation and to investigate the sensor performance. It can provide a reference for the implementation and application of SCF-based SPR sensors in the intelligent sensing systems.