A Temperature Plasmonic Sensor Based on a Side Opening Hollow Fiber Filled with High Refractive Index Sensing Medium

A surface plasmon resonance temperature sensor based on a side opening hollow-core microstructured optical fiber is proposed in this paper. This design employs a gold nanowire to excite the plasmon mode, and can be easily filled with the sensing medium through the side opening of the fiber, which not only simplifies the fabrication of the sensor but can also use the high refractive index sensing medium. The coupling characteristics, sensing performance and fabrication tolerance of the sensor are analyzed by using the finite element method. The simulation results indicate that the maximum sensitivity is 3.21 nm/°C for the x-polarized core mode in the temperature range of 13.27–50.99 °C, and 4.98 nm/°C for the y-polarized core mode in the temperature range of 14.55–51.19 °C, when benzene is used as the sensing medium. The sensor also shows a good stability in the range of ±10% fabrication tolerance.

In these reported MOF-SPR temperature sensors [12][13][14], the sensing medium are filled into the cladding holes of the MOF. In order to maintain the light guiding mechanism of the total reflection, the highest RI of the sensing medium must be lower than the RI of the fiber material. For example, it is usually less than 1.42 in fibers made of silica whose RI is assumed to be 1.45 [12][13][14]. Therefore, these SPR temperature sensors cannot employ some high RI sensing media which have a high thermal coefficient, such as toluene, benzene, liquid crystal materials, etc. [23,24]. Besides, the air hole diameter of the MOF is usually a few microns [12][13][14]. Coating the walls of such small holes with the metal layer and filling them with the sensing medium requires high precision and complicated processes.
To solve the problems mentioned above, we designed a SPR temperature sensor based on a side opening hollow MOF in this paper. So far, the hollow fibers filled with the liquid have demonstrated that they can work effectively when the RI of the liquid is higher than that of the fiber material [25,26].
Additionally, the open-structured MOFs, such as exposed-core MOFs, have also been studied and the liquids can easily be filled into the sensing region [27][28][29][30][31][32]. This design combines the advantages of the hollow fibers and open-structured MOFs, and thus can employ high RI sensing media without the complex filling process. Moreover, the sensor adopts a gold nanowire to excite the surface plasmon polaritons (SPP) mode, which avoids the complex fabrication of the metal coating. We used the COMSOL Multiphysics software to analyze the SPR character and sensing performance of the sensor, and we also discuss sensor stability in the range of ±10% fabrication tolerance.

Structure and Principle
As shown in Figure 1a, the hollow core of the MOF-SPR sensor is surrounded by a double-layered hexagonal array of air holes. The sensing medium and the gold nanowire are filled in the hollow core of the fiber. A slot is cut along the length of the fiber to connect the outside and the hollow core, which can accelerate the filling process of the sensing medium. The slot can be fabricated by some mature technologies such as focused ion beam milling [33,34] or femtosecond laser micromachining [35,36]. Both ends of the sensor can be connected to the single mode fiber (SMF) to access the sensing system for practical experimental testing, as shown in Figure 1b. Sensors 2019, 19, x FOR PEER REVIEW 2 of 10 metal layer and filling them with the sensing medium requires high precision and complicated processes.
To solve the problems mentioned above, we designed a SPR temperature sensor based on a side opening hollow MOF in this paper. So far, the hollow fibers filled with the liquid have demonstrated that they can work effectively when the RI of the liquid is higher than that of the fiber material [25,26].
Additionally, the open-structured MOFs, such as exposed-core MOFs, have also been studied and the liquids can easily be filled into the sensing region [27][28][29][30][31][32]. This design combines the advantages of the hollow fibers and open-structured MOFs, and thus can employ high RI sensing media without the complex filling process. Moreover, the sensor adopts a gold nanowire to excite the surface plasmon polaritons (SPP) mode, which avoids the complex fabrication of the metal coating. We used the COMSOL Multiphysics software to analyze the SPR character and sensing performance of the sensor, and we also discuss sensor stability in the range of ±10% fabrication tolerance.

Structure and Principle
As shown in Figure 1a, the hollow core of the MOF-SPR sensor is surrounded by a doublelayered hexagonal array of air holes. The sensing medium and the gold nanowire are filled in the hollow core of the fiber. A slot is cut along the length of the fiber to connect the outside and the hollow core, which can accelerate the filling process of the sensing medium. The slot can be fabricated by some mature technologies such as focused ion beam milling [33,34] or femtosecond laser micromachining [35,36]. Both ends of the sensor can be connected to the single mode fiber (SMF) to access the sensing system for practical experimental testing, as shown in Figure 1b. The electromagnetic mode of the MOF is studied by finite element method (FEM). The sensor structure parameters are shown in Figure 1, where the lattice constant (Λ) of the MOF is 2 μm. Both the diameter of the air holes (d) and the width of the slot (w) are 0.4 Λ, and the diameter of the gold nanowire (dg) is 200 nm. The opening depth (h) and the core diameter (dc) of the MOF are 2 Λ and 2.6 Λ, respectively. Here, we ignore the material dispersion of the fused silica RI, assuming it is 1.45. The RI of air is assumed to be 1, and the permittivity (ϵ DL ) of the gold can be calculated by the Drude-Lorentz model as [37]: The electromagnetic mode of the MOF is studied by finite element method (FEM). The sensor structure parameters are shown in Figure 1, where the lattice constant (Λ) of the MOF is 2 µm. Both the diameter of the air holes (d) and the width of the slot (w) are 0.4 Λ, and the diameter of the gold nanowire (d g ) is 200 nm. The opening depth (h) and the core diameter (d c ) of the MOF are 2 Λ and 2.6 Λ, respectively. Here, we ignore the material dispersion of the fused silica RI, assuming it is 1.45. The RI of air is assumed to be 1, and the permittivity ( DL ) of the gold can be calculated by the Drude-Lorentz model as [37]: where the parameters and values can be found in Reference [37]. The perfectly matched layer (PML) and the triangular sub-domain are used to match the outmost layer and discretize the computation region, respectively. In order to satisfy the conditions for total reflection and ensure the sensor can work normally, the sensing medium RI used here must be higher than the silica RI. In Figure 2, we present the real part of the n eff [Re(n eff )] curve, loss spectra and the electric field distribution of the correlation mode of the sensor when the sensing medium RI (n) is 1.47. The red dashed lines in Figure 2a,b denote the Re(n eff ) of the xand y-polarized SPP modes excited on the surface of the nanowire. The black solid lines and blue dashed lines in Figure 2a,b represent the Re(n eff ) and loss spectra of the xand y-polarized core modes. As a result, the x-polarized resonance peak is at 1.066 µm (phase matching point C) and the y-polarized resonance peak is at 1.037 µm (phase matching point F). At non-resonance wavelengths, the xand y-polarized core modes are well limited in the core region as shown by patterns A and D in Figure 2c, while the xand y-polarized SPP modes are well limited on the surface of the nanowire, as shown by patterns B and E in Figure 2c. At resonance wavelength, as seen from patterns C and F in Figure 2c, the xand y-polarized core modes show syncretic patterns which means that they are coupled to the xand y-polarized SPP modes respectively, and thus generating the resonance peaks in the loss spectra. If the n is changed by the temperature, the Re(n eff ) of the relevant mode is also changed accordingly, and causes the shift of the resonance peak. Therefore, this mechanism can be used to detect the temperature changes.
where the parameters and values can be found in Reference [37]. The perfectly matched layer (PML) and the triangular sub-domain are used to match the outmost layer and discretize the computation region, respectively. In order to satisfy the conditions for total reflection and ensure the sensor can work normally, the sensing medium RI used here must be higher than the silica RI. In Figure 2, we present the real part of the neff [Re(neff)] curve, loss spectra and the electric field distribution of the correlation mode of the sensor when the sensing medium RI (n) is 1.47. The red dashed lines in Figure 2a,b denote the Re(neff) of the x-and y-polarized SPP modes excited on the surface of the nanowire. The black solid lines and blue dashed lines in Figure 2a,b represent the Re(neff) and loss spectra of the x-and ypolarized core modes. As a result, the x-polarized resonance peak is at 1.066 μm (phase matching point C) and the y-polarized resonance peak is at 1.037 μm (phase matching point F). At nonresonance wavelengths, the x-and y-polarized core modes are well limited in the core region as shown by patterns A and D in Figure 2c, while the x-and y-polarized SPP modes are well limited on the surface of the nanowire, as shown by patterns B and E in Figure 2c. At resonance wavelength, as seen from patterns C and F in Figure 2c, the x-and y-polarized core modes show syncretic patterns which means that they are coupled to the x-and y-polarized SPP modes respectively, and thus generating the resonance peaks in the loss spectra. If the n is changed by the temperature, the Re(neff) of the relevant mode is also changed accordingly, and causes the shift of the resonance peak. Therefore, this mechanism can be used to detect the temperature changes.

Sensing Performance
Here, we adopt benzene as the sensing medium, and its dispersion equation is given as [

Sensing Performance
Here, we adopt benzene as the sensing medium, and its dispersion equation is given as [23]: The temperature-induced change of the benzene RI (n) is evaluated by [12][13][14]: where the thermal coefficient (dn/dT) of the benzene is 7.594 × 10 −4 / • C at the reference temperature T 0 = 20 • C [23]. Here, in order to simplify the calculation method, the thermal coefficients of the gold and the silica are negligible because they are much lower than liquids. Therefore, temperature changes can be assumed to change the n only. To investigate the sensing performance of the proposed sensor for temperature sensing, in Figure 3 we present the loss spectra of the x-and y-polarized core modes at different n affected by temperature changes. Here, as we observe the temperature (T) decreasing, the position of the resonance peak shifts to a shorter wavelength, which is consistent with the phenomena of the hollow MOF-SPR sensors [25,26]. The temperature sensitivity is calculated by [12][13][14]. The temperature-induced change of the benzene RI (n) is evaluated by [12][13][14]: where the thermal coefficient (dn/dT) of the benzene is 7.594 × 10 -4 /°C at the reference temperature T0 = 20 °C [23]. Here, in order to simplify the calculation method, the thermal coefficients of the gold and the silica are negligible because they are much lower than liquids. Therefore, temperature changes can be assumed to change the n only. To investigate the sensing performance of the proposed sensor for temperature sensing, in Figure 3 we present the loss spectra of the x-and y-polarized core modes at different n affected by temperature changes. Here, as we observe the temperature (T) decreasing, the position of the resonance peak shifts to a shorter wavelength, which is consistent with the phenomena of the hollow MOF-SPR sensors [25,26]. The temperature sensitivity is calculated by [12][13][14].  Figure 4 shows the temperature sensitivities of the x-and y-polarized core modes at different temperatures. In general, the y-polarized sensitivities are higher than the x-polarized sensitivities, and they are gradually increasing with increasing temperatures. The maximum x-and y-polarized sensitivities are 3.21 nm/°C in the detection range of 13.27-50.99 °C and 4.98 nm/°C in the detection range of 14.55-51.19 °C, respectively. This value is much higher than that of other fiber optic temperature sensors, as shown in Table 1. Note that the sensitivity and detection range of the proposed sensor can be changed if using other sensing media. For example, the maximum sensitivities are 2.21 nm/°C for the x-polarized core mode in the temperature range of 13.27-59.15 °C, and 3.40 nm/°C for the y-polarized core mode in the temperature range of 14.55-59.38 °C, when we employ the toluene as the sensing medium whose thermal coefficient and dispersion equation can be found in Reference [23]. Furthermore, they also can be adjusted to a desirable value by using some tunable RI sensing media such as liquid crystal [24] and liquid mixture [12].  Figure 4 shows the temperature sensitivities of the xand y-polarized core modes at different temperatures. In general, the y-polarized sensitivities are higher than the x-polarized sensitivities, and they are gradually increasing with increasing temperatures. The maximum xand y-polarized sensitivities are 3.21 nm/ • C in the detection range of 13.27-50.99 • C and 4.98 nm/ • C in the detection range of 14.55-51.19 • C, respectively. This value is much higher than that of other fiber optic temperature sensors, as shown in Table 1. Note that the sensitivity and detection range of the proposed sensor can be changed if using other sensing media. For example, the maximum sensitivities are 2.21 nm/ • C for the x-polarized core mode in the temperature range of 13.27-59.15 • C, and 3.40 nm/ • C for the y-polarized core mode in the temperature range of 14.55-59.38 • C, when we employ the toluene as the sensing medium whose thermal coefficient and dispersion equation can be found in Reference [23]. Furthermore, they also can be adjusted to a desirable value by using some tunable RI sensing media such as liquid crystal [24] and liquid mixture [12].

Fabrication Tolerance
For the nanowire filled MOF-SPR temperature sensor in this paper, some fabrication tolerances that occur in actual manufacturing may have an impact on the sensing performance. Therefore, in the next section, we discuss the effect of fabrication tolerances in the range of ±10%.
The first fabrication tolerance to be considered is the effect of gold nanowire positions on the SPR spectra. This manufacturing method of filling the nanowire directly into the MOF hollow core simplifies the manufacturing process compared to the previously mentioned coating process [9][10][11][12][13]. However, it is hard to keep the position of the nanowire in the MOF hole stationary. Here, we only consider the effect of the nanowire at the bottom region of the hole under gravity, as shown in Figure  5. The rotation angle (θ) is used to describe the position of the nanowire, and the case where θ is positive indicates that the nanowire is deflected to the right. Because of symmetry, only the case where θ is positive is considered. When θ changes from 0° to 20° in Figure 6, the x-and y-polarized resonance peaks move to shorter wavelengths and the moving distance is very small, which has a smaller effect on the corresponding sensitivity, especially in the range of 0° to 10°.

Fabrication Tolerance
For the nanowire filled MOF-SPR temperature sensor in this paper, some fabrication tolerances that occur in actual manufacturing may have an impact on the sensing performance. Therefore, in the next section, we discuss the effect of fabrication tolerances in the range of ±10%.
The first fabrication tolerance to be considered is the effect of gold nanowire positions on the SPR spectra. This manufacturing method of filling the nanowire directly into the MOF hollow core simplifies the manufacturing process compared to the previously mentioned coating process [9][10][11][12][13]. However, it is hard to keep the position of the nanowire in the MOF hole stationary. Here, we only consider the effect of the nanowire at the bottom region of the hole under gravity, as shown in Figure 5. The rotation angle (θ) is used to describe the position of the nanowire, and the case where θ is positive indicates that the nanowire is deflected to the right. Because of symmetry, only the case where θ is positive is considered. When θ changes from 0 • to 20 • in Figure 6, the xand y-polarized resonance peaks move to shorter wavelengths and the moving distance is very small, which has a smaller effect on the corresponding sensitivity, especially in the range of 0 • to 10 • .     Figure 7, the position of the resonance peak is less affected by w, indicating that the sensor has good stability in the range of ±10% fabrication tolerance of w. However, as the dc increases in Figure 8, the resonance peak shifts toward the short wavelength direction, which is because the increase in dc causes the Re(neff) of the core mode to become larger, as shown in Figure 8a,b, resulting in the intersection of the Re(neff) curves of the core mode and the SPP mode, that is, the peak shifts to the short wavelength direction. The increase in dc also reduces the loss of the core mode, which can make the resonance peak width narrower, as seen from Figure 8c,d, and leads to a better resolution. Figure 9 shows the effect of dg on the loss spectra of the proposed sensor, where dg changes in the range of -10% to 10%, and the resonance peak shifts toward the long wavelength direction as dg increases. This is because the increases in dg increases the Re(neff) of the SPP mode, as shown in Figure 9a,b, and thus leads to the intersection (the peak) which moves toward the long wavelength, as seen from Figure 9c,d. In general, when the gold nanowire is within ±20° deflection range and the sensor parameters (w, dc, and dg) are within ± 10% tolerances, the SPR phenomenon is relatively stable, indicating that the sensor can work normally.  Figure 7, the position of the resonance peak is less affected by w, indicating that the sensor has good stability in the range of ±10% fabrication tolerance of w. However, as the d c increases in Figure 8, the resonance peak shifts toward the short wavelength direction, which is because the increase in d c causes the Re(n eff ) of the core mode to become larger, as shown in Figure 8a,b, resulting in the intersection of the Re(n eff ) curves of the core mode and the SPP mode, that is, the peak shifts to the short wavelength direction. The increase in d c also reduces the loss of the core mode, which can make the resonance peak width narrower, as seen from Figure 8c,d, and leads to a better resolution. Figure 9 shows the effect of d g on the loss spectra of the proposed sensor, where d g changes in the range of -10% to 10%, and the resonance peak shifts toward the long wavelength direction as d g increases. This is because the increases in d g increases the Re(n eff ) of the SPP mode, as shown in Figure 9a,b, and thus leads to the intersection (the peak) which moves toward the long wavelength, as seen from Figure 9c,d. In general, when the gold nanowire is within ±20 • deflection range and the sensor parameters (w, d c , and d g ) are within ± 10% tolerances, the SPR phenomenon is relatively stable, indicating that the sensor can work normally.

Conclusions
This paper describes a SPR temperature sensor based on a side opening hollow-core MOF, which improves the problems of most SPR temperature sensors which cannot use high RI sensing media and need complex coating and filling processes. Taking benzene as the sensing medium for an example, the maximum sensitivity of the sensor is 4.98 nm/°C for the y-polarized core mode in the temperature range of 14.55-51.19 °C, while maximum sensitivity and temperature range can be adjusted by changing the sensing medium. In addition, the sensor also shows good stability in the range of ± 10% fabrication tolerances. This sensor design can be used not only for temperature sensing

Conclusions
This paper describes a SPR temperature sensor based on a side opening hollow-core MOF, which improves the problems of most SPR temperature sensors which cannot use high RI sensing media and need complex coating and filling processes. Taking benzene as the sensing medium for an example, the maximum sensitivity of the sensor is 4.98 nm/ • C for the y-polarized core mode in the temperature range of 14.55-51.19 • C, while maximum sensitivity and temperature range can be adjusted by changing the sensing medium. In addition, the sensor also shows good stability in the range of ± 10% fabrication tolerances. This sensor design can be used not only for temperature sensing with the high RI sensing media, but also for the real-time sensing of high RI samples.