# Liquid Crystal-Embedded Hollow Core Fiber Temperature Sensor in Fiber Ring Laser
## 2 Working Principle and Experimental Setup
In nematic phase, \(n_{o}\) increases and \(n_{e}\) decreases with the increase of temperature. The thermo-optical coefficients of these two indexes are in the range of \(10^{4}\)-\(10^{3}\) RIU/\({}^{\circ}\)C, which is similar to that of isotropic optical liquids. In this case, the thermo-optic tuning of the liquid crystal compound acts more as an additional degree of freedom to tune the response of the photonic crystal fiber filled with the liquid crystal. In addition, the flow process of E7 induces the orientation of major molecules along the fiber axis. With the increase of temperature, the RI value of LC decreases, while the RI value of cavity mold is basically unchanged. According to Equation (2), as the temperature increases, the interference pattern will shift to the short-wave direction. With the increase of temperature, the fundamental mode distribution corresponding to the mode field penetrating the cladding decreases obviously, which indicates that the filled liquid crystal fiber is very sensitive to the change of ambient temperature. Figure 1: Configuration of LC filled NC-HC-NC structure based modal interferometer. The distributions of the fundamental mode and the effective mode area \(A_{eff}\) can be calculated by [25]:  
\[A_{eff}=\frac{\left(\iint\left|E(x,y)\right|^{2}dxdy\right)^{2}}{\iint\left|E(x,y )\right|^{4}dxdy} \tag{3}\]  
where \(E(x,y)\) represents the two-dimensional electric field distribution of the fundamental mode. Although the liquid crystal sequence is not completely parallel to the fiber axis, as shown in Figure 2, the refractive index changes linearly on the whole. When the liquid crystal reaches near the clear point (56 \({}^{\circ}\)C), the refractive index changes greatly, and the effective refractive index does not change linearly. This will lead to the mutation of the interference peak, which is manifested in the FRL system, leading to laser mode hopping. Therefore, the temperature change between 20 \({}^{\circ}\)C and 50 \({}^{\circ}\)C is selected in the experiment. Due to the linear change of refractive index, the directional translation of the output spectrum is caused. Therefore, although the orientation of the liquid crystal is not completely fixed, the refractive index of the liquid crystal at every temperature is a fixed value, ensuring the stability of the system. The temperature response of fiber filled with liquid crystal was studied by using a length of 10 mm HCF and two segments with a length of 1.5 mm NCF. In our experiment, one end of the 20 mm length HCF was sealed in a pressure tube connected to the syringe, and the other end was immersed in a bottle containing E7, as shown in Figure 3. The syringe is fixed on an electrically controlled moving table to produce a uniform differential pressure. When the plunger of the syringe is pulled, it creates a vacuum pressure in the tube. The liquid crystal filler is sucked into HCF with an injector and the HCF is cut with a cutter. It should be noted that the filling rate also depends on the material properties of the fluid, such as density and viscosity. Large diameter pores are distributed along the fiber core, and the high refractive index difference between the liquid crystal and the glass makes the liquid crystal become a multimode waveguide. When the phase matching condition is satisfied, the fundamental mode in the fiber core is coupled with the guide mode in the liquid waveguide, resulting in the coupling of light to the liquid waveguide at the phase matching wavelength. Figure 2: Temperature dependence of the refractive index of the nematic E7 liquid crystal. The pre-experiment device is shown in Figure 4. We splice an NCF at each end of the HCF filled with the liquid crystal. In order to reduce splicing loss, a negative pressure is applied to the other end of HCF before splicing, and the liquid crystal rod is moved a few millimeters to the inside of the fiber, so that the liquid crystal in the fiber will not be carbonized during discharge welding. The excess HCF is then cut off with a cutter and splice with NCF.