## 3 Experiments and Results  
### MZI Sensor  
The manual operation of the arc-discharge of the fusion splicer (Fujikura 80c) was adopted in this study to fabricate two micro tapers in a single SMF (G652D), as show in Figure 3a. Firstly, the jacket at the middle of the SMF was removed; then, both ends of the optical fiber were fixed on the fusion splicer by two fiber clamps. Multiple arc-discharges were applied to the bare fiber, and pulled the bare fiber during arc-discharges. The size of the micro taper fiber (taper transition length and taper waist diameter) can be controlled with the precise control of arc-discharged time, power, and pulling step length. In our experiments, the arc-discharged time and power were set to 200 ms and 50 bit, respectively, and the step length was set to 500 \(\upmu\)m. Figure 3b shows a microphotograph of the micro taper fiber made by the above method and parameters. An optical fiber MZI sensor can be fabricated by cascading two micro taper fibers, as shown in Figure 1. Figure 3c-e show the transmission spectra of the fabricated fiber MZI with lengths \(L\) of 1, 2, and 3 cm, respectively, at a fixed temperature of 30 \({}^{\circ}\)C. One can see that as the \(L\) increases, the intensity of interference dips increases. The corresponding Fourier space spectrum was obtained by a fast Fourier transform (FFT) of transmission spectrum. The spatial spectrogram with lengths \(L\) of 1, 2, and 3 cm are shown in Figure 3e. In addition, there is only one main peak in the Fourier spectrum. The spatial frequency of the main peaks with \(L\) = 1, 2, and 3 cm agrees well with that of the simulation results. We also considered the influence of waist diameter \(D\) on the extinction ratio of the structure. Figure 3f shows the measured Fourier space spectra with waist diameters of \(D\) = 50, 60, and 80 \(\upmu\)m, respectively. According to the experimental results, with the same length \(L\), the maximum amplitude of main peak was observed for the structure with \(D\) = 80 \(\upmu\)m, where the extinction ratio of over 10 dB with \(D\) = 80 \(\upmu\)m was observed in Figure 3c-e.  
Figure 2: **(a)** The simulated spectral response of the fiber MZI with arm lengths \(L\) of 1, 2, and 3 cm, respectively; **(b)** the corresponding spatial frequency; **(c,d)** the distributions of the optical field and the normalized optical intensity propagating along the MZI with an arm length of 3 cm at dip \(a\) 1571.2 nm and peak \(b\) 1578.8 nm. Figure 4 shows the experimental setup for temperature, strain, and RI measurements. The transmission spectra of the sensors were measured by using an SC-5-FC broadband light source (BBS) as an optical source and an optical spectrum analyzer (OSA, AQ6370) as a piece of demodulation equipment. In addition, the MZI sensor with a sandwiched SMF length of about \(L=3\) cm was selected for testing. Since the furnace used as a heat source in our experimental setup had a heat channel with a heating length of up to 20 cm, it was believed that the furnace could provide a uniform temperature distribution for our sensor with a sensor length of circa 3 cm. The temperature response of the sensor was investigated without first annealing. As can be seen from Figure 5a, as the temperature increased from 100 to 950 \({}^{\circ}\)C, the spectral dip wavelength shifted to longer wavelengths and vice versa. However, the wavelength shift during cooling did not match with that of increasing temperature. This result indicates that the sensor isn't stable within the temperature measurement range. Therefore, an annealing process on the sensor was applied to the sensor at a high temperature of 1000 \({}^{\circ}\)C for three hours, as shown in Figure 5b. Then, we used the annealed sensor to study the high-temperature sensing characteristics from 80 to 950 \({}^{\circ}\)C, as shown in Figure 5c.