## 4 Experimental Results and Discussion  
The experiments were carried out at 20 \({}^{\circ}\)C in order to ensure the reduction of the influence of temperature. Sinusoidal waves with the amplitude of 5 V and the frequency of \(\omega_{\rm u}/2\pi=50\) kHz produced by the signal generator after 10-fold amplification were used for exciting the PZT as AE sources. The sampling frequency of the DAQ was set to 1 MHz. The data were recorded in each experiment when the output voltage of the sensing system was stable. Figure 6 shows the output voltage waveform and the corresponding frequency spectrum of the fiber optic Sagnac sensing system under the action of AE signals in the initial status. As shown in Figure 6a, the amplitude of the voltage was about 0.11 V, but the waveform did not have a regular sinusoidal shape, which means there were harmonic interferences. The frequency spectrum in Figure 6b shows that the sensor can correctly recognize AE signals with a frequency of 50 kHz. However, the ratio of the amplitude of fundamental waves to that of second-harmonic waves was only 0.13, which indicates that the harmonic interferences were relatively high and therefore affected the sensor in detecting AE signals effectively. The square wave modulation voltage generated by SG1 was \(V_{\rm x}=\pm 0.785\) V and was applied to the Y-branch waveguide, which means that a bias phase of \(\Delta\phi=\pi/2\) was introduced into the sensor. The output voltage waveform and the corresponding frequency spectrum are shown in Figure 7. It can be seen from Figure 7a that the amplitude of the output voltage improved, but it is difficult to accurately identify useful features because the signals were obviously affected by the phase modulation. Compared with Figure 6b, the amplitude of fundamental voltage in Figure 7b improved by more than seven times, from 0.0066 to 0.0537, while the amplitude of second-harmonic voltage was reduced by nearly two times, from 0.0506 to 0.0187. Considering the same experimental conditions, the amplitude of the fundamental voltage increased obviously, which demonstrates that the phase sensitivity was greatly improved. In order to investigate the influence of phase modulation on phase sensitivity in a larger range, a series of square-wave voltages from \(V_{\rm x}=0\) V to \(V_{\rm x}=\pm 1.5\) V with a step of \(\Delta V_{\rm x}=\pm 0.1\) V were applied on the Y-branch waveguide to change the initial phase of the sensor. The relationship between \(V_{\rm X}\) and the corresponding amplitude of fundamental voltages is shown in Table 1. It can be seen that the amplitude of the fundamental voltage increased continuously with the increase of \(V_{\rm X}\), when \(V_{\rm X}\) was less than or equal to \(\pm 0.7\) V, whereas it decreased when \(V_{\rm X}\) was greater than \(\pm 0.7\) V. The main reason is that the half-wave voltage of the Y-branch waveguide was 3.14 V, and the bias phase introduced into the sensor was quite close to \(\pi/2\) when \(V_{\rm X}\) was equal to \(\pm 0.7\) V. It can be seen from the experimental results that the maximum phase sensitivity could be increased nearly nine times when the initial phase of the sensor was modulated. Figure 6: Output voltage of the sensor without phase modulation in the experiments. (**a**) Output voltage waveform; (**b**) Corresponding frequency spectrum. Figure 8 shows a corresponding fitting curve based on the experimental data in Table 1, with two additional data points of \(V_{\rm x}=\pm 0.785\) V and \(V_{\rm x}=\pm 1.57\) V, where the amplitude of the fundamental voltages were 0.05365 and 0.01302, respectively. The results indicate the fitting equation can be described by \(\rm y=0.02612+0.003564*sin[\pi*(x-0.17962)/1.0695]\) with a decision coefficient \(\rm R^{2}\) of 0.99345. It was found that the experimental fitting curve was in good agreement with the numerical simulation curve shown in Figure 4, which confirms the validity of the experimental results.