## 1 Introduction  
Acoustic emission (AE) is a class of phenomena whereby transient elastic waves are generated by the rapid release of energy from a localized source or sources within a solid material [1; 2], which also exists in the situation of partial discharge [3; 4]. If AE signals can be detected and located by sensors, their accurate position can be provided for damage evaluation and timely repair of the equipment [5; 6; 7; 8]. Therefore, many efforts have been made to develop various sensors for detecting AE signals [9; 10]. The conventional piezoelectric transducers (PZT) have been widely used for detecting AE signals, because of their high detecting frequency, high sensitivity, and low cost [11; 12]. However, some deficiencies such as susceptibility to electromagnetic interference (EMI) and complex installation, limit their applications in many conditions. In recent years, optical fiber sensors have undergone rapid development in AE signal detection because of their advantages, such as small size, light weight, remote sensing, efficiency at high temperature, etc. [13; 14]. [PERSON] et al. [15] and [PERSON] et al. [16] used optical fiber AE sensors to detect damages in composite structures. [PERSON] et al. [17] reported an optical fiber AE system based on the Mach-Zender interferometer sensor for monitoring molten salt attacks. [PERSON] et al. [18] employed the fiber-optic Fabry-Perot sensor to detect the simulated AE signals generated from impact and pencil-lead breaks. [PERSON] et al. [19] developed a detection system for partial discharges using the fiber optic Sagnac sensor. In addition, fiber Bragg grating (FBG) sensors have been adopted for AE monitoring in aluminum alloy material structures and delaminated glass fiber-reinforced epoxy (GFRP) composites [20; 21]. These studies show fiber optic sensors have some merits of corrosion resistance, EMI immunity, embeddability, and so on, which are very suitable for detecting AE signals. Among the optical fiber sensors, the optical fiber Sagnac sensor combines the Sagnac effect with optical fiber sensing technology, thus presenting not only the characteristics of optical fiber sensors but also the advantages of good reciprocity and low requirement for light sources. Moreover, [PERSON] et al. reported that the optical fiber Sagnac AE sensor has a higher detecting frequency of more than 3 MHz and is affected by the loop length difference of Sagnac interferometers [22]. [PERSON] et al. pointed out that the optical fiber Sagnac sensor has a wide frequency response range in the detection of AE signals [23]. It is very important to improve the sensitivity of the optical fiber Sagnac AE sensor, especially in situations where AE signals are comparatively weak, such as the initial stage of partial discharges, slow crack growth of materials, and higher background noises. Therefore, the non-reciprocal phase shifts generated by AE signals are quite small. Currently, there are a few techniques which can improve the sensitivity of the optical fiber Sagnac AE sensor, such as selecting a light source with greater power or increasing the length of sensing fiber [24]. But these have a high cost and bring difficulties in sensor miniaturization. Another way to improve the sensitivity is phase modulation of the sensor. [PERSON] et al. [25] showed that the sensitivity of surface-bonded fiber optic Sagnac AE sensors is almost twice that of noncontact-type fiber sensors. [PERSON] et al. [22] also found that optimum sensitivity can be obtained if the initial phase of the optical fiber Sagnac AE sensor is \(\pi/2\). [PERSON] et al. [26] and [PERSON] et al. [27] modulated the initial phase of the sensor using a PZT phase controller, but the modulation frequency was no more than 100 kHz and was only modulated by sinusoidal signals. Another problem in these studies is that the influence of the \(2\times 2\) single-mode fiber coupler on the initial phase was not reported. In this paper, attention is focused on the improvement of the phase sensitivity of the optical fiber Sagnac AE sensor.