# Optical Fiber Sensor with Stable Operating Point for AC Magnetic Field Measurement
## 3 Sensor Fabrication and Characterization
### Sensor Characterization  
Figure 2a,b shows measured reflection spectra of the fabricated sensor and Figure 2c,d shows the corresponding temperature and heating laser power responses of the HAFBG Bragg wavelength. For the temperature response measurement, the spectra were measured by using a board band source (BBS, Dense Light, Tanah Merah, Singapore; DL-BX9-CS5169A) with an output wavelength range of 1250-1630 nm, a circulator (DK photonics, Shenzhen, China; MCCIR-3-CL-FA), a wavelength division multiplexer (WDM, 1550/980 \(\pm\) 20 nm), and an optical spectrum analyzer (OSA; Yokogawa, Osaka, Japan; AQ6317) with a minimum wavelength resolution of 0.01 nm, arranged as shown in the inset of Figure 2c. For the heating laser power response measurement, light emitted from the BBS reaches the 1550 nm port of the WDM through the circulator, and at the same time, light emitted from a heating laser (Feibo optoelectronic technology, Shenzhen, China; FL-980 nm-600 mW-M-FA) enters at the 980 nm port of the WDM, and then the merged light propagates together to the sensor, as shown in the inset of Figure 2d. Reflection spectra are measured by the OSA. A tunable incubator (Shanghai Gixin Scientific Instrument, Shanghai, China; LRH-150) was used to change the ambient temperature around the sensor, and a thermometer (Chuangjimei, Hengshui, China; TP301) was used for real-time temperature monitoring. Each temperature setting is kept unchanged for at least 5 min to ensure a stable reflection spectrum. As shown in Figure 2c, the sensor shows a linear response to ambient temperature, and a temperature sensitivity \(S_{T}\) of 7.86 pm/\({}^{\circ}\)C was obtained by linear fitting of the data of the Bragg wavelength shift to the ambient temperature. Therefore, during the process of dynamic parameter measurement, such as the AC magnetic field measurement, the preset optimal working point will move when the ambient temperature changes, resulting in unstable and incorrect measurement results. The operating point can be stabilized by regulating the power of a heating laser targeted on the HAF using a control algorithm to compensate the temperature fluctuations of the surrounding environment. An experiment measuring the HAFBG Bragg wavelength shift due to the heating laser power was conducted to verify the feasibility of stabilizing the operating point of the sensor. The Bragg wavelength responses of the sensor to various pump powers of the heating laser are shown in Figure 2d. Measurements were made with the heating laser powers set to 152.9 mW, 267.1 mW, 370.8 mW, and 456.4 mW at an ambient temperature of 16.9 \({}^{\circ}\)C. The Bragg wavelength of the sensor is correspondingly shifted from 1549.59 nm to 1549.86 nm. The tuning coefficient \(S_{980}\) of the heating laser is calculated to be 0.604 nm/W by linear fitting of the Bragg wavelength shift to the heating laser power. Following references [36; 37], the heat generated by the heating laser power can be expressed as:  
\[Q(z)=k\alpha P_{0}\cdot e^{-\alpha z}, \tag{7}\]  
where \(Q\) is the heat; \(z\) is the position along axial direction of the HAFBG; \(\alpha\) is the absorption coefficient of the core of the HAF, which is measured to be 3.325 dB/cm @ 980 nm; \(P_{0}\) is the power of the incident pump laser; and \(k\) is the thermal conversion coefficient from optical power to heat, which is about 38%. The distribution of heat \(Q\) is not uniform and there exists a temperature gradient along the \(z\)-axis of the HAFBG [36]. Thus, a larger laser  
Figure 1: **(a–c)** Fabrication process schematic diagram of the proposed sensor. **(d)** Microscope image of the side view of the fabricated sensor. power will slightly widen the Bragg grating spectrum due to the nonuniform temperature distribution along the HAFBG. The DC magnetic field response of the sensor was also measured. As shown in Figure 3a, a parallel magnetic field was generated by a Helmholtz coil (Hunan Paisheng Technology, Changsha, China; PS4000c) with different electric current.