# Optical Fiber Sensor with Stable Operating Point for AC Magnetic Field Measurement
## 3 Sensor Fabrication and Characterization
### AC Magnetic Field Sensing and Stable Operating-Point Performance  
An AC magnetic field can be monitored by measuring the Bragg wavelength shift of the HAFBG of the sensor. However, the measurement of the HAFBG spectrum requires an OSA or another wavelength demodulation device, which is relatively expensive and has slow signal acquisition frequency. Thus, to realize relatively fast and low-cost AC magnetic field monitoring, we opted to measure the optical intensity instead of the optical spectrum using a setup based on the edge filter principle, as depicted in Figure 4. The sensor is placed in the center of a Helmholtz coil, which is driven by an AC frequency conversion power supply to generate uniform a magnetic field at varying frequencies. The output wavelength of a narrow linewidth fiber laser (NKT Photonics, Cologne, German; Koheras Boostik E15) is adjusted to the wavelength located in the slope of the HAFBG spectrum. The signal reflected from the sensor is detected by a photoelectric detector (Thorlabs, Newton, MA, USA; PDA50B2), and data are sent to a computer by a data acquisition card (ART technology, Beijing, China; USB-3106A) with a sampling rate of 10,000 Sa/s. A 980 nm pump laser is used as a heating laser, as was introduced in the previous experiment. A computer application program designed using LabVIEW is used for control and communication with the data acquisition card and the heating laser. Figure 5 plots voltage waveforms measured by the data acquisition card when the sensor is used to monitor the AC magnetic field drive by different oscillation frequencies and currents. All the signals detected by the sensor show a periodic waveform, with a frequency twice that of the AC magnetic field. Note that the magnetostrictive square rod elongates as the strength of the magnetic field increases along the length of the rod. As the magnetic field strength decreases, the magnetostrictive square rod shortens to its original length, i.e., the magnetostrictive rod stretches twice during one period of magnetic field oscillation, and thus the frequency of the magnetic field generated by the coil will be doubled in the sample. The wavelength of the narrow linewidth fiber laser is set to be in the middle of the slope of the sample spectrum to achieve as high a detection sensitivity and as large a detection range as possible. It should be noted that lights from the 980 nm heating laser at different powers are added through the circulator to ensure a stable operating point. Figure 5d shows that the measured peak-to-peak amplitude of waveform increase with driving currents and is independent of AC magnetic field frequency. Figure 4: Experimental system setup for AC magnetic field measurement. Referring to Figure 6, the operating principle and process of maintaining a stable operating point are described in the following. Prior to the experiment, an initial heating pump power \(P_{initial\_980}\) is set (here to 100 mW). The wavelength of the narrow linewidth fiber laser sweeps the entire HAFBG spectral range, and the corresponding received voltage signal \(V\) as a function of wavelength \(\lambda\) is recorded, i.e., \(f(\lambda,V)\). The midpoint voltage \(V_{m}\) is then set as the optimal operating point that is desired to be kept stable. During AC magnetic field detection, a Proportional-Integral-Differential (PID) control algorithm is used to adjust the power of the heating laser, keeping the average value \(V_{avg}\) of the received signal (the measured value in the PID algorithm) always close to the operating point \(V_{m}\) (the reference value in the PID algorithm) at all times by adjusting the proportionality coefficient \(K_{P}\), the integral coefficient \(K_{I}\), and the differential coefficient \(K_{D}\). Figure 5: Measured voltage waveforms when the frequency of the AC magnetic field is **(a)** f = 50 Hz, **(b)** f = 150 Hz, and **(c)** f = 250 Hz. The drive currents of AC frequency conversion power supply are 1 A, 3 A, 5 A, 7 A, and 9A, respectively.