# A Notched Long-Period Fiber Grating Magnetic Field Sensor Based on Nanoparticle Magnetic Fluid
## 2 Material and Method
### Experimental Setup for the NLPFG Magnetic Field Sensor  
In this experiment, the NLPFG was fabricated by using the ICP technique on the single-mode fiber. Figure 2 shows an image of NLPFG magnetic field sensor filled with the magnetic fluid in a capillary and an optical microscopy (OM) photo of the segment of a NLPFG illustrates the relative dimensions. During this experiment, the grating period \(\Lambda\) of the NLPFG was 600 \(\upmu\)m, the diameter \(\phi\) of the wet etched region was 40 \(\upmu\)m, and the length of grating structures was 30 mm. We positioned the NLPFG into a capillary, where the length \(L_{cap}\) was 50 mm with an inner diameter \(D_{cap}\) of 1 mm, and then injected the MF into it. The both sides of the capillary were then sealed by epoxy to prevent the MF from evaporating and flowing out during the experiment. Fe\({}_{3}\)O\({}_{4}\) water-based MF (EMG 605, Ferrotec.) was used in the experiment. This MF is a black-brown opaque liquid which contains 10 nm-diameter ferromagnetic nanoparticles, and the volume concentration is 3.9%. The density of this MF is \(1.18\times 10^{3}\) kg/m\({}^{3}\). Figure 3 exhibits a transmission electron microscopy (TEM) image of  
Figure 1: The schematic diagram of the manufacturing process of the notched long-period fiber grating (NLPFG).  
Fe\({}_{3}\)O\({}_{4}\) iron oxide nanoparticles dispersed in a MF [26]. The refractive index of the EMG 605 MF is estimated to be about 1.40 \(\pm\) 0.02 [15], lower than that of fiber silica cladding. When the external magnetic field strength is increased, the particles agglomerate to form columns or chains in the liquid in the direction of the magnetic field, which leads to phase separation between the particles and the carrier liquid [27; 28]. In the specific MF, its refractive index is reduced with increasing magnetic field while its scattering loss increases. Accordingly, the cladding mode will be greatly confined into the thinned cylindrical area of the cladding, leading to lower overlap with the etched grating. While with the aforementioned refractive index modification mechanism of the MF, the contrast of the relief long-period grating will increase, and the MF scattering losses can also constructively contribute to the LPFG strength [22]. The negative refractive index changes induced with the increase of the magnetic field dominate over the other two effects, leading to a reduction of the LPFG notch strength.  
The experimental setup of the proposed sensor is shown in Figure 4. An electric solenoid was placed perpendicularly to the sensor, and the magnetic field strength could be controlled by the current generated by the power supply. As the power supply was adjusted, for every increase of 1 A in current, the magnetic field of the solenoid was increased by 8.67 mT. The current was exported by the power supply based on increments of 0.4 A, increasing from 0 A (0 mT) to 3.2 A (27.74 mT). To avoid the thermal effect, we employed a pump and copper tubes to construct a water cooling system that was  
Figure 3: The transmission electron microscopy (TEM) image of iron oxide (Fe\({}_{3}\)O\({}_{4}\)) nanoparticles dispersed in a magnetic fluid [26].  
Figure 2: The image of a NLPFG magnetic field sensor filled with magnetic fluid (MF) in a capillary and in-set optical microscopy (OM) photo detailing the dimensions of the grating section of the NLPFG.  
used to keep the temperature of the electric solenoid steady. During the process of the experiment, we maintained the temperature variations within 1.5 \({}^{\circ}\)C. The NLPFG magnetic field sensor was connected to a super luminescent diode (SLD) broadband light source, a precise translation stage, a load cell, and an optical spectrum analyzer (OSA). Subsequently, the transmission spectra of the magnetic sensor were measured and recorded under distinct magnetic flux densities.