# A High-Sensitivity Magnetic Field Sensor Based on PDMS Flexible Resonator
## 3 Results and Discussion
### PDMS with Different Mixing Ratios
Through the above analysis of the optimized sandwich structure, it is clear that all three variables affect the PDMS flexible resonator in the sandwich structure. We optimize the three variables of the PDMS flexible resonator via finite element simulation to calculate the magnetic field sensitivity of the optimized sandwich structure. We reduce the radius of the PDMS flexible resonator to 0.65 mm, using a mixing ratio of PDMS polymer and curing agent of 6:1; conduct sensing tests at the 0.6 h coupling position of the PDMS flexible resonator; and perform simulations by applying an external magnetic field to affect the sandwich structure to obtain the relationship between the external magnetic field and the amount of change in the radius of the PDMS flexible resonator, and the simulation results are shown in Figure 9.  
Figure 9: Sensitivity obtained by optimizing the sandwich structure. Figure 9 shows that the magnetic field sensitivity of the sandwich structure is significantly improved when we optimize the PDMS flexible resonator radius size, coupling position and mixing ratio simultaneously. The magnetic field sensitivity is 19.02 nm/mT in the range of 0.01 mT to 0.11 mT. For the actual preparation process, the preparation difficulty increases with the decrease in the radius of the PDMS flexible resonator. Therefore, this optimization is an important guideline for the actual preparation process, so the sensitivity of the PDMS flexible resonator magnetic sensor can be effectively improved by upgrading the PDMS flexible resonator preparation process. Through the simulation analysis of the PDMS-based flexible resonator sandwich structure model, a theoretical foundation is laid for the feasibility of the scheme, and PDMS-based flexible resonator magnetic field sensing becomes a possibility for WGM-based high-sensitivity magnetic field sensing and provides a reference. Due to the limitation of the preparation process, the radius of the PDMS flexible resonator is stable between 2.8 mm and 3 mm. We prepare the sandwich structure using NdFeB magnets with 8 mm diameters, and the PDMS mixing ratio is 6:1. We measure the shift in the resonance spectrum under different magnetic fields using a sandwich structure prepared with a PDMS flexible resonator with a radius of 2.8 mm, as shown in the shaded part of Figure 10a. At different magnetic fields, we read the shift of one resonance peak, as shown in Figure 10b, and measure the slope of 1.41 nm/mT via linear fitting; R\({}^{2}\) = 0.9862. In fact, it is difficult to prepare the sandwich structure with one PDMS flexible resonator, and we improve the stability of the sandwich using three PDMS flexible resonators. Compared to the sandwich structure with one PDMS flexible resonator, the structure in our experiment actually divides the magnetic field sensitivity equally, and the final magnetic field sensitivity should be 4.23 nm/mT, which is three times that of one PDMS flexible resonator. This is almost equal to the magnetic field sensitivity obtained from our simulation. Magnetic field sensing structures prepared using a PDMS flexible resonator provide an idea for miniaturization and, more importantly, such structures can be freely tuned to provide magnetic field sensitivity in the order of nm/mT even with the limitations of the preparation process. During the experiment, only the laser affects the resonator, and the overall temperature of the sensor does not exceed 1 degree Celsius, and the resulting variation is negligible. This approach opens a window for ultra-high-sensitivity magnetic field sensing applications.