# A High-Sensitivity Magnetic Field Sensor Based on PDMS Flexible Resonator
###### Abstract  
High-sensitivity resonator magnetic sensing requires a significant magnetostrictive response, while the narrow linewidth mode of a high-Q resonator can provide a high-precision frequency resolution. Therefore, a polydimethylsiloxane (PDMS) flexible resonator with both a low Young's modulus and high optical transmittance is an ideal platform for realizing high-sensitivity magnetic sensing. Based on the sandwich structure of the PDMS flexible resonator, the mechanism of the magnetic field sensitivity of the PDMS flexible resonator sandwich structure is studied, and the impact of changes in the refractive index and radius on the sensor device is analyzed. In order to optimize the sensitivity of the sensor, when an external magnetic field acts on the sandwich structure, the impacts of three aspects on the sensitivity of the sensor are simulated and analyzed: different coupling positions of PDMS flexible resonator, different radii, and PDMS mixing ratios. The trend of sensitivity change is obtained, and the physical explanation of the sensitivity trend is analyzed. By optimizing these three aspects, the magnetic field sensitivity is eventually calculated as 19.02 nm/mT. Based on the existing experimental conditions and the preparation technology of the PDMS flexible resonator, the measured magnetic field sensitivity is 4.23 nm/mT. sandwich structure; PDMS flexible resonator; magnetic field sensor +
Footnote †: journal: Applied Physics Letters  
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external magnetic field. Optical magnetic field sensors based on WGM resonators are well suited to make up for the shortcomings of traditional magnetic field sensors, with the advantages of having a fast magnetic field response, strong anti-interference capability, good reliability, and easy integration, which have been gradually developed in recent years. Various types of WGM-resonator-based magnetic sensors have been reported. For example, [PERSON] [24] et al. reported a highly sensitive bidirectional magnetic field sensor by packaging an optofluidic micro-resonator filled with a magnetic fluid which achieved a maximum sensitivity of 304.80 pm/mT and a detection limit of 0.0656 mT. [PERSON] [25] et al., from Harbin Institute of Technology reported a hollow microbubble resonator based on fixed Terfenol-D, which achieved a tunable Q factor of 2.07 \(\times\) 10\({}^{5}\) by tuning the WGMs with magnetic fields and a magnetic field sensitivity of 0.081 pm/mT. [PERSON] [26] et al., reported a microcapillary resonator combined with magnetostrictive materials, achieving a DC magnetic field sensitivity of 0.1703 dB/Oe through AC magnetic field modulation. [PERSON] et al. reported the deflection vibration response and thermal moment of a resonator via a magnetic field [27] and illustrated the thermoelastic vibrations of a rotating resonator caused by a laser pulse heat source and sinusoidal heating in the context of three-phase thermo-elasticity [28]. Therefore, most magnetic sensors based on WGM resonators are two main types. One type is the magneto-optical sensor. Magnetic fluid is widely used as a key sensitive material for magneto-optical sensing schemes because of their tunable refractive index (RI) under different external magnetic fields. A microapillary or a hollow microfiber is filled with a magnetic fluid. As the magnetic field is changed, the RI around the WGM changes, leading to a shift in the transmission spectrum [24; 29]. Although the magnetic fluid can provide a significant response to the applied magnetic field, the magnetic fluid usually affects the optical quality of the resonator, making the detection limit of the sensor lower. Another type is a resonator combined with a magnetic material, usually consisting of a WGM resonator and a magnetostrictive material [25; 30; 31], where an external magnetic field induces mechanical forces to modify the transmission spectrum while being able to maintain a high Q-factor.