Dynamic range tuning of a WGM-based magnetometer via PID adjustment in a PDH sensing scheme

Whispering Gallery Mode (WGM) microresonators, known for their exceptionally high quality factors (Q), provide a promising platform for developing highly sensitive sensors. Among various sensing applications, magnetic field detection using WGM resonators has attracted growing interest due to their compact size, ease of fabrication and their electrical-components free configuration. However, methods for enhancing the sensitivity and dynamic performance of WGM-based sensors, particularly when employing laser stabilization techniques like the Pound-Drever-Hall (PDH) method, have not been thoroughly investigated. In this work, we present a WGM-based magnetic field sensor utilizing a Saddle-Shaped Microresonator (SSM) and a PDH-based sensing scheme. The magnetic field is monitored by tracking the PDH error signal, which arises from magnetic field-induced spectral shifts of the resonator's WGMs. Here we focus on the often-overlooked role of the Proportional-Integral-Derivative (PID) controller used in the PDH feedback loop. By adjusting the PID parameters and matching them to a specific desired frequency range, we demonstrate that a significant improvement in sensor performance can be achieved. We demonstrate tuning of the effective resonance frequency from 0.2 Hz to 30 Hz by adjusting the integral and proportional controllers’ gains. The corresponding sensitivity varies from 260 nT/Hz^0.5 at 0.5 Hz to 35 nT/Hz^0.5 at 30 Hz. Our results show that fine-tuning the PID parameters enables adjustable control over the sensor's dynamic range. These findings highlight the critical role of PID adjustment in PDH-based sensing schemes and offer a practical approach for enhancing the performance of WGM-based sensors in real-world applications.