Stable whispering gallery mode microresonator self-injection locking laser for atomic comagnetometer based on thermal dynamics

The whispering-gallery mode microresonator self-injection locking lasers for atomic comagnetometers have excellent characteristics, and their stability needs to be improved. In this study, through the analysis and simulations of optical injection rate equations with thermal dynamics of the microresonator, a frequency adjustment strategy is presented that ensures the stability of the self-injection locking laser output wavelength over time. The normalized Allan deviation of the output wavelength is 1.7 × 10⁻¹⁰, and both the 20.6 Hz / Hz laser frequency noise and the 375 Hz linewidth are maintained within one hour. These results demonstrate exceptional self-injection locking stability with the 10⁹ quality factor microresonator.