Analysis of Kerr noise in angular-rate sensing based on mode splitting in a whispering-gallery-mode microresonator

Whispering-gallery-mode (WGM) microresonators have shown their potential in high-precision gyroscopes because of their small volume and high-quality factors. However, Kerr noise can always be the limit of accuracy. Angular-rate sensing based on mode splitting treats backscattering as a measured signal, which can induce mode splitting, while it is considered as a main source of noise in conventional resonator optical gyroscopes. Meanwhile, mode splitting also provides superior noise suppression owing to its self-reference scheme. Kerr noise in this scheme has not been defined and solved yet. Here, the mechanism of the Kerr noise in the measurement is analyzed and the mathematical expressions are derived, indicating the relationship between the Kerr noise and the output of the system. The influence caused by Kerr noise on the output is simulated and discussed. Simulations show that the deviation of the splitting caused by Kerr noise is 1.913 × 10^-5 Hz at an angular rate of 5 × 10⁶ °/s and the corresponding deviation of the angular rate is 9.26 × 10^-9 °/s. It has been proven that angular-rate sensing based on mode splitting offers good suppression of Kerr noise.