Free spectral range measurement using homologous heterodyne optical phase-locked loop based on acousto-optic modulation.

We demonstrate a homologous heterodyne optical phase-locked loop for free spectral range measurement of a fiber ring resonator. In this loop, the frequency noise within the 10 Hz bandwidth is reduced by more than 40 dB from 147.350 to 0.014 Hz, and the power spectral density of the frequency noise reaches 7.69×10-8  Hz2/Hz at 10 Hz. Finally, the relative measurement accuracy of 1.39×10-9 is achieved by this loop and the free spectral range coefficient of thermal expansion is measured as -174.1±0.2  Hz/°C with a cavity finesse of 26.65. This work provides a method to measure free spectral range by tracking the resonance modes of the resonator and reducing frequency noise, especially for two signals with frequency offset.