Frequency stability of a dual-mode whispering gallery mode optical reference cavity

We report an investigation of laser frequency stabilization using a whispering gallery mode resonator that is temperature stabilized by a dual-mode technique. This dual-mode technique has yielded mode volume temperature instabilities at the nK level, suggesting that high frequency stability may also be reached. Here, we experimentally and theoretically investigate the dynamics of such a system and the important factors affecting the achievable frequency stability. We calculate that the dual-mode technique can reduce the effective fractional temperature coefficient of the reference system to 3.6x10^-8 K^-1 within the temperature feedback bandwidth. We demonstrate a 1560 nm laser stabilized to 1.3x10^-12 at 1 s and 1.1x10^-10 at 1000 s, corresponding to a long-term drift of 21 kHz/hr.