Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator

Frequency stabilization of a diode laser locked to a whispering gallery mode (WGM) reference resonator made of a MgF2 single crystal is demonstrated. The strong thermal dependence of the difference frequency between two orthogonally polarized TE an TM modes (dual-mode frequency) of the optically anisotropic crystal material allows sensitive measurement of the resonator's temperature within the optical mode volume. This dual-mode signal was used as feedback for self-referenced temperature stabilization to nanokelvin precisionresulting in frequency stability of 0.3 MHz/h at 972 nmwhich was measured by comparing with an independent ultrastable laser.