Analysis of the rutile-ring method of frequency-temperature compensating ahigh-Q whispering gallery sapphire resonator

The rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery (WG) sapphire resonator is presented. Two and three-dimensional finite element (FE) analysis has been implemented to desi gn and analyze the performance of such resonators, with excellent agreement between theory and experiment. A high-Q factor of 30 million at 13 GHz and compensation temperature of 56 K was obtained. It is shown the frequency-t emperature compensation can occur either because the rutile adds a small pe rturbation to the sapphire resonator or because of a mode interaction with a resonant mode in the rutile. The characteristics of both of these methods are described, and it is shown that for high frequency stability, it is be st to compensate perturbatively.