Optimum design of a high-Q room-temperature Whispering-Gallery-mode x-band sapphire resonator

Abstract

A process for optimal design of a room temperature Whispering Gallery mode sapphire resonator has been developed. In particular, design rules were determined to enable choice of the optimum azimuthal mode number and resonator radius for a given resonance frequency. The coupling probe design was investigated and it was found that straight antenna probes aligned radially and positioned in the mid-plane of the resonator gave the highest unloaded Q-factors due to minimized probe losses. We noted that when coupling through this technique (as compared with a perpendicular-positioned probe) the mode standing wave pattern would lock to some asymmetry in the crystal resonator itself and not to the probe. This was confirmed by noting that the coupling could be altered over a significant range by mere rotation of the resonator. Following these optimal design rules we were able to measure the Q-factors of quasi-TE and quasi-TM modes with high precision in four cylindrical sapphire resonators at room temperature. The highest attainable Q-factor was (2.1 +/- 0.1) x 10^5 at 9 GHz in a quasi-TM mode.