Optimum design of a high-Q room- temperature whispering-gallery-mode X-band sapphire resonator

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 because of minimized probe losses. We noted that when coupling through this technique (as compared with a perpendicularly 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 merely rotating 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. From this analysis, the highest attainable Q-factor is expected to be (2.1 ± 0.1) x 10⁵ at 9 GHz in a quasi-TM mode.