On the degeneracy of whispering gallery modes in a high-Q sapphire microwave resonator

Abstract: Cylindrical WGM resonators machined in high-quality sapphire monocrystal cooled down to liquid helium temperature offer exceptionally-high Q-factors in the microwave frequency domain. Such a resonator constitutes the core of an ultra-stable oscillator featuring fractional frequency stability better than 1e-15 at short integration times. As in any cylindrical resonant structure, the WGM resonator presents a two fold degeneracy. When a defect breaks the cylindrical symmetry of the resonator, the WGMs split and appear as doublets. In the high-quality sapphire resonator, the frequency separation of these twin modes varies from one mode order to another with a maximum value of a few tens of kHz. While the mode splitting for a given mode was considered until now unpredictable and intrinsic to each resonator since resulting a priori from randomly distributed defects. we show here, at the contrary, that the observed mode splitting found on all the sapphire resonators whatever their origin mainly comes from a perfectly determined defect resulting from the manufacturing processes.