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

TL;DR

This paper investigates the degeneracy and mode splitting in high-Q sapphire microwave resonators, revealing that the observed splitting is primarily caused by specific manufacturing defects rather than random imperfections.

Contribution

It demonstrates that mode splitting in sapphire WGM resonators is mainly due to a well-defined manufacturing defect, challenging previous assumptions of randomness.

Findings

Mode splitting varies with mode order, reaching up to tens of kHz.

Mode splitting is primarily caused by a specific manufacturing defect.

The defect responsible for splitting is reproducible across resonators.

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.