  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.
