Cryogenic composite whispering-gallery mode resonators for low-phase noise frequency standards

We have investigated composite whispering-gallery mode resonators with resonant frequencies around 10 GHz each consisting of two ring-shaped thin (300 and 400 μm) rutile platelets being arranged at the top- and bottom endplate of a sapphire cylinder. This composite dielectric puck is held in place inside a copper cavity via quartz spacers. For coupling we either used loops in the case of coaxial feedlines or apertures in the case of waveguides. According to numerical field simulations using MAFIA (Schmidt 1992) the fraction of electromagnetic energy stored in the rutile discs is expected to be 0.001. From experimental data of permittivity and loss tangent of rutile and sapphire this filling factor should correspond to a turning point in the temperature dependence of the resonance frequency at 62 K, an unloaded quality factor of 10⁷, and a second derivative of resonant frequency with temperature at the turning point of -0.9 ppm/K ². The latter corresponds to a relative frequency stability of 2·10^-13 for temperature deviations of 1 mK from the turning point. This number makes sapphire-rutile composite WG resonators extremely challenging for frequency standard applications. Experimentally, we have found a turning point at 65 K and Q₀=0.9·10⁷ for the loop-coupled resonator and a turning point at 79 K and Q₀=4·10⁶ for the waveguide-coupled one