Thermal control of a dual mode parametric sapphire transducer

We propose a method to keep under control the thermal contributions to the stability in sapphire dielectric transducers, made by two dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. Measuring at the same time the frequency of a WGH mode and a WGE mode allows to separate the information on gap and on temperature. A simple model, valid in quasi equilibrium conditions, describes the frequency shift of the two modes in terms of four tuning parameters. A procedure for the direct measurement of them is presented.