Thermal control of a dual mode parametric sapphire transducer

We propose a method to control the thermal stability of a sapphire dielectric transducer made with 2 dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. The simultaneous measurement of the frequencies of both a WGH mode and a WGE mode allows one to discriminate the frequency shifts due to gap variations from those due to temperature instability. A simple model, valid in quasi-equilibrium conditions, describes the frequency shift of the 2 modes in terms of 4 tuning parameters. A procedure for their direct measurement is presented.