The study of whispering modes in anisotropic and isotropic dielectric spherical resonators

The frequency standards and metrology research group at the University of Western Australia was recently funded to perform a new Michelson-Morley (MM) experiment using a low noise dual-mode oscillator, based on a spherical microwave resonator. One option is to use a high-Q dielectrically loaded cavity. The mode structure, frequency and Q-factor of whispering modes within spherical dielectric resonators have been investigated. In particular we examined the frequency degenerate whispering spherical mode families and discuss their potential to form the basis of a sensitive MM test in the microwave regime. It is possible to solve a spherically-symmetrical system analytically but, in practice, departures from perfect sphericity occur due to the necessity of a support structure for the dielectric and hence it is necessary to implement a numerical solution. Finite element modeling is used to predict the mode structure of two spherical copper resonators, the first loaded with an isotropic fused-silica sphere loaded with cylindrical Teflon supports, and the other with a HEMEX sapphire "sphere on a stick". Predicted frequency splitting of the degenerate modes is confirmed by comparing experiment with finite element calculations, and is shown to be within experimental error set by the dimensions of the resonators.