Resonant frequencies and Q-factors of a spherical cavity loaded by an eccentric dielectric sphere

A rigorous analysis for both resonant frequency and the Q-factor of the intrinsic modes in a spherical cavity loaded by an eccentric dielectric sphere is proposed. For generality, the outer shell of the structure is considered to be an arbitrary physical medium, e.g. a conductor of large but finite conductivity or a dielectric of high permittivity. With a rigorous representation for the field of the mode, energy leaking out from the structure or dissipated in the loading dielectric of loss might be taken into account by the final characteristic equation determining complex resonant frequencies. Therefore, each complex resonance obtained from the equation contains the information of the Q-factor, as well as the resonant frequency of the corresponding mode. Higher-order modes in a metallic spherical cavity loaded by an eccentric dielectric sphere are evaluated with the formulae, and numerical results for both resonant frequencies and Q-factors are obtained