The Method of Potentials for the Frequency Spectrum of Non-Homogeneous Spherical Cavities

We develop a novel theoretical method for solving the Maxwell equations in cavity resonators with inhomogeneous and asymmetrical filling. The method relies on the transition from vector description of electromagnetic fields in the resonator to a description in terms of two scalar functions (Debye potentials) for which we derive the original control equations. The solution to these equations is carried out with the use of Green functions, for which we obtain the infinite set of coupled equations in the resonance mode representation. The equations, which contain operator-valued potentials, are solved unperturbatively, by applying the original method for resonance mode decoupling. The frequency spectrum of the resonator with central-layered dielectric infill, which is found based on the developed theory, is in good agreement with the spectrum obtained numerically directly from Maxwell equations. The analysis of the inter-frequency intervals in the spectrum reveals its gradual chaotization with breaking the resonator symmetry.