Mode Decomposition Method for the Frequency Spectrum of Double-Spherical Cavity Resonator

We present a novel theoretical method for solving the Maxwell equations to obtain the frequency spectra of inhomogeneous and asymmetric cavity resonators using only two scalar potentials. The structure we study is a layered spherical cavity resonator with symmetrically or asymmetrically embedded spherical dielectric inclusion. The comparison of the exact numerical results for the frequency spectrum of such a layered resonator with centralized inner sphere, which are obtained directly from Maxwell equations, and the frequency spectrum found based on the developed theory reveals good agreement at the initial part of the frequency scale. The coincidence accuracy depends significantly on the number of seed resonant modes that we use in numerical simulations.