  We develop a theoretical method for solving Maxwell's equations to obtain the
frequency spectra of inhomogeneous and asymmetric cavity resonators using a
couple of effective Debye-type potentials. The structure we study specifically
is the layered spherical cavity resonator with symmetrically or asymmetrically
inserted inner dielectric sphere. The comparison of the exact numerical results
obtained for the frequency spectrum of layered cavity resonator with
centrosymmetrically inserted sphere and the spectrum found from the suggested
theory reveals good agreement at the initial part of the frequency axis. The
coincidence accuracy depends on the number of trial resonant modes that we use
while approving our method numerically.
