A method of effective potentials for calculating the frequency spectrum of eccentrically layered spherical cavity resonators

Z. E. Eremenko, Yu. V. Tarasov and I. N. Volovichev

Journal of Electromagnetic Waves and Applications, 2020, vol. 34, issue 6, 802-824

Abstract: A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The spectrum is determined through the introduction of effective “dynamic” potentials which encode the infill inhomogeneity. For angularly symmetric cavity, regardless of its radial non-uniformity, the set of modes is shown to be a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being preserved, suppresses all azimuthally non-uniform modes of TM oscillations. In the absence of angular symmetry of both electric and magnetic properties of the infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The method is quite efficient for computational complex algorithms for solving different spectral problems, including those for studying the chaotic properties of systems' spectra.

Date: 2020
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DOI: 10.1080/09205071.2020.1758220

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