Abstract
The properties of the resonant frequency spectrum in the problem on the oscillations of 3D magnetodielectric resonators are studied. A theorem on the discreteness of the spectrum of resonant frequencies in the problem of oscillations in cavity resonators is proved. The problem is reduced to the analysis of a system of volumetric singular integral equations that defines a holomorphic Fredholm operator function of the spectral parameter. The system of Maxwell equations is solved in the case of a space with a dielectric ball by reduction to the solution of a scalar equation for Debye potentials. A characteristic equation of a radially three-layer ball with arbitrary sizes and permeabilities of the layers is obtained and studied.
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This work was supported by the Russian Science Foundation, project no. 20-11-20087.
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Translated by V. Potapchouck
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Smirnov, Y.G., Petrova, Y.A. Numerical and Analytical Study of the Problem of Electromagnetic Oscillations in Open Inhomogeneous Resonators. Diff Equat 58, 1258–1266 (2022). https://doi.org/10.1134/S0012266122090105
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DOI: https://doi.org/10.1134/S0012266122090105