Numerical study of the problem of electromagnetic oscillations of a three-layer spherical resonator filled with a metamaterial 

Yuriy G. Smirnov, Doctor of physical and mathematical sciences, professor, head of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mmm@pnzgu.ru
Yuliya A. Petrova, Research engineer of the Research Center “Supercomputer Simulation in Electrodynamics”, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: petroval1999@rambler.ru 

Background. The purpose of the work is to solve the problem of electromagnetic oscillations of a three–layer spherical resonator, the middle layer of which is filled with metamaterial. Materials and methods. The boundary value problem for the Maxwell system of equations is reduced to solving scalar equations for Debye potentials. The dispersion equation is obtained with respect to the spectral parameter – the circular oscillation frequency. Results. The dispersion equation is solved numerically on the complex plane. Approximate resonant frequencies having a negative imaginary part and symmetrically located relative to the real axis are found. Conclusions. A numerical method for finding the resonant frequencies of a three-layer spherical resonator, the middle layer of which is filled with metamaterial, is proposed and implemented. 

triple layered ball resonator, Maxwell’s equations, electromagnetic oscillations, Debye potentials, metamaterial 

Smirnov Yu.G., Petrova Yu.A. Numerical study of the problem of electromagnetic oscillations of a three-layer spherical resonator filled with a metamaterial. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2022;(4):69–75. (In Russ.). doi:10.21685/2072-3040-2022-4-7