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

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.