Eigenfrequencies in Microwave Eccentric Spherical Cavities by a Local Point-based Boundary Conditions Method

We have developed a method for solving the electrodynamic problem for a perfect electric conducting spherical cavity in which a spherical dielectric inhomogeneity is randomly located with respect to the center of the structure. No limitations on the size or on the relative position of the inner dielectric sphere are imposed. The electromagnetic field is appropriately expanded in terms of Hertz potentials. One of features of the method is the ability to satisfy the boundary conditions at the interface between the two media, as well as on the outer metallic spherical surface, at individual points located on these boundaries. In this case, there is no need to integrate and formulate boundary conditions for each basic mode, as it is usually done by classical methods for solving electrodynamic problems in the frequency domain. In the present contribution, we carry out a numerical study to compute the eigenfrequencies in such eccentric configurations. For this purpose, we extract the eigenfrequencies for quasi-TE and quasi-TM modes, and compare the results with an analytical technique. In addition, we validate the results and compare the computational efficiency of our method with HFSS commercial software. Our method turns out to be efficient in terms of CPU time with minimal memory consumption, as compared to the commercial solver.