A Local Point Method Based on DFS Expansion of Boundary Conditions for Eigenfrequencies Calculation of BoR Cavities

We have developed a local point method (LPM) to calculate the eigenfrequencies of perfect electric conducting (PEC) body of revolution (BoR) cavities, with or without a spherical dielectric inclusion. The dielectric inclusion is located on the axis of rotation. The distinguishing features of the method are its integration-free scheme and the no need to employ the translational addition theorem to satisfy the boundary conditions (BCs) on the dielectric insert or on the PEC surface. This is achieved by representing the electromagnetic (EM) field in scalar Hertz potentials and by expanding the prerequisite BCs in discrete Fourier series (DFS) at chosen points on cavity’s generating curve. This strategy allows for fewer computational resources, as compared to methods that rely on numerical integration. We clarify the hybrid mode appearance when the spherical symmetry of the cavity is broken, or when the inclusion is not located at the center of a spherical cavity. We exhaustively validate the method for various cavity shapes with or without the spherical dielectric inclusion. In particular, we compare the LPM with shape perturbation methods (SPMs), with an analytical technique, with the spheroidal eigenfrequency method (SEM), as well as with high-frequency structure simulator (HFSS) commercial software. The numerical convergence, the computational superiority, and the stability of the proposed technique are also discussed. The proposed method can be used for frequency spectrum determination of BoR cavities and may be of interest for engineering applications, including the determination of various key parameters for the characterization of dielectric materials.