Computed resonant frequency and far fields of isolated dielectric discs

The natural resonant frequencies of a circular dielectric disc are computed numerically. The surface integral equations are used to formulate the problem, and the method of moments is then used to reduce integral equations to a matrix equation. The natural resonant frequencies are defined as the frequencies that make the determinant of the moment matrix vanish. Since the dielectric disc is rotationally symmetric, Fourier expansions are used to expand the azimuthal variation of the unknown equivalent surface currents, which makes it possible to search for the zeros of the moment matrix for a particular azimuthal mode. Location of the zeros is computationally intensive and identification of the modes requires significant computation and careful study of the field behavior. The modes that can be obtained are of two types: modes that correspond to a dielectric disc of half the height located above a perfect electric ground plane and modes that correspond to a dielectric disc of half the height above a perfect magnetic plane.<>