Resonance Frequency Analysis of the 2D Dielectric Objects with a Rigorous Algorithm Based on the Analytical Regularization Method

Abstract

The resonance frequencies of the system of dielectric objects are investigated with a previously constructed rigorous algorithm based on the Analytical Regularization Method (ARM) which is widely used to construct well-conditioned algebraic equation systems of the second kind by using some problem-dependent left and right hand- side regularizers. In this paper the previous algorithm is extended to handle arbitrary boundaries and the integral equation system is constructed in a way that eliminates the inner resonances of the perfectly conducting object of the same shape. The algebraic equation system resulting from the discretization of the boundary integral equation system is a first-kind one and does not allow to search of the eigenvalues of the matrix numerically. That is why through the operators of ARM, this algebraic equation system is transformed to a second kind one for which the matrix entries are convenient for the search of eigenvalues numerically. The numerical results show that the ARM-based algorithm allows finding the eigenvalues of the system of a dielectric object accurately whereas the first kind of system does not because of numerical overflow during the root search algorithm.