Rigorous analysis of the TM0n modes in a dielectric-post resonator with an annular slot in the upper plate

The problem of a cylindrical dielectric-post resonator with an annular slot in the upper plate is rigorously solved. The analysis is based on an integral equation for the electric field in the slot which in the absence of external excitation has nontrivial solutions only at the complex resonant frequencies of the structure. This integral equation is solved numerically by the method of moments, and the resonant frequencies are determined as the zeros of the associated matrix determinant in the complex frequency plane. Attention is limited to the axisymmetric TM_0n modes. Sample numerical results are given, including the complex resonant frequencies, the associated modal fields, and the radiation patterns of the first few resonator modes. The dependence of these quantities on the width and location of the annular slot is shown