On the solution of eigenvalue problems deriving from the MoM analysis of EBG structures

This paper describes an efficient method for calculating the dispersion diagram of planar electromagnetic band-gap (EBG) structures. When using an integral equation approach, the calculation of the dispersion diagram is based on an iterative procedure (with a double loop in frequency and propagation constant), which involves a full-wave analysis and the solution of an eigenvalue problem. In our approach, the full-wave analysis is performed by using the MoM/BI-RME method, which is based on the formulation of an integral equation and its solution by the Method of Moments (MOM) with entire-domain basis functions. For a given value of propagation constant and frequency, this full-wave analysis leads to a matrix eigenvalue problem, and the frequencies where the eigenvalue problem presents non-trivial solutions determine the points of the dispersion diagram. The search of the such frequencies is tipically based on the search of the zeros of the determinant of the MOM matrix. In this paper, we propose a different method, based on the tracking of the eigenvalues of the MOM matrix in the complex plane when varying the frequency. This approach proved more reliable than the classical method based on the direct search of the determinant zeros. The method is applied to the analysis of the classical uniplanar compact photonic-bandgap structure, and some results show the accuracy and the efficiency of the method. A comparison between the method based on the tracking of the eigenvalues and the one based on the search of the determinant zeros permits to highlight the advantage of the proposed approach.