A NUMERICAL ABSORBING BOUNDARY-CONDITION FOR FINITE-DIFFERENCE AND FINITE-ELEMENT ANALYSIS OF OPEN PERIODIC STRUCTURES

In this paper we present a novel approach to deriving local boundary c onditions, that can be employed in conjunction with the Finite Differe nce/Finite Element Methods (FD/FEM) to solve electromagnetic scatterin g and radiation problems involving periodic structures. The key step i n this approach is to derive linear relationships that link the value of the field at a boundary grid point to those at the neighboring poin ts. These linear relationships are identically satisfied not only by a ll of the propagating Floquet modes but by a few of the leading evanes cent ones as well. They can thus be used in lieu of absorbing boundary conditions (ABCs) in place of the usual FD/FEM equations for the boun dary points. Guidelines for selecting the orders of the evanescent Flo quet modes to be absorbed are given in the paper. The present approach not only provides a simple way to derive an accurate boundary conditi on for mesh truncation, but also preserves the banded structure of the FD/FEM matrices. The accuracy of the proposed method is verified by u sing an internal check and by comparing the numerical results with the analytic solution for perfectly conducting strip gratings.