LOW-TRUNCATION-ERROR FINITE-DIFFERENCE REPRESENTATIONS OF THE 2-D HELMHOLTZ-EQUATION

A methodology is presented that allows the derivation of low-truncatio n-error finite difference representations of the two-dimensional scala r Helmholtz equation. This methodology is a direct two-dimensional ana log of an approach previously derived for one-dimensional beam propaga tion. The resulting finite difference equations are appropriate for mo deling the electromagnetic response to single-frequency excitation of a structure made up of a finite number of rectangular regions of const ant index. They are shown to be accurate to fourth order in the grid s ize (except at dielectric corners), valid for nonuniform grids, and ar e useful for modeling reflections from a very general class of dielect ric structures.