Higher-order mode interaction in planar periodic structures

A method for the inclusion of higher-order evanescent modes in planar periodic structures is presented. The approach utilises the wave matrix method that is extended to account for the nonpropagating orders. As an example, the case of two closely spaced singly periodic gratings is demonstrated. In order to produce suitable data concerning reflection and transmission matrices, an integral equation formulation is used to describe the scattering behaviour of the grating. The application of the theory is intended for the design of multilayer dichroic surfaces.