Reflection and transmission characteristics of thin periodic interfaces

Abstract
The reflection and transmission characteristics of an arbitrary, periodic interface characterized by either a surface admittance function or surface impedance function are presented. Two dual formulations are presented and the convergence properties of each are studied in detail. As contrasted to most techniques employing moment methods, the matrix elements of the resulting admittance or impedance matrix used in the computation are computed from simple analytical expressions. We show that the convergence properties of each formulation are highly sensitive to incident polarization. Furthermore, the technique applied in most cases of practical interest yields a rapidly converging solution for the reflected or transmitted field. Peculiar resonances associated with certain periodic structures are examined in detail. For example it is shown that the use of a dielectric mounting structure for a metal-free-space grating can significantly alter the transmission characteristics of the grating.