Generalized Reciprocity Relations for Perfectly Conducting Gratings

Abstract

Two generalized reciprocity relations are demonstrated for perfectly conducting gratings in the two cases of polarization. Each of them involves two electromagnetic fields, which may correspond not only to different incident fields, but also (which is new) to different profiles of the scatterers. Several well-known consequences are then derived: energy conservation, classical reciprocity, relations between far fields and surface currents. Moreover, the linear relation (the so-called functional derivative) between a small variation of the profile of the grooves and the corresponding variation of a complex coefficient in any order are deduced in a straightforward manner; this technique yields very short and elegant formulae.