Plane-wave expansions used to describe the field diffracted by a grating

Abstract

The properties of plane waves are well known, and it is probably because they are that we often try to represent any unknown field as a combination of such waves. Is such a representation always efficient or even correct? We try to answer this question for a simple problem arising in the electromagnetic study of gratings. We first summarize in a didactic way some important theoretical results that are probably not well known to those working in optics. Thereafter we report on recently performed numerical experiments. Plane-wave field representations indeed permit us to obtain quickly reliable results for some particular profiles. Nevertheless, the methods leading to the solution of an integral equation are the most useful because they are applicable to a larger class of groove profiles.