Homogenization Techniques as Applied in the Electromagnetic Theory of Gratings

Abstract

ABSTRACT Homogenization theory deals with asymptotic methods in periodic structures. In this paper we apply these methods to the study of a dielectric or conducting grating when the spacing of the grating, supposed to be periodic with respect to x, tends to zero. We prove, from a mathematical point of view, that it is in effect possible to replace the groove region by a stratified layer whose optical index is x-independant. Our results, obtained in a rigorous way, confirm and strengthen those foreseen by colleagues of the University of Sydney.