Homogenization Techniques as Applied in the Electromagnetic Theory of Gratings

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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.

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