Abstract

A mathematical tool for the analysis of wave propagation in modulated media is presented. Modulated medium here means a medium in which the refractive index can be held to be periodic in small regions but in such a manner that the period, or the direction of the modulation (i.e., the grating vector), can vary on a macroscopic scale. The most common realizations of such media are holograms. Uniformly periodic media (in which the grating vector is constant) are particular cases of modulated media. The main concepts of modulated media are introduced and applied to the case of uniformly periodic media to show their relationships to usual theories. The method presented uses modal expansions and is approximate; it is shown that, in the case of uniformly periodic media, the theory becomes exact and reduces then to the well-known characteristic mode theory. The purpose of the paper is to give a method for treating the complete three-dimensional (and vectorial) problem in which an arbitrarily shaped wave is diffracted by a medium of arbitrarily shaped modulation. Only the mathematical method is described.

© 1991 Optical Society of America

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