Abstract

A simple, three-dimensional, holographic grating consists of a sinusoidally modulated dielectric slab. The assumption that the modulation index, δ, is constant is at most a first-order approximation. Usually, the light beams used in making the grating are attenuated inside the recording material, hence δ varies within the dielectric slab. From known solutions for the electromagnetic field diffracted by a uniform dielectric grating, solutions for the case when δ is not constant are found, first for a lossless and then for a lossy dielectric grating. The effective modulation index of the grating at exactly Bragg-angle incidence is given by the averaged value of δ over the slab thickness.

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