Bragg diffraction of Gaussian beams by periodically modulated media*

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Abstract
Analytical and numerical results are given on the diffraction of optical beams by a periodically modulated dielectric medium, which represents a thick hologram or an acoustic column. By using a rigorous representation for the field of a realistically bounded beam incident at a Bragg angle, we examine both the refracted beam and the beam due to Bragg scattering inside the periodic medium. The Bragg-scattered beam is formed by continuous coupling of energy from the refracted beam into the Bragg-scattered wave. As the Bragg-scattered wave also couples part of its energy back to the refracted wave, the continuous coupling of energy back and forth between these two waves results in a diffusion of energy over a wide region. For a sufficiently thick modulated layer, both the refracted and the Bragg-scattered beams split into two beams. Because of this distortion of the beam profiles, the diffraction efficiency is found to be smaller than that accounted for by previous approaches using a single incident plane-wave model.