A two-dimensional theory of volume holograms with electric polarization in the plane of the grating

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Abstract
The properties of lossless volume holograms, recorded with the aid of two waves satisfying geometrical optics whose electric field vectors and propagation vectors all lie in the same plane, are investigated. Coupled vector differential equations are derived for the amplitudes of the diffracted and transmitted waves during reconstruction, and by studying the resulting scalar differential equations it is shown that the electric field components in the direction of propagation are negligible. Examples involving plane and cylindrical waves are studied and the mathematical problems are compared with the corresponding ones for perpendicular polarization.

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