Efficiency and polarization characteristics of photorefractive diffraction in a Bi_12SiO_20 crystal

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Abstract
We study the polarization properties of volume phase gratings induced in photorefractive materials that are both optically active and linearly birefringent, such as Bi12SiO20, Bi12GeO20, and Bi12TiO20. Analytic expressions for the diffraction efficiency and for the orientation and the ellipticity of the diffracted light have been derived for the 〈110〉 and 〈001〉 configurations under the assumption of a nondepleted readout beam. The physical parameters that determine the polarization characteristics of the diffracted light are the orientation of the readout vector, the crystal thickness, the optical activity, and the electric-field-induced linear birefringence. Our results are valid for arbitrary values of these parameters. The particular cases of zero optical activity, zero linear birefringence, a thin crystal, or a specific readout-vector orientation can be deduced from the general formulas. The analytic expressions that we have derived permit an optimal choice of different parameters for the image-processing and beam-coupling applications of these materials.