Determination of optimal directions of the wave vector of the phase holographic grating in cubic photorefractive crystal

The dependence of the change in the components of the inverse permittivity tensor of a cubic photorefractive Bi₁₂SiO₂₀ crystal on the direction of the wave vector of holographic grating in the crystal coordinate system has been studied. It is shown that, when recording a phase hologram, the largest change in the refractive index of Bi₁₂SiO₂₀ crystal is attained when the holographic grating wave vector is oriented along symmetrically equivalent <111> directions. The maximum possible modulation amplitude of the refractive index of a holographic grating with the wave vector oriented along the <110> directions is found to exceed that in the case of orientation along the <100> directions. The components of the inverse permittivity tensor of Bi₁₂SiO₂₀ crystal were calculated taking into account that a phase hologram is recorded under linear electro-optic, photoelastic, and inverse piezoelectric effects.