Diffractive properties of volume phase gratings in photorefractive sillenite crystals of arbitrary cut under the influence of an external electric field

We study the influence of bias dc electric field on the optical properties of volume phase gratings formed in optically active photorefractive sillenite crystals. By considering a general case where the external electric bias direction, the grating vector orientation, the light propagation direction (crystal cut), and state of polarization are arbitrary, we deduce analytical expressions for the diffraction efficiency and the polarization state of the diffracted beam. The influence of the inverse piezoelectric effect is taken into account both in the uniform and the spatially varying part of the impermeability tensor, as well as into the calculation of the effective static permittivity. A theoretical comparative study of the dynamic behavior of the diffraction efficiency as a function of the physical parameters that affect the diffraction process (crystal cut, electric bias, input polarization, and grating orientation) along with experimental verification is provided. The general analytical solution provides means of exploitation of the capabilities of sillenite crystals in several applications.