Photorefractive grating near the surface of a cubic crystal subjected to an electric field

The structure of a photorefractive grating near the surface of a cubic crystal subjected to an external static electric field is considered in the approximation of a given distribution of photoexcited electrons in the conduction band. This approximation is used to analyse structures of the space-charge field, of the elastic fields, and of perturbations of the permittivity tensor $\Delta \hat{\epsilon}$ in the surface region of the crystal. It is shown that, when the grating vector is oriented along the [001] crystallographic axis, elastic displacements and diagonal elements of the tensor $\Delta \hat{\epsilon}$ exist in the surface region but are absent in the bulk of the sample. The relative amplitudes of the elastic strains and of the permittivity perturbations are proportional to the applied field $E_0$ and, in a crystal of Bi$_{12}$SiO$_{20}$ , they can reach $\sim$ 10$^{-6}$ and 10$^{-5}$ , respectively, for $E_0$ = 10 kV cm$^{-1}$.