ИСТИНА

It is known that localized elastic and electric fields appear near the surface of piezoelectric crystals under photorefractive grating formation. We report the results of the analysis of the elastic field structure in the region near the (I) Y-plane and (II) X-plane of the KNbO3 crystal. The photorefractive grating vector kg is parallel to Z-axis of the crystal. Taking the crystal surface to be traction free we consider two cases: (a) dielectric boundary and (b) short-circuited boundary. The assumption of given interference light pattern with a fringe spacing  and an independent on y (or x) modulation index m at steady-state is used. It was shown that components U2,1 and U3 depend from the boundary conditions strongly. Also the elastic displacements differ considerably from their values in the volume of the crystal. The amplitude h of the surface relief that is defined by transverse component U2,1 of elastic displacement vector has maximum for a short-circuited boundary x=0 of a crystal. We have analyzed the changes in dielectric tensor ij at optical frequencies. Near the crystal surfaces, the changes in the dielectric tensor are different from their volume values. For example, the component 23 exists near boundary y=0 of the crystal only. For short-circuited boundary a value of the component 23 is roughly one order higher than the values of diagonal components. This clearly demonstrates the possibility for strong coupling of light waves or photorefractive surface waves with orthogonal polarizations, which are propagated near a crystal boundary.