Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain

The frequency dependence of the photorefractive effect is considered. The frequencies can be applied by introducing a temporal phase shift in one of the beams in a two-wave mixing configuration. The analysis of the Kukhtarev equations is based on the small modulation approximation, but in contrast to earlier papers, no a priori approximations are made. The analysis results in a second-order model with an explicit dependence on both the grating spacing and the temporal grating frequency. Curves for the modulus and the imaginary part of the space-charge field are obtained, and it is concluded that, for small fringe spacings, the second-order model presented here provides important information on the photorefractive effect. Furthermore, the π/2 phase shift between the intensity pattern and the space-charge field becomes difficult to obtain for small fringe spacings since the applicable frequency range becomes narrow. It is shown that the current density in general has a component perpendicular to the grating wave vector. This component vanishes when the applied field is either zero or parallel to the grating wave vector. In experiments where this is not the case, this component produces a change in the refractive index along the grating wave vector.