An electron-hole transport model for the analysis of the photorefractive harmonic gratings

The steady-state exact solution for the higher harmonic gratings that synthesize the space-charge field is derived without restrictions within an electron-hole transport model which allows the behavior of these harmonic gratings to be determined rigorously in terms of the main photorefractive parameters. The model predicts the independence of the fundamental and harmonic amplitudes on the average excitation intensity. With respect to the modulation depth m, the dependence of each ν-harmonic order is established as m^ν which is the result obtained in the single-level model. In terms of the grating spacing, three regions of quite different behavior are identified as the linear, transition, and nonlinear regions. The extent of each region in terms of Λ strongly depends on the acceptor density relative to the donor density. If the acceptor density is much greater or smaller than the donor density, the linear region spreads out toward the lowest spacing, the nonlinear region extends toward the highest spacing, and the intermediate region is located in-between, as in the Kukhtarev model. But, for similar concentrations, the nonlinear region is shifted toward smaller spacing with respect to the linear region. On the other hand, the electron-hole competition can be deleterious for recording the grating, due to the charge compensation produced by the additional charge carrier that screens the internal space-charge field. Also, the relative importance of the higher harmonics is apparent for the smallest values of the external field as in the single-level model