Modeling of the nonlinear response of photorefractive crystals

The problem of photorefractive coupling between two light beams under the combined influence of an applied electric field, E₀, and a moving grating has been analytically treated by a number of authors in the limit of small modulation depths, m, for which linear approximations are good. In this dissertation, the problem is treated numerically by solving the time-dependent Kukhtarev's equations governing the photorefractive effect. For this purpose, a one-dimensional numerical model of a photorefractive crystal, as part of a circuit, is developed allowing for a self-consistently applied electric field, moving grating, and arbitrarily large modulation depth in the intensity profile. Bismuth silicon oxide (BSO) is used as the working material for this nonlinear analysis.; The transient behavior of the space-charge electric field, E_SC, is predicted including the temporal behavior of its spatial harmonics for moving and nonmoving grating and a range of applied fields, E₀. When m is large, it is possible to have a large photorefractive response, but at the expense of longer settling times.; The numerical results are used to fully define the nonlinear frequency response over a broad range of moving grating velocities which are determined by the detuning frequency, f, between the two incident lights beams. For low f, the response is superlinear and for relatively large f, it is sublinear. For the first time, a characteristic mid-range frequency, f_l, is predicted at which the response is linear despite the presence of nonlinearly generated higher-harmonics of the fundamental grating wave number. At f = f _l, the sublinearity of the fundamental spatial harmonic is closely compensated by the higher-harmonics to yield a linear response for the composite space-charge electric field.; The results from the numerical model are compared with the solutions given by the available perturbational analysis, indicating that the perturbational analysis is sufficiently accurate only for relatively small values of m.; The model is used to examine the time harmonic contents of the photorefractive response. The temporal data show strong nonlinearities for f < f_l, as in the spatial case; that is, strong higher-harmonics at 2f, 3f, etc., are generated.