Kinetics of the higher-order response of photorefractive materials

The analytic expressions for the first three higher-order harmonics of the space-charge field versus time are obtained by use of the hopping model of Feinberg et al. [J. Appl. Phys. 51, 1297 (1980)]. The results are valid for arbitrary strengths of characteristic fields in the photorefractive materials with arbitrary values of the modulation depths. The dependence of the fundamental space-charge field on the higher-order fields is strong as the modulation depth increases. There is an apparent peak that originates from the contributions of the higher-order harmonics during the evolution of the fundamental harmonic of the space-charge field. We also determine the next-order correction to the fundamental space-charge field, which indicates that the ratio of the next-order correction term to the fundamental term is strongly dependent on the modulation depths m.