Spatial solitons in biased photorefractive materials with both the linear and quadratic electro-optic effects

Unlike previous cases discussed, non-linear changes of refractive index in the photorefractive (PR) materials are governed by both the linear and quadratic electro-optic (EO) effects simultaneously now. Here, the evolution equations of one-dimension spatial solitons resulting from both the linear and quadratic EO effect are presented firstly. Under appropriate conditions, our analysis indicates that bright, dark, and gray solitons can exist in the steady-state regime. Moreover, stabilities of bright and dark soliton propagation are analyzed by means of beam propagation methods. The analytical solutions in the low-amplitude regime are also obtained. The self-deflection of such bright spatial solitons arising from diffusion effect in biased PR crystals involving both the linear and quadratic EO effects has been investigated symmetrically by the use of numerical techniques and perturbation methods.