Spatial solitons in biased two-photon photorefractive crystals with both the linear and quadratic electro-optic effect

•We study spatial solitons due to electro-optic effects in two-photon crystals.•We present evolution equation, existence conditions and properties of solitons.•Self-deflection of bright solitons due to diffusion effect is discussed in detail.

The evolution equation of one-dimension spatial optical solitons resulting from two-photon effect in biased photorefractive crystals with both the linear and quadratic electro-optic effect is presented theoretically. Under appropriate conditions, our analysis indicates that bright, dark photorefractive spatial solitons can exist in the steady-state regime. The analytical solutions in the low amplitude regime are also obtained. Moreover, we theoretically discuss the self-deflection of bright solitons by taking the diffusion effect into account. Both the self-deflection effects follow a cubic polynomial of the applied bias field, and increase considerably at higher values of applied bias field. Relevant examples are provided.