Low-amplitude coherently coupled spatial soliton pairs due to both the linear and quadratic electro-optic effects

A comprehensive study of coherent coupling of low-amplitude spatial solitons that co-propagate in biased photorefractive crystals with both the linear and quadratic electro-optic effects was presented. Our results were shown that coherently coupled bright-bright and dark-dark spatial soliton pairs in the low-amplitude regime could be formed under appropriate conditions. The evolution equations, analytic solutions and the expressions of soliton pair widths of these low-amplitude coherently coupled spatial soliton pairs were obtained. It was proven that the existence, property and propagation of these soliton pairs due to co-effects of both the linear and quadratic electro-optic effects was greatly influenced by the photorefractive effects which could be enhanced, weakened or even counteracted because of the interaction of these two electro-optic effects. Moreover, the effects of three physical factors, i.e., the initial phase difference between two incident coherent beams, the intensity ratio and various external bias field on the existence conditions, properties of these low-amplitude coherently coupled soliton pairs have been discussed in detail. Finally, the self-deflection of low-amplitude bright-bright soliton pairs had also been investigated by means of perturbation procedure.