Self-deflection of a bright soliton in a separate bright－dark spatial soliton pair based on a higher-order space charge field

The self-deflection of a bright solitary beam can be controlled by a dark solitary beam via a parametric coupling effect between the bright and dark solitary beams in a separate bright－dark spatial soliton pair supported by an unbiased series photorefractive crystal circuit. The spatial shift of the bright solitary beam centre as a function of the input intensity of the dark solitary beam (\hat\rho) is investigated by taking into account the higher-order space charge field in the dynamics of the bright solitary beam via both numerical and perturbation methods under steady-state conditions. The deflection amount (\Delta s_0), defined as the value of the spatial shift at the output surface of the crystal, is a monotonic and nonlinear function of \hat\rho. When \hat\rho is weak or strong enough, \Delta s_0 is, in fact, unchanged with \hat\rho, whereas \Delta s_0 increases or decreases monotonically with \hat\rho in a middle range of \hat\rho. The corresponding variation range (\delta s) depends strongly on the value of the input intensity of the bright solitary beam (r). There are some peak and valley values in the curve of \delta s versus r under some conditions. When \hat\rho increases, the bright solitary beam can scan toward both the direction same as and opposite to the crystal's c-axis. Whether the direction is the same as or opposite to the c-axis depends on the parameter values and configuration of the crystal circuit, as well as the value of r. Some potential applications are discussed.