Self-deflection of dark and gray photovoltaic solitons

We use both the numerical method and the perturbation technique to investigate the self-deflection process of a dark photovoltaic spatial soliton in a photovoltaic photorefractive crystal with diffusion effect. It is found that the dark soliton does not propagate along a parabolic trajectory, and it becomes grayer during the propagation in the photorefractive crystal. In the normalized coordinate system(ξ,ζ), the dark soliton deflects to the direction of ξ>0, which is different from that of the bright soliton. Besides, the deflection of dark solitons can be controlled effectively by modulating the ratio of effective Glass coefficient r and the intensity of the signal beam. We also investigated numerically the self-deflection characteristic of gray solitons, which depend on the direction of its initial transverse velocity v. When v>0, gray soliton deflects to the direction of ξ>0 in the coordinate system(ξ,ζ); when vξξ>0 after propagating for a small distance.