Evolution of Dark Spatial Soliton in Quasi-phase-matched Quadratic Media

We theoretically investigate the evolvement of dark spatial soliton withcascading quadratic nonlinearity in quasi-phase-matched second harmonicgeneration. It is shown that the dark solitary wave can propagate stablywhen background intensity is large enough, in which diffraction of beam canbe balanced by the cascading quadratic nonlinearity. We also analyze theinfluence of phase-mismatch on the stability of dark soliton propagation.