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

We theoretically investigate the evolvement of dark spatial soliton with cascading quadratic nonlinearity in quasi-phase-matched second harmonic generation. It is shown that the dark solitary wave can propagate stably when background intensity is large enough, in which diffraction of beam can be balanced by the cascading quadratic nonlinearity. We also analyze the influence of phase-mismatch on the stability of dark soliton propagation.