Nonlinear phase shift resulting from two-color multistep cascading

We propose a novel type of cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves. Self-phase modulation of the fundamental wave results from a cascading process consisting of four second-order subprocesses, the direct and reverse subprocesses of Type I second-harmonic generation (SHG) and the direct and reverse subprocesses of Type II SHG. It is found analytically and numerically that the fundamental wave passing through a quadratic medium, tuned for simultaneous near phase matching for these two processes, collects 60% more nonlinear phase shift than does the corresponding two-step cascading. We also obtain the conditions for stationary waves (nonlinear modes) supported by such multistep cascading processes.