Engineered quasi-phase matching for multiple parametric generation

We develop a rapid and efficient numeric technique for the design of arbitrary quasi-phase matched lattices for parametric generation of single and multiple pulses with any prescribed amplitude and phase profiles from fundamental frequency excitation in the regime of pump depletion. We examine the case of simultaneous of 2nd and 3rd harmonic generation in arbitrary quasi-phase matched gratings taking into account the group velocity mismatch and dispersion