Second-harmonic pulse shaping with engineered quasi-phase-matching gratings in the strongly depleted pump regime

In this paper, a powerful approach for arbitrary pulse shaping based on SHG is discussed in engineered quasi phase matching in the case of strong pump depletion. We used a simulated-annealing algorithm (SAA), numerically solving the coupled-wave equations for fundamental and second harmonic (SH) pulses, taking into account both group velocity mismatch and group velocity dispersion. In order to reduce the SAA iteration time and increase computing speed, we employed simple fast Fourier transform and fourth-order Runge-Kutta algorithms. To design a QPM grating for the generation of an arbitrary target SH pulse, we start the SAA with an initial guess for a fixed number of integration domains and a given fundamental wave pulse.