Femtosecond pulse synthesis by efficient second-harmonic generation in engineered quasi phase matching gratings

We numerically design quasi-phase matched crystals with domains of arbitrary sizes for second harmonic generation by femtosecond pulses, taking into account both group velocity mismatch and dispersion. An efficient simulated-annealing algorithm is developed to design quasi-phase matching gratings which can yield the desired amplitude and phase of second-harmonic pulses in the presence of pump depletion. The method is illustrated with reference to single, double-hump and chirped fs Gaussian pulses in a lithium niobate crystal.