We investigate backward second-harmonic generation in short-period quasi-phase-matched gratings by means of a finite-difference time-domain method adapted to modelling dispersive nonlinear propagation in the one-dimensional quasi-scalar approximation. Particular emphasis is placed on instability phenomena, encompassing bistability, limiting (frustrated bistability), and self-pulsing. We check the behaviour of the frequency conversion process against the prediction of the coupled-mode theory.
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