From regular to pseudo-stochastic recurrence of modulation instability in cascaded second-harmonic generation

We address the recurrent regime of depleted two-color modulational instability in second-harmonic generation in the cascading limit. We validate a description based on simple algebraic formulas, based on asymptotic matching, establishing quantitatively the limit of validity of this approach. In the low mismatch regime, where such description breaks down, the system is found to undergo pseudo-stochastic alternations between two types of deterministic recurrence.