Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator

We study the stability of the interaction between a pump wave and a counter propagating second-harmonic wave phase-matched in a periodically poled χ⁽²⁾ material using both analytical and numerical methods. In contrast to the more usual copropagating case, backward phase-matched frequency doubling displays richer and more complex behavior, owing to the presence of built-in feedback.