Hexagonal patterns in multistep optical parametric processes

Abstract

The existence and competition of a novel class of hexagonal patterns in a nonlinear optical system are reported. These states are found in a mean-field model of a doubly resonant frequency divide-by-3 optical parametric oscillator $\left(3\omega \to 2\omega +\omega \right)$ in which the multistep parametric process, $2\omega =\omega +\omega$, is weakly phase matched. A generalized Swift–Hohenberg equation and a set of amplitude equations are derived to describe the coexistence of hexagonal patterns formed by the superposition of either three or six phase-locked tilted waves.

© 2001 Optical Society of America

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