Hexagonal patterns in multistep optical parametric processes

The existence and competition of a novel class of hexagonal patterns in a n onlinear optical system are reported. These states are found in a mean-fiel d model of a doubly resonant frequency divide-by-3 optical parametric oscil lator (3 omega --> 2 omega + omega) in which the multistep parametric proce ss, 2 omega = omega + omega, is weakly phase matched. A generalized Swift-H ohenberg 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. (C) 2001 Optical Society of Americ a.