Hexagonal patterns in multistep optical parametric processes.
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 (3omega?2omega+omega) in which the multistep parametric process, 2omega=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.
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Longhi