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 (3ω→2ω+ω) in which the multistep parametric process, 2ω=ω+ω , 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
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
Stefano Longhi, "Hexagonal patterns in multistep optical parametric processes," Opt. Lett. 26, 713-715 (2001)