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Optics Letters

Optics Letters


  • Vol. 26, Iss. 10 — May. 15, 2001
  • pp: 713–715

Hexagonal patterns in multistep optical parametric processes

Stefano Longhi  »View Author Affiliations

Optics Letters, Vol. 26, Issue 10, pp. 713-715 (2001)

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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

OCIS Codes
(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)

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  17. Hexagonal patterns corresponding to mixed states are generally unstable in the framework of the usual amplitude equations that describe subcritical hexagon formation.2,16 It is rather remarkable that the amplitude equations reported here can stabilize these unusual hexagonal states.

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