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Polarization patterns in Kerr media

AuthorsHoyuelos, Miguel; Colet, Pere ; San Miguel, Maxi ; Walgraef, Daniel
Issue Date1998
PublisherAmerican Physical Society
CitationPhysical Review E- Statistical, Nonlinear, and Soft Matter Physics 58: 2992-3007 (1998)
AbstractWe study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern (for linearly polarized driving) to a circularly polarized hexagonal pattern (for circularly polarized driving). Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations.
Identifiersdoi: 10.1109/EQEC.1998.715062
issn: 1063-651X
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