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Three-dimensional simulations and analysis of hexagonal pattern formation in a Kerr medium

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Abstract

We report a detailed series of simulations of counterpropagation of Gaussian beams in a slab of Kerr medium. Inclusion of a second transverse dimension dramatically expands the range of behaviors compared with previous work.1 In particular we observe the formation of stable hexagonal patterns, often with stable or long-lived defect structures. Hexagonal patterns of this type have been observed in sodium vapor2 at frequencies sufficiently detuned from resonance that the Kerr medium approximation may be viable. Severe computer demands are imposed by the need to simulate all three dimensions together with the time, and there is a real need for reduced models retaining only the transverse space variables, which then evolve on a slow time scale.

© 1991 Optical Society of America

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