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Physical Review A

Hexagonal patterns in optical bistability

W. J. Firth, Andrew J. Scroggie, Graham S. McDonald, L. A. Lugiato

Published Oct 1, 1992• 105 citations
Publisher

Abstract

The mean-field model of optical bistability in a ring cavity is extended to include diffraction in two transverse dimensions. Nonlinear analysis in the neighborhood of the instability of the homogeneous solution indicates the formation of stable hexagonal patterns, and this is confirmed by numerical simulation, with reasonable quantitative agreement. Simulations with higher excitation show defect structures and complex dynamical patterns.

DOI
10.1103/physreva.46.r3609

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The mean-field model of optical bistability in a ring cavity is extended to include diffraction in two transverse dimensions. Nonlinear analysis in the neighborhood of the instability of the homogeneous solution indicates the formation of stable hexagonal patterns, and this is confirmed by numerical simulation, with reasonable quantitative agreement. Simulations with higher excitation show defect structures and complex dynamical patterns.
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A ring-cavity system, filled with an isotropic nonlinear medium and driven by a linearly polarized coherent input field, has been the subject of intense study over the last decade. This system can show a number of non-equilibrium phase transitions, including optical bistability (OB), and transverse pattern formation. The instability responsible for pattern formation then simply serves to drive the system from the unstable lower branch to the stable upper branch. This conclusion, however, is based on the assumption that the internal field in the nonlinear ring-cavity preserves its polarization state as that of the input field. Here we extend the mean field model to include polarization effects.>
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