Faceting and coarsening dynamics in the complex Swift-Hohenberg equation

Lendert Gelens and Edgar Knobloch
Phys. Rev. E 80, 046221 – Published 30 October 2009

Abstract

The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.

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  • Received 20 July 2009

DOI:https://doi.org/10.1103/PhysRevE.80.046221

©2009 American Physical Society

Authors & Affiliations

Lendert Gelens1,* and Edgar Knobloch2

  • 1Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium
  • 2Department of Physics, University of California, Berkeley, California 94720, USA

  • *lendert.gelens@vub.ac.be

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Vol. 80, Iss. 4 — October 2009

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