Coarsening and frozen faceted structures in the supercritical complex Swift-Hohenberg equation
Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
2 Department of Physics, University of California, Berkeley, CA, 94720, USA
Corresponding author: a firstname.lastname@example.org
Revised: 7 April 2010
Published online: 12 May 2010
The supercritical complex Swift-Hohenberg equation models pattern formation in lasers, optical parametric oscillators and photorefractive oscillators. Simulations of this equation in one spatial dimension reveal that much of the observed dynamics can be understood in terms of the properties of exact solutions of phase-winding type. With real coefficients these states take the form of time-independent spatial oscillations with a constant phase difference between the real and imaginary parts of the order parameter and may be unstable to a longwave instability. Depending on parameters the evolution of this instability may or may not conserve phase. In the former case the system undergoes slow coarsening described by a Cahn-Hilliard equation; in the latter it undergoes repeated phase-slips leading either to a stable phase-winding state or to a faceted state consisting of an array of frozen defects connecting phase-winding states with equal and opposite phase. The transitions between these regimes are studied and their location in parameter space is determined.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010