Gelens Lendert, Knobloch Edgar
Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Brussel, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046221. doi: 10.1103/PhysRevE.80.046221. Epub 2009 Oct 30.
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.
复杂的斯威夫特 - 霍恩伯格方程模拟了由起始时具有有限波数的振荡不稳定性产生的图案形成，并在激光、光学参量振荡器和光折变振荡器中得到应用。我们表明，对于实系数，该方程呈现出两类局域态：仅在幅度上局域或在幅度和相位上都局域。后者与相位缠绕态相关，其中序参量的实部和虚部周期性振荡，但它们之间具有恒定的相位差。局域态采取缺陷的形式，这些缺陷连接具有相等且相反相位滞后的相位缠绕态，并且在很宽的参数范围内可以是稳定的。这些缺陷的形成导致初始时空间均匀相位的态出现刻面。根据参数的不同，这些刻面可能会像由卡恩 - 希利厄德方程所描述的那样无限粗化，或者粗化停止，导致形成冻结的刻面结构。
