Paulau P V, Gomila D, Colet P, Malomed B A, Firth W J
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07071 Palma de Mallorca, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 2):036213. doi: 10.1103/PhysRevE.84.036213. Epub 2011 Sep 23.
We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m=∞, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.
我们将与耗散线性方程线性耦合的三次复金兹堡 - 朗道方程用作具有外部频率选择反馈的激光器模型。该系统也可作为由固有增益和选择反馈驱动的介质中的一般图案形成模型。严格来说，用三次项近似激光非线性仅在小场强时有效，但它定性地再现了在整个孤子存在的参数区域中具有更复杂非线性的模型中获得的耗散孤子的结果。分析集中在二维条纹状和涡旋孤子上。条纹孤子的解析表达式由已知的一维孤子解得到，并突出了其与涡旋孤子的关系。涡旋的半径随其拓扑电荷m线性增加，因此条纹状孤子可解释为m = ∞的涡旋，反之，涡旋孤子可实现为弯曲成稳定环的不稳定条纹。涡旋的结果适用于广泛的物理系统。
