Shear-Induced Bifurcations and Chaos in Models of Three Coupled Lasers
Shear-Induced Bifurcations and Chaos in Models of Three Coupled Lasers
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DOI：
10.1137/100817383
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发表时间：
2011-01-01
影响因子：
2.1
通讯作者：
Wieczorek, Sebastian
中科院分区：
文献类型：
--
作者：
Blackbeard, Nicholas;Erzgraeber, Hartmut;Wieczorek, Sebastian
本文研究了具有转动S-1和反射Z（2）对称性的三个耦合激光振荡器线性阵列中的非线性动力学。重点是耦合激光模型依赖于三个参数：激光耦合强度，Kappa，激光频率失谐，三角洲，和程度之间的耦合的激光，α的振幅和相位，也被称为剪切或非等时性。数值分岔分析与李雅普诺夫指数计算一起使用，研究系统动力学的不同方面。首先，在（kappa，Delta）平面中具有稳定相位锁定的区域的形状和范围随着α急剧变化。我们解释这些变化的codimension-two和-三分叉（相对）平衡。此外，我们确定锁定解锁过渡，由于全球同宿和异宿分支和相关的无限级联的局部分支。第二，确定性混沌的广大地区出现在（kappa，Delta）平面非零α。我们给出了一个直观的解释，这种效果在阿尔法引起的拉伸和折叠的行动，创造马蹄铁和讨论不同的拓扑结构的混沌吸引子。一个更准确的复合腔模式模型的类似分析揭示了良好的协议与耦合激光模型的本地和全球的分叉以及混沌动力学的水平，只要激光器之间的耦合不是太强。这些结果为研究激光器阵列的非线性行为提供了新的建模途径和方法。
We study nonlinear dynamics in a linear array of three coupled laser oscillators with rotational S-1 and reflectional Z(2) symmetry. The focus is on a coupled-laser model with dependence on three parameters: laser coupling strength, kappa, laser frequency detuning, Delta, and degree of coupling between the amplitude and phase of the laser, alpha, also known as shear or nonisochronicity. Numerical bifurcation analysis is used in conjunction with Lyapunov exponent calculations to study the different aspects of the system dynamics. First, the shape and extent of regions with stable phase locking in the (kappa, Delta) plane change drastically with alpha. We explain these changes in terms of codimension-two and -three bifurcations of (relative) equilibria. Furthermore, we identify locking-unlocking transitions due to global homoclinic and heteroclinic bifurcations and the associated infinite cascades of local bifurcations. Second, vast regions of deterministic chaos emerge in the (kappa, Delta) plane for nonzero alpha. We give an intuitive explanation of this effect in terms of alpha-induced stretch-and-fold action that creates horseshoes and discuss chaotic attractors with different topologies. Similar analysis of a more accurate composite-cavity mode model reveals good agreement with the coupled-laser model on the level of local and global bifurcations as well as chaotic dynamics, provided that coupling between lasers is not too strong. The results give new insight into modeling approaches and methodologies for studying nonlinear behavior of laser arrays.