Bifurcations of n-homoclinic orbits in optically injected lasers
Bifurcations of n-homoclinic orbits in optically injected lasers
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DOI：
10.1088/0951-7715/18/3/010
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发表时间：
2005-05
期刊：
影响因子：
1.7
通讯作者：
S. Wieczorek;B. Krauskopf
中科院分区：
文献类型：
--
作者：
S. Wieczorek;B. Krauskopf
本文详细研究了半导体激光器三维速率方程模型中的同宿分岔的复杂结构。具体地说，我们发现并遵循在（K，ω）-平面曲线的n-同宿分支，其中鞍焦点是连接到自己的第n个返回到一个邻域的鞍。我们揭示了一个复杂的相互作用的余维二双同宿和T-点分岔。此外，我们还研究了分叉图随激光器线宽增强因子α的变化。特别是，我们发现折叠（最小值）的T-点分歧和双同宿分歧曲线，这是积累了无限多的变化的分歧图，由于过渡通过奇点的表面同宿分歧。注入激光器出现作为一个系统，允许一个研究余维二分叉的n-同宿轨道在一个具体的向量场。同时，（K，ω）平面上的分岔图具有物理意义。一个例子是识别多脉冲激发性的区域及其对参数α的依赖性，其中激光器通过发出n个脉冲来对单个小扰动做出反应。
We study in detail complex structures of homoclinic bifurcations in a three-dimensional rate-equation model of a semiconductor laser receiving optically injected light of amplitude K and frequency detuning ω. Specifically, we find and follow in the (K, ω)-plane curves of n-homoclinic bifurcations, where a saddle-focus is connected to itself at the nth return to a neighbourhood of the saddle. We reveal an intricate interplay of codimension-two double-homoclinic and T-point bifurcations. Furthermore, we study how the bifurcation diagram changes with an additional parameter, the so-called linewidth enhancement factor α of the laser. In particular, we find folds (minima) of T-point bifurcation and double-homoclinic bifurcation curves, which are accumulated by infinitely many changes of the bifurcation diagram due to transitions through singularities of surfaces of homoclinic bifurcations. The injection laser emerges as a system that allows one to study codimension-two bifurcations of n-homoclinic orbits in a concrete vector field. At the same time, the bifurcation diagram in the (K, ω)-plane is of physical relevance. An example is the identification of regions, and their dependence on the parameter α, of multi-pulse excitability where the laser reacts to a single small perturbation by sending out n pulses.