延时反馈双环掺铒光纤激光器互注入系统中的混沌同步研究

Chaos and synchronization in mutually coupled erbium-doped fiber ring lasers with time delay

分析了延时反馈双环掺铒光纤(EDF)激光器互注入系统的动态特性,并引入一种量化时间序列复杂度的评价方法——排列熵(PE,permutation entropy),对激光器输出状态和混沌同步质量与复杂度的关系进行讨论。研究表明,通过调节反馈延迟时间和反馈强度可控制系统的输出状态,使系统输出为周期态和混沌态,而且利用PE熵计算激光器输出信号的复杂度相对于分岔图同样能直观准确的反映出系统动态行为;在激光器独立工作情况下,输出信号的混沌区域内夹杂有较多的周期态,而在互注入情况下,混沌区域增宽且较为平坦,同时输出信号复杂度的PE值较高,互注入系统有利于参数选择的范围和提高混沌通信系统的安全性;提高注入强度可得到高质量的混沌同步,两个激光器在同步和不同步时输出信号的复杂度是不同的,可见研究激光器输出信号的复杂度可成为分析混沌同步质量的一种参考。

In this paper, the output dynamics of mutually-coupled erbium doped fiber ring lasers with time-delayed optical feedback is investigated quantitatively and discussed briefly,in terms of an informa- tion-theory-based quantifier derived from information theory, i. e. , the permutation entropy （PE）. The relationship between the quality of chaos synchronization and the chaotic complexity is mainly focused on throughout our work. It is shown that the PE can be effectively used to detect the dynamical changes qualitatively and quantitatively, such as steady state,periodic state and chaotic state. Besides, the PE values calculated from the output of the mutually-coupled scheme are much higher and more stable than those for the solitary laser,which means that more complex chaotic carriers can be generated from the former system, leading to the security enhancement of the chaotic optical communications. Moreover, we also find that, the PE values for these mutually-coupled lasers versus the embedding dimension are almost the same under the condition that the high-quality synchronization between them is achieved. In contrast,these PE values become sufficiently different when the good synchronization is not obtained, which further indicates that the PE quantifier could be employed as an effective tool to distinguish the synchronization quality between the coupled lasers, or at least capable of providing additional information on the performance of chaos synchronization.