Zhong Dongzhou, Yang Hua, Xi Jiangtao, Zeng Neng, Xu Zhe
Opt Express. 2020 Aug 31;28(18):25778-25794. doi: 10.1364/OE.403076.
We have developed a theory model for a three-element laser array where three lasers are laterally coupled using the coupled mode theory and Maxwell equations. New chaotic synchronization properties have been observed systematically in the master-slave configuration, consisting of the driving three-element laser array with self-feedback and the response three-element laser array subjected to the parallel injection or cross injection. Under the parallel injection, the dynamic evolutions of high-quality complete chaotic synchronization between laser elements in different parameter spaces seriously depend on the self-feedback mode of the driving laser elements, such as one, two and all of them with self-feedback. It is found that when only the driving middle one or all of the driving laser elements are subject to self-feedback, high-quality complete chaotic synchronization of all laser elements can be achieved in the same large region of the most of the parameter spaces. In addition, we report here for the first time (to our knowledge) the interestingly symmetrical properties of leader/ laggard chaotic synchronization in the configuration under the cross-injection. Namely, the leader/ laggard chaotic synchronization with high quality between laser elements periodically varies with the delay differences, under the key parameters limited to a certain range. The varying traces of these synchronizations are like sine wave. The mirror symmetry between the laggard chaotic synchronization with in-phase (anti-phase) and the leader one with in-phase (anti-phase) can be achieved by the optimization of the structural parameters of laser waveguides. With the optimization of the related operating parameters, for one of the side-lasers, its leader/ laggard chaotic synchronization can be achieved the anti-symmetry between in-phase and anti-phase. On the other hand, for two symmetrical side-lasers, their leader/ laggard chaotic synchronization with in-phase and anti-phase can reach the anti-symmetry.
我们利用耦合模理论和麦克斯韦方程组，建立了一个三元件激光阵列的理论模型，其中三个激光器通过横向耦合。在主从配置中系统地观察到了新的混沌同步特性，该配置由具有自反馈的驱动三元件激光阵列和受到并行注入或交叉注入的响应三元件激光阵列组成。在并行注入下，不同参数空间中激光元件之间高质量完全混沌同步的动态演化严重依赖于驱动激光元件的自反馈模式，例如其中一个、两个以及全部都具有自反馈。研究发现，当仅驱动中间的一个或所有驱动激光元件具有自反馈时，在大多数参数空间的相同大区域内可以实现所有激光元件的高质量完全混沌同步。此外，据我们所知，我们首次在此报告了交叉注入配置下超前/滞后混沌同步的有趣对称特性。即，在关键参数限制在一定范围内时，激光元件之间高质量的超前/滞后混沌同步会随着延迟差异周期性变化。这些同步的变化轨迹类似正弦波。通过优化激光波导的结构参数，可以实现滞后同相（反相）混沌同步与超前同相（反相）混沌同步之间的镜像对称。通过优化相关操作参数，对于其中一个侧边激光器，其超前/滞后混沌同步可以实现同相和反相之间的反对称性。另一方面，对于两个对称的侧边激光器，它们同相和反相的超前/滞后混沌同步可以达到反对称性。
