Zhang Hao, Xiang Shuiying, Zhang Yahui, Guo Xingxing
Appl Opt. 2017 Aug 20;56(24):6728-6734. doi: 10.1364/AO.56.006728.
The complexity properties of polarization-resolved chaotic signals generated in a ring network of vertical-cavity surface-emitting lasers (VCSELs) mutually coupled with multiple delays are investigated quantitatively by using the proposed mean permutation entropy (MPE). For direct comparison, the complexity of polarization-resolved chaos in a ring network of VCSELs coupled with single delay is also considered. The effects of injection current, coupling strength, and frequency detuning on the chaotic complexity for both a single-delay ring network (SDRN) and a multiple-delay ring network (MDRN) are evaluated quantitatively and compared by the MPE. The effects of internal parameters of VCSELs on the complexity are also discussed, and the correlation properties between different polarization-resolved modes are also analyzed. It is shown that the complexity of chaos in two polarization-resolved modes of VCSELs in MDRN is much higher than those in SDRN in a much wider parameter region. Besides, wider range of injection current, coupling strength, and frequency detuning can be tuned to achieve the enhancement of chaotic complexity in MDRN. These results provide an effective quantifier, the proposed MPE, to evaluate quantitatively the complexity of chaos generated in systems with multiple delays, and the multichannel complexity-enhanced polarization-resolved chaos generated in MDRN of mutually coupled VCSELs is extremely meaningful for the chaos-based random number generators.
利用所提出的均值排列熵（MPE），对垂直腔面发射激光器（VCSEL）环形网络中相互耦合且具有多个延迟产生的偏振分辨混沌信号的复杂性特性进行了定量研究。为了进行直接比较，还考虑了具有单个延迟的VCSEL环形网络中偏振分辨混沌的复杂性。通过MPE定量评估并比较了注入电流、耦合强度和频率失谐对单延迟环形网络（SDRN）和多延迟环形网络（MDRN）混沌复杂性的影响。还讨论了VCSEL内部参数对复杂性的影响，并分析了不同偏振分辨模式之间的相关性。结果表明，在更宽的参数区域内，MDRN中VCSEL的两种偏振分辨模式下的混沌复杂性远高于SDRN中的混沌复杂性。此外，在MDRN中，可以调节更宽范围的注入电流、耦合强度和频率失谐以实现混沌复杂性的增强。这些结果提供了一种有效的量化指标，即所提出的MPE，用于定量评估具有多个延迟的系统中产生的混沌复杂性，并且相互耦合的VCSEL的MDRN中产生的多通道复杂性增强的偏振分辨混沌对于基于混沌的随机数发生器具有极其重要的意义。
