Heavy-Tailed Fluctuations in the Spiking Output Intensity of Semiconductor Lasers with Optical Feedback

Although heavy-tailed fluctuations are ubiquitous in complex systems, a good understanding of the mechanisms that generate them is still lacking. Optical complex systems are ideal candidates for investigating heavy-tailed fluctuations, as they allow recording large datasets under controllable experimental conditions. A dynamical regime that has attracted a lot of attention over the years is the so-called low-frequency fluctuations (LFFs) of semiconductor lasers with optical feedback. In this regime, the laser output intensity is characterized by abrupt and apparently random dropouts. The statistical analysis of the inter-dropout-intervals (IDIs) has provided many useful insights into the underlying dynamics. However, the presence of large temporal fluctuations in the IDI sequence has not yet been investigated. Here, by applying fluctuation analysis we show that the experimental distribution of IDI fluctuations is heavy-tailed, and specifically, is well-modeled by a non-Gaussian stable distribution. We find a good qualitative agreement with simulations of the Lang-Kobayashi model. Moreover, we uncover a transition from a less-heavy-tailed state at low pump current to a more-heavy-tailed state at higher pump current. Our results indicate that fluctuation analysis can be a useful tool for investigating the output signals of complex optical systems; it can be used for detecting underlying regime shifts, for model validation and parameter estimation.

尽管重尾波动（heavy-tailed fluctuations）在复杂系统中无处不在，但学界对其产生机制仍缺乏充分认知。光学复杂系统是研究重尾波动的理想研究对象，因其可在可控实验条件下记录大规模数据集。多年来备受关注的一类动力学状态，是带光反馈的半导体激光器的所谓低频波动（low-frequency fluctuations, LFFs）。在此状态下，激光器输出强度会呈现出突发性且看似随机的强度跌落。对跌落间隔（inter-dropout-intervals, IDIs）的统计分析，已为其背后的动力学机制提供了诸多有价值的见解。然而，学界尚未对跌落间隔序列中的大幅时间波动展开研究。本文通过波动分析方法，证明了跌落间隔波动的实验分布为重尾分布，且可通过非高斯稳定分布（non-Gaussian stable distribution）实现良好拟合。我们发现，该结果与Lang-Kobayashi模型（Lang-Kobayashi model）的仿真结果具有良好的定性一致性。此外，我们还揭示了一种状态转变：在低泵浦电流下为重尾程度较弱的状态，而在高泵浦电流下则为重尾程度更强的状态。本研究结果表明，波动分析可作为研究复杂光学系统输出信号的有效工具，可用于检测潜在的状态转变、开展模型验证以及参数估计。