Spatiotemporal mode-locked (STML) lasers are ideal platforms for investigating high-dimensional nonlinear dynamics. This study presents an experimental observation and theoretical investigation of a novel high-dimensional nonlinear dynamics, which we term spatiotemporal period-doubling bifurcation (SPB), in the STML lasers. In the SPB state, not only the temporal shape but also the spatial beam (i.e., the spatiotemporal structure) of the pulses exhibit period-doubling bifurcation. As a result, it is observed that the pulse train modulation varies with the transverse mode, and the output beam profile fluctuates rapidly and periodically. Our numerical simulations are in good agreement with the experimental observations. In addition, a simple iterative model is presented to underline the physical insights of SPB, by considering the mode-dependent saturable absorption effect. Based on these results, spatial-dependent saturable absorption is believed to be the key factor for the unique spatiotemporal characteristic of SPB in multimode lasers. This study contributes to the understanding of the complex spatiotemporal dynamics in STML multimode lasers and to the discovery of novel dynamics in high-dimensional nonlinear systems.

中文翻译：

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锁模多模光纤激光器中的时空倍周期分岔

时空锁模 (STML) 激光器是研究高维非线性动力学的理想平台。本研究提出了一种新型高维非线性动力学的实验观察和理论研究，我们将其称为 STML 激光器中的时空倍周期分岔 (SPB)。在 SPB 状态下，脉冲的时间形状和空间光束（即时空结构）都表现出倍周期分岔。结果，观察到脉冲串调制随横向模式而变化，并且输出光束轮廓快速且周期性地波动。我们的数值模拟与实验观察结果非常吻合。此外，还提出了一个简单的迭代模型来强调 SPB 的物理见解，通过考虑模式相关的可饱和吸收效应。基于这些结果，空间相关的可饱和吸收被认为是多模激光器中 SPB 独特时空特性的关键因素。这项研究有助于理解 STML 多模激光器中复杂的时空动力学，并有助于发现高维非线性系统中的新动力学。