Wu Xiuqi, Zhang Ying, Peng Junsong, Boscolo Sonia, Finot Christophe, Zeng Heping
State Key Laboratory of Precision Spectroscopy, East China Normal University, 200241, Shanghai, China.
Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China.
Nat Commun. 2022 Oct 2;13(1):5784. doi: 10.1038/s41467-022-33525-0.
Nonlinear systems with two competing frequencies show locking or resonances. In lasers, the two interacting frequencies can be the cavity repetition rate and a frequency externally applied to the system. Conversely, the excitation of breather oscillations in lasers naturally triggers a second characteristic frequency in the system, therefore showing competition between the cavity repetition rate and the breathing frequency. Yet, the link between breathing solitons and frequency locking is missing. Here we demonstrate frequency locking at Farey fractions of a breather laser. The winding numbers exhibit the hierarchy of the Farey tree and the structure of a devil's staircase. Numerical simulations of a discrete laser model confirm the experimental findings. The breather laser may therefore serve as a simple test bed to explore ubiquitous synchronization dynamics of nonlinear systems. The locked breathing frequencies feature a high signal-to-noise ratio and can give rise to dense radio-frequency combs, which are attractive for applications.
具有两个竞争频率的非线性系统会出现锁定或共振现象。在激光器中，两个相互作用的频率可以是腔重复率和外部施加到系统的频率。相反，激光器中呼吸子振荡的激发自然会在系统中触发第二个特征频率，从而显示出腔重复率与呼吸频率之间的竞争。然而，呼吸子孤子与频率锁定之间的联系尚不清楚。在此，我们展示了呼吸子激光器在法雷分数处的频率锁定。缠绕数呈现出法雷树的层次结构和魔鬼阶梯的结构。离散激光模型的数值模拟证实了实验结果。因此，呼吸子激光器可作为一个简单的试验台，用于探索非线性系统中普遍存在的同步动力学。锁定的呼吸频率具有高信噪比，并且可以产生密集的射频梳，这在应用中很有吸引力。
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