Farey tree and devil’s staircase of frequency-locked breathers in ultrafast lasers

Xiuqi Wu, Ying Zhang, Junsong Peng*, Sonia Boscolo, Christophe Finot, Heping Zeng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number5784
Number of pages10
JournalNature Communications
Issue number1
Early online date2 Oct 2022
Publication statusPublished - 2 Oct 2022

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