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

Xiuqi Wu, Ying Zhang, Junsong Peng (), Sonia Boscolo, Christophe Finot and Heping Zeng ()
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Xiuqi Wu: East China Normal University
Ying Zhang: East China Normal University
Junsong Peng: East China Normal University
Sonia Boscolo: Aston University
Christophe Finot: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS—Université de Bourgogne Franche-Comté
Heping Zeng: East China Normal University

Nature Communications, 2022, vol. 13, issue 1, 1-10

Abstract: Abstract 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.

Date: 2022
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DOI: 10.1038/s41467-022-33525-0

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