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


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.

Publication DOI: https://doi.org/10.1038/s41467-022-33525-0
Divisions: College of Engineering & Physical Sciences > Aston Institute of Photonics Technology (AIPT)
Additional Information: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
Publication ISSN: 2041-1723
Last Modified: 13 Jun 2024 07:22
Date Deposited: 04 Oct 2022 13:11
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Related URLs: https://www.nat ... 467-022-33525-0 (Publisher URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2022-10-02
Published Online Date: 2022-10-02
Accepted Date: 2022-09-21
Authors: Wu, Xiuqi
Zhang, Ying
Peng, Junsong
Boscolo, Sonia (ORCID Profile 0000-0001-5388-2893)
Finot, Christophe
Zeng, Heping



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