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

doi:10.1038/s41467-022-33525-0

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

Aston Institute of Photonic Technologies (AiPT)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	5784
Number of pages	10
Journal	Nature Communications
Volume	13
Issue number	1
Early online date	2 Oct 2022
DOIs	https://doi.org/10.1038/s41467-022-33525-0
Publication status	Published - 2 Oct 2022

Bibliographical note

© 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/.

Access to Document

10.1038/s41467-022-33525-0Licence: CC BY 4.0

new9_CF_SBAccepted author manuscript, 7.3 MB
s41467-022-33525-0
© 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/.
Final published version, 1.54 MBLicence: CC BY 4.0

Cite this

@article{f587c8df31f04457854d835c62fbc582,

title = "Farey tree and devil{\textquoteright}s staircase of frequency-locked breathers in ultrafast lasers",

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{\textquoteright}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.",

author = "Xiuqi Wu and Ying Zhang and Junsong Peng and Sonia Boscolo and Christophe Finot and Heping Zeng",

note = "{\textcopyright} 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{\textquoteright}s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article{\textquoteright}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/.",

year = "2022",

month = oct,

day = "2",

doi = "10.1038/s41467-022-33525-0",

language = "English",

volume = "13",

journal = "Nature Communications",

issn = "2041-1723",

publisher = "Nature Publishing Group",

number = "1",

}

TY - JOUR

T1 - Farey tree and devil’s staircase of frequency-locked breathers in ultrafast lasers

AU - Wu, Xiuqi

AU - Zhang, Ying

AU - Peng, Junsong

AU - Boscolo, Sonia

AU - Finot, Christophe

AU - Zeng, Heping

N1 - © 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/.

PY - 2022/10/2

Y1 - 2022/10/2

N2 - 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.

AB - 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.

UR - https://www.nature.com/articles/s41467-022-33525-0

UR - http://www.scopus.com/inward/record.url?scp=85139167775&partnerID=8YFLogxK

U2 - 10.1038/s41467-022-33525-0

DO - 10.1038/s41467-022-33525-0

M3 - Article

C2 - 36184670

SN - 2041-1723

VL - 13

JO - Nature Communications

JF - Nature Communications

IS - 1

M1 - 5784

ER -

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

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Farey Tree and Devil’s Staircase of a Breather Mode-Locked Fibre Laser

Cite this