Abstract
Synchronization is a universal phenomenon underpinning various natural processes and finds direct application in control engineering and photonics. Among several synchronization mechanisms, subharmonic entrainment (SHE) is a nonlinear synchronization phenomenon where an oscillator locks to an external drive with a fraction of the oscillator’s frequency. While its mechanism is well understood for scalar couplings and finds application in the stabilization of ultrafast laser pulses, the potential of SHE with vectorial coupling is still unexplored. In this work, we demonstrate vector SHE (VSHE) using a passively mode-locked fiber laser as a testbed. We unveil the mechanism of vector SHE, in which weak external signals can entrain internal laser dynamics through vector coupling. Vector SHE presents in the form of synchronization between the subharmonic of mode-locking-driven oscillations and continuous wave (CW) signal with an evolving state of polarization. This CW signal, driven by the internal dynamics of the injected signal, causes VSHE with the frequencies’ ratios of multiples of ten, resulting in a partially mode locking regime operation. Our findings offer new control techniques over mode-locking and additional dimension such as polarization states.
| Original language | English |
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| Journal | Communications Physics |
| Early online date | 21 Jan 2026 |
| DOIs | |
| Publication status | E-pub ahead of print - 21 Jan 2026 |
Bibliographical note
Copyright © 2026, The Author(s). 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit https://creativecommons.org/licenses/by/4.0/.Data Access Statement
The code that supports the plots within this paper is described in the Methods and Supplementary Information and is available from the corresponding author upon request.Funding
This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [grant number EP/W002868/1], Leverhulme Trust grant HARVEST [RPG-2023-073], National Natural Science Foundation of China [62135007], National Natural Science Foundation of China [61975107] and Natural Science Foundation of Shanghai Municipality [24ZR1422000]“111” project [D20031].