Nonlinear wave propagation governed by a fractional derivative
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1.
University of Sydney
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2.
Australian Research Council
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3.
California Institute of Technology
Abstract
The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in systems with nonlocal temporal or spatial interactions. However, systematic experiments have been rare because the physical implementation is challenging. Here we report the observation and full characterization of a family of temporal solitons that are governed by a fractional nonlinear wave equation. We demonstrate that these solitons have non-exponential tails, reflecting their nonlocal character, and have a very small time-bandwidth product.
Copyright and License
© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. 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 http://creativecommons.org/licenses/by-nc-nd/4.0/.
Acknowledgement
This research was supported by the Australian Research Council (ARC) Centre of Excellence in Optical Microcombs for Breakthrough Science (project no. CE230100006), funded by the Australian Government. A.F.J.R. is supported by the ARC Discovery Early Career Researcher Award (DE220100509). V.T.H., A.F.J.R. & C.M.d.S. are also supported by an ARC Discovery Project (DP230102200). The authors thank Professor Panayotis Kevrekidis for useful discussions in the early phases of this work.
Data Availability
The data that support the plots within this paper and the supplementary materials are available at https://doi.org/10.5281/zenodo.15300723.
Supplemental Material
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Additional details
- Alternative title
- Observation of fractional evolution in nonlinear optics
- PMCID
- PMC12215005
- Australian Research Council
- CE230100006
- Australian Research Council
- DE220100509
- Australian Research Council
- DP230102200
- Accepted
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2025-05-23
- Caltech groups
- Division of Engineering and Applied Science (EAS)
- Publication Status
- Published