Analysis of laser radiation using the Nonlinear Fourier transform

Srikanth Sugavanam; Morteza Kamalian Kopae; Junsong Peng; Jaroslaw E. Prilepsky; Sergei K. Turitsyn

doi:10.1038/s41467-019-13265-4

Analysis of laser radiation using the Nonlinear Fourier transform

Srikanth Sugavanam^*, Morteza Kamalian Kopae, Junsong Peng, Jaroslaw E. Prilepsky, Sergei K. Turitsyn^*

^*Corresponding author for this work

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

Abstract

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Original language	English
Article number	5663
Journal	Nature Communications
Volume	10
Issue number	1
DOIs	https://doi.org/10.1038/s41467-019-13265-4
Publication status	Published - 11 Dec 2019

Bibliographical note

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/.
Funding: he work of S.K.T. was supported by the Russian Science Foundation (Grant No. 17-72-30006), Y.P. was supported by the Leverhulme Trust (RPG-2018-063), and M.K. was supported by the EPSRC programme grant TRANSNET (EP/ R035342/1). S.S. acknowledges support of the H2020 MSCF Action Programme COFUND MULTIPLY.

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10.1038/s41467-019-13265-4Licence: CC BY 3.0

Analysis of laser radiation using the Nonlinear Fourier transform
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, 1.18 MBLicence: CC BY 3.0

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abstract = "Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.",

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Analysis of laser radiation using the Nonlinear Fourier transform

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Author Correction: Analysis of laser radiation using the Nonlinear Fourier transform (Nature Communications, (2019), 10, 1, (5663), 10.1038/s41467-019-13265-4)

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