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The Peregrine soliton in nonlinear fibre optics

Nature Physics volume 6, pages 790–795 (2010)Cite this article

Abstract

The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system1. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation2 to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions that do not correspond to the mathematical ideal, our results may impact widely on studies of hydrodynamic wave instabilities where the Peregrine soliton is considered a freak-wave prototype3,4,5,6,7.

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Figure 1: Plotted Akhmediev breather solutions using equation (2) for modulation parameter a=0.25, a=0.45 and a=0.48, as well as the ideal Peregrine soliton of equation (3), the limiting case of the Akhmediev breather as a→1/2.
Figure 2: Evolution towards Peregrine soliton characteristics with increasing modulation parameter for temporal profile characteristics and localization behaviour.
Figure 3: Experimental set-up.
Figure 4: The variation in temporal and spectral characteristics with normalized propagation distance to confirm expected dynamical evolution.
Figure 5: Experimental results showing the measured temporal characteristics of the maximally compressed pulse at ξ=2.5, and comparison with the predicted Peregrine soliton.

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Acknowledgements

We acknowledge support from the French Agence Nationale de la Recherche projects MANUREVA ANR-08-SYSC-019 and IMFINI ANR-09-BLAN-0065, the Academy of Finland Research grants 132279 and 130099, the 2008 Framework Program for Research, Technological development and Innovation of the Cyprus Research Promotion Foundation under the Project ASTI/0308(BE)/05 and the Australian Research Council Discovery Project scheme DP0985394.

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Authors and Affiliations

  1. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS — Université de Bourgogne, Dijon, France

    B. Kibler, J. Fatome, C. Finot & G. Millot

  2. Centre de Mathématiques et de Leurs Applications (CMLA), ENS Cachan, 94230 Cachan, France

    F. Dias

  3. UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

    F. Dias

  4. Tampere University of Technology, Optics Laboratory, FI-33101 Tampere, Finland

    G. Genty

  5. Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra ACT 0200, Australia

    N. Akhmediev

  6. Institut FEMTO-ST, UMR 6174 CNRS— Université de Franche-Comté, 25030 Besançon, France

    J. M. Dudley

Authors
  1. B. Kibler
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  2. J. Fatome
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  3. C. Finot
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  4. G. Millot
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  5. F. Dias
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  7. N. Akhmediev
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  8. J. M. Dudley
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Contributions

B.K., J.F., C.F. and J.M.D. carried out experiments. The development of analytical tools and simulations was carried out by B.K., G.M., G.G., F.D., N.A. and J.M.D. All authors participated in the analysis and interpretation of the results and the writing of the paper.

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Correspondence to J. M. Dudley.

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The authors declare no competing financial interests.

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Kibler, B., Fatome, J., Finot, C. et al. The Peregrine soliton in nonlinear fibre optics. Nature Phys 6, 790–795 (2010). https://doi.org/10.1038/nphys1740

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