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The laminar–turbulent transition in a fibre laser

Nature Photonics volume 7, pages 783786 (2013) | Download Citation

Abstract

Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type1,2. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance3,4,5. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar–turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium.

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References

  1. 1.

    & Fluid Mechanics Ch. 26–28 (Pergamon, 1959).

  2. 2.

    et al. The onset of turbulence in pipe flow. Science 333, 192–196 (2011).

  3. 3.

    Lasers (University Science Books, 1986).

  4. 4.

    & Optical Coherence and Quantum Optics Ch. 18, 19 (Cambridge Univ. Press, 1995).

  5. 5.

    & Laser Physics Ch. 13 (Wiley, 2010).

  6. 6.

    & Pattern-formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1123 (1993).

  7. 7.

    Parametrically excited water surface ripples as ensembles of oscillations. Phys. Rev. Lett. 108, 03452 (2012).

  8. 8.

    & Suppressing wall turbulence by means of a transverse travelling wave. Science 288, 1230–1234 (2000).

  9. 9.

    et al. Experimental observation of nonlinear travelling waves in turbulent pipe flow. Science 305, 1594–1597 (2004).

  10. 10.

    Nonlinear Fiber Optics Ch. 5 (Academic, 2001).

  11. 11.

    , , & Optical turbulence and spectral condensate in long-fiber lasers. Phys. Rev. A 80, 031804R (2009).

  12. 12.

    et al. Optical turbulence and spectral condensate in long fibre lasers. Proc. R. Soc. A 468, 2496–2508 (2012).

  13. 13.

    et al. Observation of the kinetic condensation of classical waves. Nature Phys. 8, 470–474 (2012).

  14. 14.

    , , & Bose–Einstein condensation of photons in an optical microcavity. Nature 468, 545–548 (2010).

  15. 15.

    & Advances in Wave Turbulence Ch. 4 (World Scientific, 2013).

  16. 16.

    , , & One-dimensional optical wave turbulence: experiment and theory. Phys. Rep. 514, 121–175 (2012).

  17. 17.

    et al. FWM-induced turbulent spectral broadening in a long Raman fibre laser. J. Opt. Soc. Am. B 24, 1729–1738 (2007).

  18. 18.

    , & Toward a wave turbulence formulation of statistical nonlinear optics. J. Opt. Soc. Am. B 29, 2229–2242 (2012).

  19. 19.

    , & Kolmogorov Spectra of Turbulence Ch. 2, 3 (Springer, 1992).

  20. 20.

    , , & Er3+:Yb3+-co-doped fiber distributed-feedback laser. Opt. Lett. 19, 2101–2103 (1994).

  21. 21.

    , & Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser. Opt. Lett. 37, 1544–1546 (2012).

  22. 22.

    et al. The Peregrine soliton in nonlinear fibre optics. Nature Phys. 6, 790–795 (2010).

  23. 23.

    et al. Observation of Kuznetsov–Ma soliton dynamics in optical fibre. Sci. Rep. 2, 463 (2012).

  24. 24.

    , , & Optical rogue waves. Nature 450, 1054–1057 (2007).

  25. 25.

    , , & Fluctuations and correlations in modulation instability. Nature Photon. 6, 463–468 (2012).

  26. 26.

    (ed.) Fiber Lasers (Wiley-VCH, 2012).

  27. 27.

    , & Statistical properties of partially coherent CW fiber lasers. Opt. Lett. 35, 3288–3290 (2010).

  28. 28.

    On the theory of superfluidity. J. Phys. (USSR) 11, 23–32 (1947).

  29. 29.

    & Optical dark solitons: physics and applications. Phys. Rep. 298, 81–197 (1998).

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Acknowledgements

The authors thank I. Vatnik for his support at the very early stage of the experiments. This work was supported by the Israel Science Foundation and US-Israel Binational Science Foundation grants (Israel), the European Research Council (project ULTRALASER), the Leverhulme Trust, the Royal Society (UK), the Russian Ministry of Science and Education (agreement 14.B25.31.0003) and the Dynasty Foundation (Russia).

Author information

Affiliations

  1. Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, UK

    • E. G. Turitsyna
    • , S. Sugavanam
    • , N. Tarasov
    • , X. Shu
    • , D. V. Churkin
    •  & S. K. Turitsyn
  2. Novosibirsk State University, Novosibirsk 630090, Russia

    • S. V. Smirnov
    • , S. A. Babin
    • , E. V. Podivilov
    • , D. V. Churkin
    •  & S. K. Turitsyn
  3. Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Russia

    • S. A. Babin
    • , E. V. Podivilov
    •  & D. V. Churkin
  4. Weizmann Institute of Science, Rehovot 76100, Israel

    • G. Falkovich
  5. Institute for Information Transmission Problems, Moscow 127994, Russia

    • G. Falkovich

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Contributions

S.K.T. and G.F. initiated the study. D.V.C. conceived the experiment and, with S.S. and N.T., carried it out. E.G.T. and S.V.S. designed and conducted the numerical modelling. E.G.T. and X.S. designed the special laser mirrors. X.S. fabricated the laser mirrors. G.F., S.K.T. and D.V.C. guided the theoretical and experimental investigations. G.F., S.K.T., D.V.C., E.V.P., S.A.B., S.V.S., E.G.T., S.S. and N.T. analysed the data. G.F., S.K.T. and D.V.C. wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to S. K. Turitsyn.

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DOI

https://doi.org/10.1038/nphoton.2013.246

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