Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Optical rogue waves

Nature volume 450, pages 1054–1057 (2007)Cite this article

Abstract

Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics1,2,3. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation4,5—a noise-sensitive5,6,7 nonlinear process in which extremely broadband radiation is generated from a narrowband input8. We model the generation of these rogue waves using the generalized nonlinear Schrödinger equation9 and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Experimental observation of optical rogue waves.
Figure 2: Simulation of optical rogue waves using the generalized nonlinear Schrödinger equation.
Figure 3: Time–wavelength profile of an optical rogue wave obtained from a short-time Fourier transform.

Similar content being viewed by others

References

  1. Hopkin, M. Sea snapshots will map frequency of freak waves. Nature 430, 492 (2004)

    Article  CAS  ADS  Google Scholar 

  2. Perkins, S. Dashing rogues: freak ocean waves pose threat to ships, deep-sea oil platforms. Science News 170, 328–329 (2006)

    Article  Google Scholar 

  3. Broad, W. J. Rogue giants at sea. The New York Times (July 11, 2006)

    Google Scholar 

  4. Herrmann, J. et al. Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers. Phys. Rev. Lett. 88, 173901 (2002)

    Article  CAS  ADS  Google Scholar 

  5. Dudley, J. M., Genty, G. & Coen, S. Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135–1184 (2006)

    Article  CAS  ADS  Google Scholar 

  6. Corwin, K. L. et al. Fundamental noise limitations to supercontinuum generation in microstructure fiber. Phys. Rev. Lett. 90, 113904 (2003)

    Article  CAS  ADS  Google Scholar 

  7. Gaeta, A. L. Nonlinear propagation and continuum generation in microstructured optical fibers. Opt. Lett. 27, 924–926 (2002)

    Article  ADS  Google Scholar 

  8. Alfano, R. R. The ultimate white light. Sci. Am. 295, 87–93 (2006)

    Article  Google Scholar 

  9. Agrawal, G. P. Nonlinear Fiber Optics 3rd edn (Academic, San Diego, 2001)

    MATH  Google Scholar 

  10. Kharif, C. & Pelinovsky, E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B Fluids 22, 603–634 (2003)

    Article  MathSciNet  Google Scholar 

  11. Dean, R. G. & in Water Wave Kinematics (eds Tørum, A. & Gudmestad, O. T.) 609–612 (Kluwer, Amsterdam, 1990)

    Book  Google Scholar 

  12. Muller, P. Garrett, C. & Osborne, A. Rogue waves. Oceanography 18, 66–75 (2005)

    Article  Google Scholar 

  13. Walker, D. A. G., Taylor, P. H. & Taylor, R. E. The shape of large surface waves on the open sea and the Draupner New Year wave. Appl. Ocean. Res. 26, 73–83 (2004)

    Article  Google Scholar 

  14. Dysthe, K., Socquet-Juglard, H., Trulsen, K., Krogstad, H. E. & Liu, J. “Freak” waves and large-scale simulations of surface gravity waves. Rogue Waves, Proc. 14th 'Aha Huliko'a Hawaiian Winter Workshop 91–99 (Univ. Hawaii, Honolulu, 2005)

    Google Scholar 

  15. Liu, P. C. & MacHutchon, K. R. Are there different kinds of rogue waves? Proc. OMAE2006, 25th Int. Conf. Offshore Mechanics and Arctic Engineering, Paper No. 92619 1–6 (American Society of Mechanical Engineers, New York, 2006)

    Google Scholar 

  16. Henderson, K. L., Peregrine, K. L. & Dold, J. W. Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation. Wave Motion 29, 341–361 (1999)

    Article  MathSciNet  Google Scholar 

  17. Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834 (2001)

    Article  CAS  ADS  Google Scholar 

  18. Onorato, M., Osborne, A. R. & Serio, M. Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves. Phys. Rev. Lett. 96, 014503 (2006)

    Article  CAS  ADS  Google Scholar 

  19. Shukla, P. K., Kourakis, I., Eliasson, B., Marklund, M. & Stenflo, L. Instability and evolution of nonlinearly interacting water waves. Phys. Rev. Lett. 97, 094501 (2006)

    Article  CAS  ADS  Google Scholar 

  20. Janssen, P. A. E. M. Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  21. White, B. S. & Fornberg, B. On the chance of freak waves at sea. J. Fluid Mech. 355, 113–138 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  22. Ranka, J. K., Windeler, R. S. & Stentz, A. J. Visible continuum generation in air–silica microstructure optical fibers with anomalous dispersion at 800 nm. Opt. Lett. 25, 25–27 (2000)

    Article  CAS  ADS  Google Scholar 

  23. Segur, H. et al. Stabilizing the Benjamin–Feir instability. J. Fluid Mech. 539, 229–271 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  24. Islam, M. N. et al. Femtosecond distributed soliton spectrum in fibers. J. Opt. Soc. Am. B 6, 1149–1158 (1989)

    Article  CAS  ADS  Google Scholar 

  25. Kutz, J. N., Lyngå, C. & Eggleton, B. J. Enhanced supercontinuum generation through dispersion-management. Opt. Express 13, 3989–3998 (2005)

    Article  ADS  Google Scholar 

  26. Han, Y., Boyraz, O. & Jalali, B. Tera-sample per second real-time waveform digitizer. Appl. Phys. Lett. 87, 241116 (2005)

    Article  ADS  Google Scholar 

  27. Gu, X. et al. Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum. Opt. Lett. 27, 1174–1176 (2002)

    Article  ADS  Google Scholar 

  28. Nakazawa, M., Kubota, H. & Tamura, K. Random evolution and coherence degradation of a high-order optical soliton train in the presence of noise. Opt. Lett. 24, 318–320 (1999)

    Article  CAS  ADS  Google Scholar 

  29. Boyraz, O., Kim, J., Islam, M. N., Coppinger, F. & Jalali, B. 10 Gb/s multiple wavelength, coherent short pulse source based on spectral carving of supercontinuum generated in fibers. J. Lightwave Technol. 18, 2167–2175 (2000)

    Article  ADS  Google Scholar 

  30. Trulsen, K. & Dysthe, K. B. A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281–289 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of California, Los Angeles 90095, USA

    D. R. Solli, C. Ropers, P. Koonath & B. Jalali

  2. Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, D-12489 Berlin, Germany

    C. Ropers

Authors
  1. D. R. Solli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Ropers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Koonath
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Jalali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. R. Solli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solli, D., Ropers, C., Koonath, P. et al. Optical rogue waves. Nature 450, 1054–1057 (2007). https://doi.org/10.1038/nature06402

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06402

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing