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Abstract.

Numerical simulations are used to discuss various aspects of “optical rogue wave” statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show that the unfiltered statistical distribution can still exhibit a long-tail, but the extreme-events in this case correspond to collisions between solitons of different frequencies. These results confirm the importance of collision dynamics in supercontinuum generation. We also show that the collision-induced events satisfy an extended hydrodynamic definition of “rogue wave” characteristics.

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References

  1. A.W. Scott, The Nonlinear Universe (Springer, Berlin, 2007)

  2. J.M. Dudley, G. Genty, S. Coen, Rev. Mod. Phys. 78Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1135 (2006)

    Article  ADS  Google Scholar 

  3. M.N. Islam, G. Sucha, I. Bar-Joseph, M. Wegener, J.P. Gordon, D.S. Chemla, Opt. Lett. 14Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 370 (1989)

    Article  ADS  Google Scholar 

  4. M.N. Islam, G. Sucha, I. Bar-Joseph, M. Wegener, J.P. Gordon, D.S. Chemla, J. Opt. Soc. Am. B 6Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1149 (1989)

    Article  ADS  Google Scholar 

  5. M. Nakazawa, K.R. Tamura, H. Kubota, E. Yoshida, Opt. Fib. Tech. 4Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 215 (1998)

    Article  Google Scholar 

  6. M. Nakazawa, H. Kubota, K.R. Tamura, Opt. Lett. 24Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 318 (1999)

    Article  ADS  Google Scholar 

  7. K.L. Corwin, N.R. Newbury, J.M. Dudley, S. Coen, S.A. Diddams, K. Weber, R.S. Windeler, Phys. Rev. Lett. 90Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 113904 (2003)

    Article  ADS  Google Scholar 

  8. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1054 (2007)

    Article  ADS  Google Scholar 

  9. J.M. Dudley, G. Genty, B.J. Eggleton, Opt. Express 16Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 3644 (2008)

    Article  ADS  Google Scholar 

  10. G. Genty, J.M. Dudley, B.J. Eggleton, Appl. Phys. B 94Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 187 (2009) [arXiv:0809.2388v1]

    Article  ADS  Google Scholar 

  11. M. Erkintalo, G. Genty, J.M. Dudley, Opt. Lett. 34Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2468 (2009), ISSN 0146-9592

    Article  ADS  Google Scholar 

  12. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, M. Taki, Opt. Express 17Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 17010 (2009)

    Article  ADS  Google Scholar 

  13. B. Barviau, B. Kibler, S. Coen, A. Picozzi, Opt. Lett. 33Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2833 (2008)

    Article  ADS  Google Scholar 

  14. M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, M. Douay, Phys. Lett. A 374Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 691 (2010)

    Article  ADS  Google Scholar 

  15. G. Genty, C. de Sterke, O. Bang, F. Dias, N. Akhmediev, J.M. Dudley, Phys. Lett. A 374Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 989 (2010)

    Article  ADS  Google Scholar 

  16. N. Akhmediev, V.I. Korneev, Theor. Math. Phys. 69Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1089 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. J.M. Dudley, G. Genty, F. Dias, B. Kibler, N. Akhmediev, Opt. Express 17Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 21497 (2009)

    Article  ADS  Google Scholar 

  18. N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 675 (2009)

    Article  ADS  Google Scholar 

  19. N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Lett. A 373Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 2137 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  20. M. Onorato, A.R. Osborne, M. Serio, Phys. Rev. Lett. 96Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 014503 (2006)

    Article  ADS  Google Scholar 

  21. P.K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, L. Stenflo, Phys. Rev. Lett. 97Discussion & Debate : Rogue Waves - Towards a Unifying Concept?094501 (2006)

    Article  ADS  Google Scholar 

  22. M.H. Frosz, O. Bang, A. Bjarklev, Opt. Express 14Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 9391 (2006)

    Article  ADS  Google Scholar 

  23. F. Luan, D.V. Skryabin, A.V. Yulin, J.C. Knight, Opt. Express 14Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 9844 (2006)

    Article  ADS  Google Scholar 

  24. M. Erkintalo, G. Genty, J.M. Dudley, Opt. Lett. 35Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 658 (2010)

    Article  ADS  Google Scholar 

  25. C. Lafargue, J. Bolger, G. Genty, F. Dias, J.M. Dudley, B.J. Eggleton, Electron. Lett. 45Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 217 (2009)

    Article  Google Scholar 

  26. E. Pelinovsky, C. Kharif (eds.), Extreme Ocean Waves (Springer, Berlin, 2008)

  27. S. Kumar, A. Selvarajan, G.V. Anand, Opt. Commun. 102Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 329 (1993)

    Article  ADS  Google Scholar 

  28. G.P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic Press, San Diego, 2006)

  29. B.A. Malomed, Phys. Rev. A 44Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1412 (1991)

    Article  ADS  Google Scholar 

  30. T.I. Lakoba, D.J. Kaup, Opt. Lett. 24Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 808 (1999)

    Article  ADS  Google Scholar 

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Erkintalo, M., Genty, G. & Dudley, J. On the statistical interpretation of optical rogue waves. Eur. Phys. J. Spec. Top. 185, 135–144 (2010). https://doi.org/10.1140/epjst/e2010-01244-9

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