On the Spectral Dynamics of Noise-Seeded Modulation Instability in Optical Fibers

  • P. I. FierensEmail author
  • S. M. Hernandez
  • J. Bonetti
  • D. F. Grosz
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)


We revisit modulation instability in optical fibers, including all relevant effects, such as higher-order dispersion terms, self-steepening, and the Raman response. Our analysis allows us to calculate the spectral evolution of a small perturbation to a continuous pump, and thus obtain an analytical expression for the small-signal spectral dynamics, showing excellent agreement with numerical simulations. We apply the expression for the spectral evolution to the case of white Gaussian noise and calculate some relevant metrics of the resulting signal, such as its coherence and signal-to-noise ratio. These calculations might shed some light on the nonlinear phenomena of supercontinuum generation.


Modulation Instability Rogue Wave Spectral Evolution Supercontinuum Generation Freak Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    T.B. Benjamin, J.E. Feir, J. Fluid Mech. 27, 417 (1967). doi: 10.1017/S002211206700045X CrossRefGoogle Scholar
  2. 2.
    A. Shabat, V. Zakharov, Sov. Phys. JETP 34, 62 (1972)Google Scholar
  3. 3.
    V.E. Zakharov, Sov. Phys. JETP 35, 908 (1972)Google Scholar
  4. 4.
    N. Akhmediev, V. Korneev, Theoret. Math. Phys. 69(2), 1089 (1986)CrossRefGoogle Scholar
  5. 5.
    K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986). doi: 10.1103/PhysRevLett.56.135 CrossRefGoogle Scholar
  6. 6.
    M.J. Potasek, Opt. Lett. 12(11), 921 (1987). doi: 10.1364/OL.12.000921 CrossRefGoogle Scholar
  7. 7.
    J.M. Dudley, G. Genty, S. Coen, Rev. Mod. Phys. 78, 1135 (2006). doi: 10.1103/RevModPhys.78.1135 CrossRefGoogle Scholar
  8. 8.
    D. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450(7172), 1054 (2007)CrossRefGoogle Scholar
  9. 9.
    P. Béjot, B. Kibler, E. Hertz, B. Lavorel, O. Faucher, Phys. Rev. A 83, 013830 (2011). doi: 10.1103/PhysRevA.83.013830 CrossRefGoogle Scholar
  10. 10.
    A. Demircan, U. Bandelow, Opt. Commun. 244(1), 181 (2005)CrossRefGoogle Scholar
  11. 11.
    M.H. Frosz, O. Bang, A. Bjarklev, Opt. Express 14(20), 9391 (2006). doi: 10.1364/OE.14.009391 CrossRefGoogle Scholar
  12. 12.
    T. Sylvestre, A. Vedadi, H. Maillotte, F. Vanholsbeeck, S. Coen, Opt. Lett. 31(13), 2036 (2006). doi: 10.1364/OL.31.002036 CrossRefGoogle Scholar
  13. 13.
    A. Demircan, U. Bandelow, Appl. Phys. B 86(1), 31 (2007)CrossRefGoogle Scholar
  14. 14.
    J.M. Dudley, J.R. Taylor (eds.), Supercontinuum Generation in Optical Fibers (Cambridge University Press, 2010)Google Scholar
  15. 15.
    J.M. Soto-Crespo, A. Ankiewicz, N. Devine, N. Akhmediev, JOSA B 29(8), 1930 (2012)CrossRefGoogle Scholar
  16. 16.
    J.H. Price, X. Feng, A.M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W.H. Loh, H.N. Rutt, D.J. Richardson, Opt. Fiber Technol. 18(5), 327 (2012). doi: 10.1016/j.yofte.2012.07.013. Fiber Supercontinuum sources and their applications
  17. 17.
    V.V. Alexander, O.P. Kulkarni, M. Kumar, C. Xia, M.N. Islam, F.L.T. Jr., M.J. Welsh, K. Ke, M.J. Freeman, M. Neelakandan, A. Chan, Opt. Fiber Technol. 18(5), 349 (2012). doi: 10.1016/j.yofte.2012.07.014. Fiber Supercontinuum sources and their applications
  18. 18.
    J.M. Dudley, F. Dias, M. Erkintalo, G. Genty, Nat. Photonics 8(10), 755 (2014)CrossRefGoogle Scholar
  19. 19.
    S.B. Cavalcanti, G.P. Agrawal, M. Yu, Phys. Rev. A 51, 4086 (1995). doi: 10.1103/PhysRevA.51.4086 CrossRefGoogle Scholar
  20. 20.
    J.M. Dudley, S. Coen, Opt. Lett. 27(13), 1180 (2002). doi: 10.1364/OL.27.001180 CrossRefGoogle Scholar
  21. 21.
    K. Corwin, N. Newbury, J. Dudley, S. Coen, S. Diddams, B. Washburn, K. Weber, R. Windeler, Appl. Phys. B 77(2–3), 269 (2003). doi: 10.1007/s00340-003-1175-x CrossRefGoogle Scholar
  22. 22.
    K.L. Corwin, N.R. Newbury, J.M. Dudley, S. Coen, S.A. Diddams, K. Weber, R.S. Windeler, Phys. Rev. Lett. 90, 113904 (2003). doi: 10.1103/PhysRevLett.90.113904 CrossRefGoogle Scholar
  23. 23.
    N.R. Newbury, B.R. Washburn, K.L. Corwin, R.S. Windeler, Opt. Lett. 28(11), 944 (2003). doi: 10.1364/OL.28.000944 CrossRefGoogle Scholar
  24. 24.
    B. Kibler, C. Michel, J. Garnier, A. Picozzi, Opt. Lett. 37(13), 2472 (2012). doi: 10.1364/OL.37.002472 CrossRefGoogle Scholar
  25. 25.
    D. Solli, G. Herink, B. Jalali, C. Ropers, Nat. Photonics 6(7), 463 (2012)CrossRefGoogle Scholar
  26. 26.
    S.T. Sørensen, O. Bang, B. Wetzel, J.M. Dudley, Opt. Commun. 285(9), 2451 (2012). doi: 10.1016/j.optcom.2012.01.030 CrossRefGoogle Scholar
  27. 27.
    S.T. Sørensen, C. Larsen, U. Møller, P.M. Moselund, C.L. Thomsen, O. Bang, J. Opt. Soc. Am. B 29(10), 2875 (2012). doi: 10.1364/JOSAB.29.002875 CrossRefGoogle Scholar
  28. 28.
    G. Agrawal, Nonlinear Fiber Optics, 5th edn. Optics and Photonics (Academic Press, 2012)Google Scholar
  29. 29.
    M.H. Frosz, T. Sørensen, O. Bang, J. Opt. Soc. Am. B 23(8), 1692 (2006). doi: 10.1364/JOSAB.23.001692 CrossRefGoogle Scholar
  30. 30.
    F. Abdullaev, S. Darmanyan, S. Bischoff, P. Christiansen, M. Sørensen, Opt. Commun. 108(1–3), 60 (1994). doi: 10.1016/0030-4018(94)90216-X CrossRefGoogle Scholar
  31. 31.
    F.K. Abdullaev, S.A. Darmanyan, S. Bischoff, M.P. Sørensen, JOSA B 14(1), 27 (1997)CrossRefGoogle Scholar
  32. 32.
    M.R. Karim, B.M.A. Rahman, G.P. Agrawal, Opt. Express 23(5), 6903 (2015). doi: 10.1364/OE.23.006903 CrossRefGoogle Scholar
  33. 33.
    A. Schliesser, N. Picqué, T.W. Hänsch, Nat. Photonics 6(7), 440 (2012)CrossRefGoogle Scholar
  34. 34.
    J. Hult, J. Lightwave Technol. 25(12), 3770 (2007). doi: 10.1109/JLT.2007.909373 CrossRefGoogle Scholar
  35. 35.
    G. Kallianpur, Stochastic Filtering Theory (Springer, 1980)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • P. I. Fierens
    • 1
    Email author
  • S. M. Hernandez
    • 2
  • J. Bonetti
    • 3
  • D. F. Grosz
    • 4
  1. 1.Instituto Tecnológico de Buenos Aires (ITBA) and Consejo Nacional de Investigaciones Científicas Y Técnicas (CONICET)Buenos AiresArgentina
  2. 2.Instituto Balseiro (IB)BarilocheArgentina
  3. 3.IBBarilocheArgentina
  4. 4.IB and CONICETBuenos AiresArgentina

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