Soliton Propagation in Optical Fibers with Random Parameters

  • D. Gurarie
  • P. Mishnayevskiy
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 11)


We study a system of nonlinear Schrödinger equations that models propagation of optical pulses in a monomode fiber. It includes linear terms (second and third order dispersions, and attenuation) as well as nonlinear terms (cross-phase modulation,and Raman scattering). The Whitham variational (averaging) method is used to reduce the nonlinear partial differential equations to an ordinary differential system for a finite number of soliton parameters: distance between pulses, phase frequency, width and amplitude. When the random medium coefficients are turned on the reduced ODE’s becomes a stochastic system. We derive the corresponding Fokker-Planck equation and discuss its solutions in special cases. The stationary Fokker-Planck solution (equilibrium ensemble) gives the expected mean values and correlations of soliton parameters over large spatial scales and allows us to analyze the long-term effects of the random fiber on the 2-pulse system.


Manifold Attenuation Soliton Librium Vicin 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A.B. Aceves, Soliton Turbulence in Nonlinear Optical Phenomena, this volume, p. 199.Google Scholar
  2. [2]
    M.J. Ablowitz, H. Segur, Solitons and the inverse scattering transform, SIAM, Philadelphia, 1985.Google Scholar
  3. [3]
    D. Anderson and M. Lisak, Bandwidth limits due to incoherent soliton interaction in optical-fiber communications systems., Phys. Rev. A 32, pp.2270–2274, 1985.CrossRefGoogle Scholar
  4. [4]
    A.B. Aceves, S. Wabnitz, Switching Dynamics of Helical Solitons in a Periodically Twisted Biréfringent Fiber Filter, Optics Letters, v.17, No1, p.25–27, 1992.CrossRefGoogle Scholar
  5. [5]
    H. Haken, Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices, Springer-Verlag, New-York 1983.Google Scholar
  6. [6]
    A. Hasegawa and F. Tappert, Transmission of stationary optical pulses in distersive dielectric fibers. I. Anomalous dispersion., Appl. Phys. Lett., v.23, pp.142–144, 1973.CrossRefGoogle Scholar
  7. [7]
    A. Hasegawa and F. Tappert, Transmission of stationary optical pulses in distersive dielectric fibers. II. Normal dispersion., Appl. Phys. Lett., v.23, pp.171–172, 1973.CrossRefGoogle Scholar
  8. [8]
    L.M. Kovachev, Influence of cross-phase modulation and four-fhoton parametric mixing on relative motion of optical pulses, Optical and Quantum Electronics, 23, 1091–1102,1991.CrossRefGoogle Scholar
  9. [9]
    Yuji Kodama, Akira Hasegawa, Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect, Optics Letters, v.17, No 1, 31–33, 1992.CrossRefGoogle Scholar
  10. [10]
    L.F. Mollenauer, M.J. Neubelt, M. Haner, E. Lightman, S.G. Evangelides, B.M. Nyman, Demonstration of Error-Free Soliton Transmission at 2.5 Gbit/s over more than 14000 km., Electronics Letters, v.27, No 22, 2055–2056, 1991.CrossRefGoogle Scholar
  11. [11]
    A.C. Newell, Solitons in Mathematics and Physics, Society for Industrial and Applied Mathematics,1985.Google Scholar
  12. [12]
    T. Ueda and W.L. Kath, Dynamics of optical pulses in randomly biréfringent fibers, Physica D 55, 166–181, 1992.CrossRefGoogle Scholar
  13. [13]
    G.B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons, New York, 1974.Google Scholar
  14. [14]
    P.K.A. Wai, H.H. Chen, Y.C. Lee, Radiations by “solitons” at zero group-dispersion wavelength of single-mode optical fibers., Physical Review A, v.41, No 1, 426–439,1990.CrossRefGoogle Scholar
  15. [15]
    V.E. Zakharov, E.I. Shulman, On integrability of system of nonlinear Schrödinger equation, Physics D, v.4, p.270–274, 1982.CrossRefGoogle Scholar
  16. [16]
    V.E.Zakharov, A.B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) (Soviet Physics JETP 34, 62 (1972)).Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • D. Gurarie
  • P. Mishnayevskiy

There are no affiliations available

Personalised recommendations