Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

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Abstract

We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N-sequence transmission is described by a generalized N-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model’s predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

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Keywords

Optical Phenomena and Photonics 

References

  1. 1.
    G.P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, CA, 2001)Google Scholar
  2. 2.
    F. Forghieri, R.W. Tkach, A.R. Chraplyvy, in Optical Fiber Telecommunications III, edited by I.P. Kaminow, T.L. Koch (Academic, San Diego, CA, 1997), Chap. 8Google Scholar
  3. 3.
    L.F. Mollenauer, J.P. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic, San Diego, CA, 2006)Google Scholar
  4. 4.
    A.H. Gnauck, R.W. Tkach, A.R. Chraplyvy, T. Li, J. Lightwave Technol. 26, 1032 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, B. Goebel, J. Lightwave Technol. 28, 662 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    Q. Lin, O.J. Painter, G.P. Agrawal, Opt. Express 15, 16604 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    R. Dekker, N. Usechak, M. Först, A. Driessen, J. Phys. D 40, R249 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, Opt. Express 16, 1300 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, I. Bennion, IEEE Photon. Technol. Lett. 8, 60 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    H. Shi, J. Finlay, G.A. Alphonse, J.C. Connolly, P.J. Delfyett, IEEE Photon. Technol. Lett. 9, 1439 (1997)ADSCrossRefGoogle Scholar
  11. 11.
    H. Zhang, D.Y. Tang, X. Wu, L.M. Zhao, Opt. Express 17, 12692 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    X.M. Liu, D.D. Han, Z.P. Sun, C. Zeng, H. Lu, D. Mao, Y.D. Cui, F.Q. Wang, Sci. Rep. 3, 2718 (2013)ADSGoogle Scholar
  13. 13.
    E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998)Google Scholar
  14. 14.
    L.F. Mollenauer, P.V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    Q.M. Nguyen, A. Peleg, Opt. Commun. 283, 3500 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    A. Peleg, Q.M. Nguyen, Y. Chung, Phys. Rev. A 82, 053830 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    A. Peleg, Y. Chung, Phys. Rev. A 85, 063828 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    D. Chakraborty, A. Peleg, J.-H. Jung, Phys. Rev. A 88, 023845 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    Q.M. Nguyen, A. Peleg, T.P. Tran, Phys. Rev. A 91, 013839 (2015)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Peleg, Q.M. Nguyen, T.P. Tran, Opt. Commun. 380, 41 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    A.R. Chraplyvy, Electron. Lett. 20, 58 (1984)ADSCrossRefGoogle Scholar
  22. 22.
    F. Forghieri, R.W. Tkach, A.R. Chraplyvy, IEEE Photon. Technol. Lett. 7, 101 (1995)ADSCrossRefGoogle Scholar
  23. 23.
    K.-P. Ho, J. Lightwave Technol. 18, 915 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    T. Yamamoto, S. Norimatsu, J. Lightwave Technol. 21, 2229 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    A. Peleg, Opt. Lett. 29, 1980 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    A. Peleg, Phys. Lett. A 360, 533 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Chung, A. Peleg, Phys. Rev. A 77, 063835 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    B. Bakhshi, L. Richardson, E.A. Golovchenko, in Proceedings of the Optical Fiber Communication Conference, San Diego, CA, 2009, paper OThC4.Google Scholar
  29. 29.
    A. Peleg, Y. Chung, Opt. Commun. 285, 1429 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    M.N. Islam, Raman Amplifiers for Telecommunications 1: Physical Principles (Springer, New York, 2004)Google Scholar
  31. 31.
    C. Headley, G.P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, San Diego, CA, 2005)Google Scholar
  32. 32.
    Y. Okawachi, O. Kuzucu, M.A. Foster, R. Salem, A.C. Turner-Foster, A. Biberman, N. Ophir, K. Bergman, M. Lipson, A.L. Gaeta, IEEE Photon. Technol. Lett. 24, 185 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    A. Peleg, Q.M. Nguyen, P. Glenn, Phys. Rev. E 89, 043201 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    S. Chi, S. Wen, Opt. Lett. 14, 1216 (1989)ADSCrossRefGoogle Scholar
  35. 35.
    A.J. Lotka, Elements of Physical Biology (Williams and Wilkins, Baltimore, 1925)Google Scholar
  36. 36.
    V. Volterra, J. Cons. Int. Explor. Mer 3, 1 (1928)CrossRefGoogle Scholar
  37. 37.
    B.A. Malomed, Phys. Rev. A 44, 1412 (1991)ADSCrossRefGoogle Scholar
  38. 38.
    S. Kumar, Opt. Lett. 23, 1450 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    T.I. Lakoba, D.J. Kaup, Opt. Lett. 24, 808 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    Y. Chung, A. Peleg, Nonlinearity 18, 1555 (2005)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Q.M. Nguyen, A. Peleg, J. Opt. Soc. Am. B 27, 1985 (2010)ADSCrossRefGoogle Scholar
  42. 42.
    D. Chakraborty, A. Peleg, Q.M. Nguyen, Opt. Commun. 371, 252 (2016)ADSCrossRefGoogle Scholar
  43. 43.
    H.A. Haus, J. Appl. Phys. 46, 3049 (1975)ADSCrossRefGoogle Scholar
  44. 44.
    J.D. Moores, Opt. Commun. 96, 65 (1993)ADSCrossRefGoogle Scholar
  45. 45.
    H.A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Exact SciencesTel AvivIsrael
  2. 2.Department of MathematicsInternational University, Vietnam National University-HCMCHo Chi Minh CityVietnam
  3. 3.Department of MathematicsUniversity of Medicine and Pharmacy-HCMCHo Chi Minh CityVietnam
  4. 4.Department of MathematicsUniversity of Science, Vietnam National University-HCMCHo Chi Minh CityVietnam

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