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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1746–1758

Regular and chaotic dynamics of periodically amplified picosecond solitons

Yannis Kominis and Kyriakos Hizanidis  »View Author Affiliations


JOSA B, Vol. 19, Issue 8, pp. 1746-1758 (2002)
http://dx.doi.org/10.1364/JOSAB.19.001746


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Abstract

Chirped-pulse propagation under periodic amplification is considered on the basis of the variational method, and the resulting pulse-shape chaotic oscillations are studied. The system of equations governing the evolution of the parameter functions is nonintegrable and is solved by the canonical perturbation method and the construction of local approximate invariants embracing all the essential features of the phase-space dynamics. The latter provide useful guidelines for choosing the appropriate launching-pulse width and chirp for stable propagation for each specific transmission-link configuration. This fact is supported by comparison of the analytic results with the respective numerical ones of the exact dynamical system obtained by the variational method and by the direct integration of the nonlinear Schrödinger equation as well. The structure of the chaotic layer between the two distinct modes of behavior of a propagating pulse, namely, breathing and spreading/decaying, is also investigated qualitatively by utilizing Melnikov’s method. Examples from technologically realistic configurations are given for 4–14-ps pulses and for amplification periods of 40–100 km.

© 2002 Optical Society of America

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2410) Fiber optics and optical communications : Fibers, erbium
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Citation
Yannis Kominis and Kyriakos Hizanidis, "Regular and chaotic dynamics of periodically amplified picosecond solitons," J. Opt. Soc. Am. B 19, 1746-1758 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-8-1746


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References

  1. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
  2. M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er3+-doped fiber repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).
  3. R. G. Bauer and L. A. Melnikov, “Multi-soliton fission and quasi-periodicity in a fiber with a periodically modulated core diameter,” Opt. Commun. 115, 190–198 (1995).
  4. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
  5. S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
  6. H. Sugahara, K. Hiroki, I. Takashi, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547–1559 (1999).
  7. B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
  8. B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).
  9. T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).
  10. J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, “Hamiltonian dynamics of dispersion-managed breathers,” J. Opt. Soc. Am. B 15, 87–96 (1998).
  11. P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM J. Appl. Math. 59, 1288–1302 (1999).
  12. I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
  13. J. P. Gordon, “Dispersive perturbations of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
  14. N. J. Smith and N. J. Doran, “Picosecond soliton transmission using concatenated nonlinear optical loop-mirror intensity filters,” J. Opt. Soc. Am. B 12, 1117–1125 (1995).
  15. R.-J. Essiambre and G. P. Agrawal, “Soliton communication beyond the average-soliton regime,” J. Opt. Soc. Am. B 12, 2420–2425 (1995).
  16. W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).
  17. Z. M. Liao, C. J. McKinstrie, and G. P. Agrawal, “Importance of prechirping in constant-dispersion fiber links with a large amplifier spacing,” J. Opt. Soc. Am. B 17, 514–518 (2000).
  18. F. Kh. Abdullaev and J. G. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
  19. F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).
  20. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
  21. D. Anderson, M. Lisak, and T. Reichel, “Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system,” J. Opt. Soc. Am. B 5, 207–210 (1988).
  22. E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
  23. R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
  24. B. A. Malomed, “Resonant transmission of a chirped soliton in a long optical fiber with periodic amplification,” J. Opt. Soc. Am. B 13, 677–686 (1996).
  25. H. Gyldén, “Die Bahnbewegung in einem Systeme von zwei Körpern in dem Falle dass die Massen Veränderungen unterworfen sind,” Astron. Nachr. 109, 1–6 (1884).
  26. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
  27. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980).
  28. B. V. Chirikov, “A universal instability of many-dimensional oscillator systems,” Phys. Rep. 52, 263–379 (1979).
  29. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
  30. F. Diacu and D. Şelaru, “Chaos in the Gyldén problem,” J. Math. Phys. 39, 6537–6546 (1998).
  31. G. M. Zaslavsky, “The width of exponentially narrow stochastic layers,” Chaos 4, 589–591 (1994).
  32. J. B. Taylor and E. W. Laing, “Invariant for a particle interacting with an electrostatic wave in a magnetic field,” Phys. Rev. Lett. 35, 1306–1307 (1975).

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