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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 20, Iss. 3 — Mar. 1, 2003
  • pp: 545–553

Nonlinear mode investigation in optical pulse propagation under periodic amplification and filtering

Yannis Kominis and Kyriakos Hizanidis  »View Author Affiliations


JOSA B, Vol. 20, Issue 3, pp. 545-553 (2003)
http://dx.doi.org/10.1364/JOSAB.20.000545


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Abstract

Propagating and periodically amplified and filtered pulses are considered as resonant periodic orbits of the applied variational model. Launching conditions (initial width and chirp) resulting in selection of particular nonlinear modes are given by a Poincaré map analysis. The resonant periodic orbits and the corresponding nonlinear modes of the real system are shown to be destroyed under strong filtering. Application of Melnikov’s method provides estimates of filtering margin for specific nonlinear mode preservation. Direct simulations of the real system show that the nonlinear modes that are characterized by large-amplitude pulse-shape oscillations exhibit a remarkably low radiation emission.

© 2003 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, "Nonlinear mode investigation in optical pulse propagation under periodic amplification and filtering," J. Opt. Soc. Am. B 20, 545-553 (2003)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-20-3-545


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References

  1. M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er3+-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).
  2. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, UK, 1995).
  3. 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).
  4. 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).
  5. 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).
  6. 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).
  7. B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).
  8. 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).
  9. 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).
  10. P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 59, 1288–1302 (1999).
  11. N. J. Smith and N. J. Doran, “Picosecond soliton transmis-sion using concatenated nonlinear optical loop-mirror intensity filters,” J. Opt. Soc. Am. B 12, 1117–1125 (1995).
  12. R.-J. Essiambre and G. P. Agrawal, “Soliton communication beyond the average-soliton regime,” J. Opt. Soc. Am. B 12, 2420–2425 (1995).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
  18. 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).
  19. B. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt. 43, 69 (2002).
  20. 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).
  21. 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).
  22. Y. Kominis and K. Hizanidis, “Regular and chaotic dynamics of periodically amplified picosecond solitons,” J. Opt. Soc. Am. B 19, 1746–1758 (2002).
  23. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980).
  24. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
  25. B. V. Chirikov, “A universal instability of many-dimensional oscillator systems,” Phys. Rep. 52, 263–379 (1979).
  26. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
  27. Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
  28. A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).
  29. B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

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