Abstract

Analytic and numerical evidence is presented that demonstrates that a dispersion-managed breather can be supported in an optical fiber even when the average dispersion is in the normal regime. This nonlinear behavior, which is contrary to guiding-center theory, is shown to originate from the reversible dynamics associated with the strong quadratic chirp that is generated in both the anomalous and the normal dispersion regimes.

© 1998 Optical Society of America

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References

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  1. N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.
  2. N. Bergano, presented at the 10th Annual IEEE/Lasers and Electro-Optics Society Annual Meeting, San Francisco, Calif., November 10–13, 1997.
  3. J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
    [CrossRef]
  4. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
    [CrossRef]
  5. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
    [CrossRef]
  6. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
    [CrossRef] [PubMed]
  7. E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, Opt. Lett. 22, 289 (1997).
    [CrossRef] [PubMed]
  8. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  9. A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  10. T. S. Yang and W. L. Kath, Opt. Lett. 22, 985 (1997).
    [CrossRef] [PubMed]
  11. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  12. J. C. Bronski and J. N. Kutz, J. Opt. Soc. Am. B 14, 903 (1997).
    [CrossRef]
  13. J. C. Bronski and J. N. Kutz, Physica D 108, 315 (1997).
    [CrossRef]
  14. R. L. Devaney, Trans. Am. Math. Soc. 218, 89 (1976).
    [CrossRef]
  15. P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM J. Appl. Math. (to be published).

1998 (1)

1997 (7)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, Opt. Lett. 22, 289 (1997).
[CrossRef] [PubMed]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

T. S. Yang and W. L. Kath, Opt. Lett. 22, 985 (1997).
[CrossRef] [PubMed]

J. C. Bronski and J. N. Kutz, J. Opt. Soc. Am. B 14, 903 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, Physica D 108, 315 (1997).
[CrossRef]

1996 (1)

1992 (1)

1990 (1)

1976 (1)

R. L. Devaney, Trans. Am. Math. Soc. 218, 89 (1976).
[CrossRef]

Akiba, S.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Bergano, N.

N. Bergano, presented at the 10th Annual IEEE/Lasers and Electro-Optics Society Annual Meeting, San Francisco, Calif., November 10–13, 1997.

Bronski, J. C.

J. C. Bronski and J. N. Kutz, Physica D 108, 315 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, J. Opt. Soc. Am. B 14, 903 (1997).
[CrossRef]

Carter, G. M.

Devaney, R. L.

R. L. Devaney, Trans. Am. Math. Soc. 218, 89 (1976).
[CrossRef]

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

Edagawa, N.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Evangelides, S. G.

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

Hasegawa, A.

Holmes, P.

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
[CrossRef]

P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM J. Appl. Math. (to be published).

Jacob, J. M.

Kath, W. L.

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, Opt. Lett. 21, 1981 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Kutz, J. N.

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
[CrossRef]

J. C. Bronski and J. N. Kutz, J. Opt. Soc. Am. B 14, 903 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, Physica D 108, 315 (1997).
[CrossRef]

P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM J. Appl. Math. (to be published).

Menyuk, C. R.

Morita, I.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Pilipetskii, A. N.

Shapiro, E. G.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Smith, N. J.

Susuki, M.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Taga, H.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Turitsyn, S. K.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Yamamoto, S.

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

Yang, T. S.

Electron. Lett. (1)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Phys. Rev. E 55, 3624 (1997).
[CrossRef]

Physica D (1)

J. C. Bronski and J. N. Kutz, Physica D 108, 315 (1997).
[CrossRef]

Trans. Am. Math. Soc. (1)

R. L. Devaney, Trans. Am. Math. Soc. 218, 89 (1976).
[CrossRef]

Other (3)

P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM J. Appl. Math. (to be published).

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, in 21st European Conference on Optical Communications (Institute of Electrical Engineers, Brussels, 1985), paper Th.A 3.5.

N. Bergano, presented at the 10th Annual IEEE/Lasers and Electro-Optics Society Annual Meeting, San Francisco, Calif., November 10–13, 1997.

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Figures (3)

Fig. 1
Fig. 1

Qualitative geometric representation of the phase-plane dynamics over a single dispersion-map period.

Fig. 2
Fig. 2

Phase-plane (curves) and Poincaré map (circles) dynamics for Eqs.  (4) with mean-dispersion in the normal [Dave-0.04 ps/km nm, Z+=53 km, E02=10.251 mW]; zero [Dave=0 ps/km nm, Z+=54.155 km, E02=7.056 mW]; and anomalous [Dave=0.064 ps/km nm, Z+=56 km, E02=0.407 mW] dispersion regimes.

Fig. 3
Fig. 3

Pulse evolution with Dave=-0.04 ps/km nm over 50,000  km, depicting a persistent localized structure. This evolution is in contrast to the purely linear regime, in which the pulse intensity (and the inverse width) is decreased by a factor of 4.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

iQZ+σZ22QT2+Q2Q=0,
DZ=D-0<Z<Z-/2ZNLD+Z-/2ZNL<Z<Z-/2+Z+/ZNLD-Z-/2+Z+/ZNL<Z<P,
QZ, T=η exp-κηT2+iβκ2T2+ϕ,
dηdZ=-2κ2σZβη,
dβdZ=2κ2σZη4-β2-22η3.

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