Abstract

An analytic description is presented for the pulse dynamics in a dispersion-managed communications system in which the average dispersion is in the anomalous regime. A variational formalism reduces the governing equations to a planar Hamiltonian system for which a geometrical interpretation of the pulse dynamics is given. The reduced model gives a simple method for calculating the ideal enhanced initial power for a dispersion-managed breather and further exhibits a long-time periodic behavior, which is present in the full governing equations. Extensive numerical simulations verify the range of validity of the reduced equations.

© 1998 Optical Society of America

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  1. A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
    [CrossRef]
  2. N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, “20 Gb/s, 8100 km straight line single channel soliton based RZ transmission experiment using periodic dispersion compensation,” in European Conference on Optical Communications Proceedings (Institution of Electrical Engineers, Brussels, 1995), paper Th. A 3.5.
  3. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
    [CrossRef]
  4. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
    [CrossRef] [PubMed]
  5. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5, 1250–1253 (1993).
    [CrossRef]
  6. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
    [CrossRef]
  7. I. Gabitov and S. K. Turitsyn, “Breathing solitons in optical fiber links,” Pisma v JETP 63, 814–819 (1996).
  8. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
    [CrossRef]
  9. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
    [CrossRef]
  10. E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
    [CrossRef] [PubMed]
  11. J. C. Bronski and J. N. Kutz, “Guiding-center pulse dynamics in nonreturn-to-zero (return-to-zero) communications systems with mean-zero dispersion,” J. Opt. Soc. Am. B 14, 903–911 (1997).
    [CrossRef]
  12. J. C. Bronski and J. N. Kutz, “Asymptotic behavior of the nonlinear Schrödinger equation with a rapidly-varying, mean-zero dispersion,” Physica D 108, 315–329 (1997).
    [CrossRef]
  13. A. Hasegawa and Y. Kodama, “Guiding-center soliton in optical fibers,” Opt. Lett. 15, 1443–1445 (1990).
    [CrossRef] [PubMed]
  14. I. R. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
    [CrossRef]
  15. L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
    [CrossRef]
  16. M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
    [CrossRef]
  17. A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
    [CrossRef] [PubMed]
  18. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), Chap. 14.
  19. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
    [CrossRef]
  20. J. N. Kutz, S. D. Koehler, L. Leng, and K. Bergman, “Analytic study of orthogonally polarized solitons interacting in highly birefringent optical fibers,” J. Opt. Soc. Am. B 14, 636–642 (1997).
    [CrossRef]
  21. T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
    [CrossRef] [PubMed]
  22. Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menuyk, “Numerical modeling of soliton-dragging logic gates,” J. Opt. Soc. Am. B 10, 2030–2039 (1993).
    [CrossRef]
  23. D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
    [CrossRef]
  24. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 2.
  25. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, New York, 1976), Chap. 1.
  26. J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
    [CrossRef]
  27. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (Wiley, New York, 1986), Chap. 9.
  28. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamics Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

1997 (6)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, “Asymptotic behavior of the nonlinear Schrödinger equation with a rapidly-varying, mean-zero dispersion,” Physica D 108, 315–329 (1997).
[CrossRef]

J. N. Kutz, S. D. Koehler, L. Leng, and K. Bergman, “Analytic study of orthogonally polarized solitons interacting in highly birefringent optical fibers,” J. Opt. Soc. Am. B 14, 636–642 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, “Guiding-center pulse dynamics in nonreturn-to-zero (return-to-zero) communications systems with mean-zero dispersion,” J. Opt. Soc. Am. B 14, 903–911 (1997).
[CrossRef]

E. A. Golovchenko, J. M. Jacob, A. N. Pilipetskii, C. R. Menyuk, and G. M. Carter, “Dispersion-managed solitons in a fiber loop with in-line filtering,” Opt. Lett. 22, 289–291 (1997).
[CrossRef] [PubMed]

1996 (4)

I. R. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

1995 (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

1993 (4)

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5, 1250–1253 (1993).
[CrossRef]

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
[CrossRef]

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menuyk, “Numerical modeling of soliton-dragging logic gates,” J. Opt. Soc. Am. B 10, 2030–2039 (1993).
[CrossRef]

1992 (2)

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
[CrossRef]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

1990 (2)

A. Hasegawa and Y. Kodama, “Guiding-center soliton in optical fibers,” Opt. Lett. 15, 1443–1445 (1990).
[CrossRef] [PubMed]

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[CrossRef] [PubMed]

1988 (1)

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

1983 (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Anderson, D.

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Bergman, K.

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Bronski, J. C.

J. C. Bronski and J. N. Kutz, “Asymptotic behavior of the nonlinear Schrödinger equation with a rapidly-varying, mean-zero dispersion,” Physica D 108, 315–329 (1997).
[CrossRef]

J. C. Bronski and J. N. Kutz, “Guiding-center pulse dynamics in nonreturn-to-zero (return-to-zero) communications systems with mean-zero dispersion,” J. Opt. Soc. Am. B 14, 903–911 (1997).
[CrossRef]

Carter, G. M.

Chen, C.-J.

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Forysiak, W.

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

Gabitov, I. R.

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

Hasegawa, A.

Hawkins, R. J.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Jacob, J. M.

Kath, W. L.

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[CrossRef] [PubMed]

Kaup, D. J.

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
[CrossRef]

Kimura, Y.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Kirschner, E. M.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Koehler, S. D.

Kubota, H.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Kurtzke, C.

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5, 1250–1253 (1993).
[CrossRef]

Kutz, J. N.

Leaird, D. E.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Leng, L.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

Malomed, B. A.

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
[CrossRef]

Matsuda, T.

A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
[CrossRef]

Menuyk, C. R.

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

Naka, A.

A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

Nyman, B. M.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

Pilipetskii, A. N.

Saito, S.

A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
[CrossRef]

Shapiro, E. G.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

Smith, N. J.

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Susuki, K.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Takaya, M.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Tasgal, R. S.

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
[CrossRef]

Thurston, R. N.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Tomlinson, W. J.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Turitsyn, S. K.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

Ueda, T.

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[CrossRef] [PubMed]

Wai, P. K. A.

Wang, Q.

Weiner, A. M.

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Yamada, E.

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Electron. Lett. (4)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

A. Naka, T. Matsuda, and S. Saito, “Optical RZ signal straight line transmission with dispersion compensation over 5220 km at 20 Gb/s and 2160 km at 2X20 Gb/s,” Electron. Lett. 32, 1694–1696 (1996).
[CrossRef]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, and B. M. Nyman, “Demonstration of error-free soliton transmission over more than 15000km at 2.5 Gbit/s, single-channel, and over more than 11000km at 10 Gbit/s in 2-channel WDM,” Electron. Lett. 28, 792–794 (1992).
[CrossRef]

M. Nakazawa, K. Susuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data-transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5, 1250–1253 (1993).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “4-Photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

T. Ueda and W. L. Kath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (2)

D. J. Kaup, B. A. Malomed, and R. S. Tasgal, “Internal dynamics of a vector soliton in a nonlinear optical fiber,” Phys. Rev. E 48, 3049–3053 (1993).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission system with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

A. M. Weiner, W. J. Tomlinson, R. N. Thurston, D. E. Leaird, J. P. Heritage, E. M. Kirschner, and R. J. Hawkins, “Experimental-observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Physica D (1)

J. C. Bronski and J. N. Kutz, “Asymptotic behavior of the nonlinear Schrödinger equation with a rapidly-varying, mean-zero dispersion,” Physica D 108, 315–329 (1997).
[CrossRef]

Other (7)

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), Chap. 14.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 2.

L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, New York, 1976), Chap. 1.

W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (Wiley, New York, 1986), Chap. 9.

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamics Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

N. Edagawa, I. Morita, M. Susuki, S. Yamamoto, H. Taga, and S. Akiba, “20 Gb/s, 8100 km straight line single channel soliton based RZ transmission experiment using periodic dispersion compensation,” in European Conference on Optical Communications Proceedings (Institution of Electrical Engineers, Brussels, 1995), paper Th. A 3.5.

I. Gabitov and S. K. Turitsyn, “Breathing solitons in optical fiber links,” Pisma v JETP 63, 814–819 (1996).

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Figures (12)

Fig. 1
Fig. 1

Typical dispersion map used in experiments. Note here that the average dispersion is D¯=0.2 ps/(km-nm) with Z- =450 km, Z+=60 km, D-=-2.1 ps/(km-nm), and D+ =17.45 ps/(km-nm).

Fig. 2
Fig. 2

Phase-plane dynamics for σ=-1 and A=1 plotted for values of η0. The origin, which is the only fixed point for η 0, is degenerate.

Fig. 3
Fig. 3

Phase-plane dynamics for σ=1 and A=1 plotted for values of η>0. The origin is a degenerate fixed point while the fixed point at η=η00, β=0 is a center. The separatrix is represented by the dark solid curve.

Fig. 4
Fig. 4

Qualitative depiction of the pulse dynamics on the phase plane. The top picture represents the flow through the first part of the normal dispersion segment (see Fig. 1) as given in Fig. 2. The middle picture represents the flow under anomalous dispersion as given by Fig. 3 (the dotted curve is the flow of the previous fiber segment). The bottom picture is the final segment of the normal-dispersion fiber. Note that if the parameters are chosen appropriately, a periodic orbit can be constructed.

Fig. 5
Fig. 5

Normalized intensity (η), width (1/η), and chirp (β) fluctuations for α=0.4 with comparison between the ODE model (solid curve) and the governing dispersion-managed NLS equation (dashed curve).

Fig. 6
Fig. 6

Normalized intensity (η), width (1/η), and chirp (β) fluctuations for α=0.723 with comparison between the ODE model (solid curve) and the governing dispersion-managed NLS equation (dashed curve).

Fig. 7
Fig. 7

Normalized intensity (η), width (1/η), and chirp (β) fluctuations for α=1.5 with comparison between the ODE model (solid curve) and the governing dispersion-managed NLS equation (dashed curve).

Fig. 8
Fig. 8

Comparison of η and β fluctuations after 20 dispersion-map periods.

Fig. 9
Fig. 9

Comparison of η and β fluctuations after 38 dispersion-map periods.

Fig. 10
Fig. 10

Phase-plane dynamics of the ODE model (left) and governing dispersion-managed NLS (right). The light gray curves represent the η and β fluctuations as a function of Z, while the dots represent the solution after every dispersion map period, i.e., the Poincaré map. The spiraling in the partial-differential-equation model is from energy loss to the continuum.

Fig. 11
Fig. 11

Poincaré section dynamics on the phase plane for differing initial values of η and with α=αc=0.723. The point (η, β)=(1, 0) is a center, while the origin is again a degenerate fixed point. The structure of the Poincaré section is similar to the phase-plane dynamics of Fig. 3, for which a separatrix divides regions of periodic solutions from homoclinic orbits.

Fig. 12
Fig. 12

Dependence of αc on various dispersion-map configurations and pulse widths. Note that the parameter αc can be much different than 0.7 for certain dispersion maps.

Equations (40)

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i QZ+σ(Z)2 2QT2+|Q|2Q=0,
Z0=2πcλ02D¯ T01.762,
|E0|2=λ0Aeff2πn2Z0,
σ(Z)=1D¯ D-0<Z<12 Z-Z0D+12 Z-Z0<Z<12 Z-Z0+Z+Z0D-12 Z-Z0+Z+Z0<Z<P=Z-+Z+Z0,
D¯=D-Z-+D+Z+Z-+Z+.
L=-L(Q, Q*)dT,
L=iQ Q*Z-Q* QZ+σ(Z)QT2-|Q|4.
Q(Z, T)=Abη exp-(κηT)2+iβκ2T2+ϕ(Z)2,
|Q|2dT=b2 exp[-2(κT)2]dT=b2κ π2,
A2=1+αλ022πcT02 [(D+-D¯)Z+-(D--D¯)Z-]2.
L=A21η2 dβdZ+2 dϕdZ-4κA2π η+2κ2σ(Z)η2+β2η2.
pβ=LdβdZ=A2η2,
H(β, pβ)=pβ dβdZ-L(β, pβ),
dβdZ=Hpβ,dpβdZ=-Hβ.
dηdZ=-2κ2σ(Z)βη,
dβdZ=2κ2σ(Z)(η4-β2)-2κπ A2η3.
γη-dϕdZ-κ2σ(Z)η2+β2η2=C,
β=±ηγη-C-dϕdZκ2σ(Z)-η21/2,
dηdZ=2κ2σ(Z)η2γη-C-dϕdZκ2σ(Z)-η21/2.
Z=12κ2σ η0η dxx2γx-C-(dϕ/dZ)κ2σ-x21/2,
I.β=0,η=0,
II.β=0,η=A2κπσ(Z)=η0.
η=η0+η˜,β=0+β˜,
dη˜dZ=-2κ2σ(Z)η0β˜,
dβ˜dZ=8κ2σ(Z)η03-6κA2π η02η˜.
λ±=±2iκ2η02σ(Z).
β=0,η=A2D¯κπD+>0,
λ±=±2iκ2η02 D+D¯.
β=±ηγηD¯κ2D+-η2,
Q(Z, T)=AηF(κηT)expiβκ2T2+ϕ(Z)2,
|Q|2dT=ηF(ηT)2dT=F(x)2dx=const.,
L=A2κ 2C1η2 dβdZ+C2 dϕdZ-C3A2η+κ2σ(Z)C4η2+4C1β2η2,
C1=x2F(x)2dx,
C2=F(x)2dx,
C3=F(x)4dx,
C4=[F(x)]2dx.
dηdZ=-2κ2σ(Z)βη
dβdZ=κ22C1 σ(Z)(C4η4-4C1β2)-C34C1 A2η3.
dηdZ=-σ(Z)βη,
dβdZ=σ(Z)(η4-β2)-η3,

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