Abstract

A higher-order, multiple-scale asymptotic analysis is made of the perturbed nonlinear Schrödinger equation in a strong dispersion-managed optical transmission system. It is found that the averaged equation with the next-order term included significantly improves the description of the characteristics of dispersion-managed solitons. The derived equation is shown to support a new class of soliton solutions, namely, multihump solitons, which depend on both the map strength and dispersion profile. Numerical evidence of the regions of existence and stability of such new solitons is discussed.

© 2002 Optical Society of America

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References

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  1. 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]
  2. T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793–795 (1997).
    [CrossRef] [PubMed]
  3. T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
    [CrossRef]
  4. A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
    [CrossRef]
  5. M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1670 (1998).
    [CrossRef]
  6. 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]
  7. Y. Kodama, “On the dispersion-managed soliton: the guiding-center theory revisited,” in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 129–138.
  8. C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
    [CrossRef]
  9. V. E. Zakharov and S. V. Manakov, “On propagation of short pulses in strong dispersion-managed optical lines,” JETP Lett. 70, 578–582 (1999).
    [CrossRef]
  10. C. Paré and P.-A. Bélanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
    [CrossRef]
  11. P. M. Lushnikov, “Dispersion-managed soliton in optical fibers with zero average dispersion,” Opt. Lett. 25, 1144–1146 (2000).
  12. T. I. Lakoba and D. E. Pelinovsky, “Persistent oscillations of scalar and vector dispersion-managed solitons,” Chaos 10, 539–550 (2000).
  13. V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).
  14. D. E. Pelinovsky, “Instabilities of dispersion-managed solitons in the normal dispersion regime,” Phys. Rev. E 62, 4283–4293 (2000).
  15. T. S. Yang and W. L. Kath, “Radiation loss of dispersion-managed solitons in optical fibers,” Physica D 149, 80–94 (2001).
  16. M. J. Ablowitz, T. Hirooka, and G. Biondini, “Quasi-linear optical pulses in strongly dispersion-managed transmission systems,” Opt. Lett. 26, 459–461 (2001).
  17. M. J. Ablowitz, G. Biondini, and E. S. Olson, “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons,” J. Opt. Soc. Am. B 18, 577–583 (2001).
  18. M. J. Ablowitz and T. Hirooka, “Nonlinear effects in quasi-linear dispersion-managed pulse transmission,” IEEE Photon. Technol. Lett. 13, 1082–1084 (2001).
  19. P. M. Lushnikov, “Dispersion-managed soliton in a strong dispersion map limit,” Opt. Lett. 26, 1535–1537 (2001).
  20. G. Biondini and S. Chakravarty, “Nonlinear chirp of dispersion-managed return-to-zero pulses,” Opt. Lett. 26, 1761–1763 (2001).
  21. M. J. Ablowitz and T. Hirooka, “Managing nonlinearity in strongly dispersion-managed optical pulse transmission,” J. Opt. Soc. Am. B 19, 425–439 (2002).
    [CrossRef]
  22. M. J. Ablowitz and T. Hirooka, “Resonant intrachannel pulse interactions in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 603–615 (2002).
    [CrossRef]
  23. A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
    [CrossRef]
  24. T.-S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
    [CrossRef] [PubMed]
  25. J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
    [CrossRef]
  26. M. J. Ablowitz, G. Biondini, and E. S. Olson, “On the evolution and interaction of dispersion-managed solitons,” Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

2002 (3)

M. J. Ablowitz and T. Hirooka, “Managing nonlinearity in strongly dispersion-managed optical pulse transmission,” J. Opt. Soc. Am. B 19, 425–439 (2002).
[CrossRef]

M. J. Ablowitz and T. Hirooka, “Resonant intrachannel pulse interactions in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 603–615 (2002).
[CrossRef]

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

2001 (7)

T. S. Yang and W. L. Kath, “Radiation loss of dispersion-managed solitons in optical fibers,” Physica D 149, 80–94 (2001).

M. J. Ablowitz, T. Hirooka, and G. Biondini, “Quasi-linear optical pulses in strongly dispersion-managed transmission systems,” Opt. Lett. 26, 459–461 (2001).

M. J. Ablowitz, G. Biondini, and E. S. Olson, “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons,” J. Opt. Soc. Am. B 18, 577–583 (2001).

M. J. Ablowitz and T. Hirooka, “Nonlinear effects in quasi-linear dispersion-managed pulse transmission,” IEEE Photon. Technol. Lett. 13, 1082–1084 (2001).

P. M. Lushnikov, “Dispersion-managed soliton in a strong dispersion map limit,” Opt. Lett. 26, 1535–1537 (2001).

G. Biondini and S. Chakravarty, “Nonlinear chirp of dispersion-managed return-to-zero pulses,” Opt. Lett. 26, 1761–1763 (2001).

A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
[CrossRef]

2000 (7)

C. Paré and P.-A. Bélanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
[CrossRef]

P. M. Lushnikov, “Dispersion-managed soliton in optical fibers with zero average dispersion,” Opt. Lett. 25, 1144–1146 (2000).

T. I. Lakoba and D. E. Pelinovsky, “Persistent oscillations of scalar and vector dispersion-managed solitons,” Chaos 10, 539–550 (2000).

V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).

D. E. Pelinovsky, “Instabilities of dispersion-managed solitons in the normal dispersion regime,” Phys. Rev. E 62, 4283–4293 (2000).

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

1999 (2)

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

V. E. Zakharov and S. V. Manakov, “On propagation of short pulses in strong dispersion-managed optical lines,” JETP Lett. 70, 578–582 (1999).
[CrossRef]

1998 (1)

1997 (2)

1996 (2)

Ablowitz, M. J.

M. J. Ablowitz and T. Hirooka, “Resonant intrachannel pulse interactions in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 603–615 (2002).
[CrossRef]

M. J. Ablowitz and T. Hirooka, “Managing nonlinearity in strongly dispersion-managed optical pulse transmission,” J. Opt. Soc. Am. B 19, 425–439 (2002).
[CrossRef]

M. J. Ablowitz, T. Hirooka, and G. Biondini, “Quasi-linear optical pulses in strongly dispersion-managed transmission systems,” Opt. Lett. 26, 459–461 (2001).

M. J. Ablowitz, G. Biondini, and E. S. Olson, “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons,” J. Opt. Soc. Am. B 18, 577–583 (2001).

M. J. Ablowitz and T. Hirooka, “Nonlinear effects in quasi-linear dispersion-managed pulse transmission,” IEEE Photon. Technol. Lett. 13, 1082–1084 (2001).

M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1670 (1998).
[CrossRef]

M. J. Ablowitz, G. Biondini, and E. S. Olson, “On the evolution and interaction of dispersion-managed solitons,” Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

Bélanger, P.-A.

C. Paré and P.-A. Bélanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
[CrossRef]

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

Biondini, G.

Cautaerts, V.

V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).

Chakravarty, S.

Doran, N. J.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[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]

Forysiak, W.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[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]

Gabitov, I. R.

Golovchenko, E. A.

Hirooka, T.

M. J. Ablowitz and T. Hirooka, “Managing nonlinearity in strongly dispersion-managed optical pulse transmission,” J. Opt. Soc. Am. B 19, 425–439 (2002).
[CrossRef]

M. J. Ablowitz and T. Hirooka, “Resonant intrachannel pulse interactions in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 603–615 (2002).
[CrossRef]

M. J. Ablowitz and T. Hirooka, “Nonlinear effects in quasi-linear dispersion-managed pulse transmission,” IEEE Photon. Technol. Lett. 13, 1082–1084 (2001).

M. J. Ablowitz, T. Hirooka, and G. Biondini, “Quasi-linear optical pulses in strongly dispersion-managed transmission systems,” Opt. Lett. 26, 459–461 (2001).

Inoue, T.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
[CrossRef]

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

Kath, W. L.

T. S. Yang and W. L. Kath, “Radiation loss of dispersion-managed solitons in optical fibers,” Physica D 149, 80–94 (2001).

T.-S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
[CrossRef] [PubMed]

Knox, F. M.

Kodama, Y.

V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

Y. Kodama, “On the dispersion-managed soliton: the guiding-center theory revisited,” in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 129–138.

Lakoba, T. I.

T. I. Lakoba and D. E. Pelinovsky, “Persistent oscillations of scalar and vector dispersion-managed solitons,” Chaos 10, 539–550 (2000).

Lesage, F.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

Lushnikov, P. M.

Manakov, S. V.

V. E. Zakharov and S. V. Manakov, “On propagation of short pulses in strong dispersion-managed optical lines,” JETP Lett. 70, 578–582 (1999).
[CrossRef]

Maruta, A.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
[CrossRef]

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).

Mathieu, P.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

Menyuk, C. R.

Nijhof, J. H. B.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Nonaka, Y.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
[CrossRef]

Olson, E. S.

M. J. Ablowitz, G. Biondini, and E. S. Olson, “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons,” J. Opt. Soc. Am. B 18, 577–583 (2001).

M. J. Ablowitz, G. Biondini, and E. S. Olson, “On the evolution and interaction of dispersion-managed solitons,” Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

Paré, C.

C. Paré and P.-A. Bélanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
[CrossRef]

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

Pelinovsky, D. E.

T. I. Lakoba and D. E. Pelinovsky, “Persistent oscillations of scalar and vector dispersion-managed solitons,” Chaos 10, 539–550 (2000).

D. E. Pelinovsky, “Instabilities of dispersion-managed solitons in the normal dispersion regime,” Phys. Rev. E 62, 4283–4293 (2000).

Pilipetskii, A. N.

Roy, V.

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

Smith, N. J.

Sugahara, H.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

Turitsyn, S. K.

Yang, T. S.

T. S. Yang and W. L. Kath, “Radiation loss of dispersion-managed solitons in optical fibers,” Physica D 149, 80–94 (2001).

Yang, T.-S.

Yoshika, Y.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

Yu, T.

Zakharov, V. E.

V. E. Zakharov and S. V. Manakov, “On propagation of short pulses in strong dispersion-managed optical lines,” JETP Lett. 70, 578–582 (1999).
[CrossRef]

Chaos (2)

T. I. Lakoba and D. E. Pelinovsky, “Persistent oscillations of scalar and vector dispersion-managed solitons,” Chaos 10, 539–550 (2000).

V. Cautaerts, A. Maruta, and Y. Kodama, “On the dispersion-managed soliton,” Chaos 10, 515–528 (2000).

Electron. Lett. (1)

A. Maruta, Y. Nonaka, and T. Inoue, “Symmetric bi-soliton solution in a dispersion-managed system,” Electron. Lett. 37, 1357–1358 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

M. J. Ablowitz and T. Hirooka, “Resonant intrachannel pulse interactions in dispersion-managed transmission systems,” IEEE J. Sel. Top. Quantum Electron. 8, 603–615 (2002).
[CrossRef]

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bi-soliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8, 640–650 (2002).
[CrossRef]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. J. Ablowitz and T. Hirooka, “Nonlinear effects in quasi-linear dispersion-managed pulse transmission,” IEEE Photon. Technol. Lett. 13, 1082–1084 (2001).

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion-managed solitons in optical-time-division-multiplexed system,” IEEE Photon. Technol. Lett. 12, 299–301 (2000).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

V. E. Zakharov and S. V. Manakov, “On propagation of short pulses in strong dispersion-managed optical lines,” JETP Lett. 70, 578–582 (1999).
[CrossRef]

Opt. Lett. (10)

C. Paré and P.-A. Bélanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
[CrossRef]

P. M. Lushnikov, “Dispersion-managed soliton in optical fibers with zero average dispersion,” Opt. Lett. 25, 1144–1146 (2000).

M. J. Ablowitz, T. Hirooka, and G. Biondini, “Quasi-linear optical pulses in strongly dispersion-managed transmission systems,” Opt. Lett. 26, 459–461 (2001).

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]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793–795 (1997).
[CrossRef] [PubMed]

M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1670 (1998).
[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]

P. M. Lushnikov, “Dispersion-managed soliton in a strong dispersion map limit,” Opt. Lett. 26, 1535–1537 (2001).

G. Biondini and S. Chakravarty, “Nonlinear chirp of dispersion-managed return-to-zero pulses,” Opt. Lett. 26, 1761–1763 (2001).

T.-S. Yang and W. L. Kath, “Analysis of enhanced-power solitons in dispersion-managed optical fibers,” Opt. Lett. 22, 985–987 (1997).
[CrossRef] [PubMed]

Phys. Rev. E (2)

C. Paré, V. Roy, F. Lesage, P. Mathieu, and P.-A. Bélanger, “Coupled-field description of zero-average dispersion management,” Phys. Rev. E 60, 4836–4842 (1999).
[CrossRef]

D. E. Pelinovsky, “Instabilities of dispersion-managed solitons in the normal dispersion regime,” Phys. Rev. E 62, 4283–4293 (2000).

Physica D (1)

T. S. Yang and W. L. Kath, “Radiation loss of dispersion-managed solitons in optical fibers,” Physica D 149, 80–94 (2001).

Other (2)

Y. Kodama, “On the dispersion-managed soliton: the guiding-center theory revisited,” in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 129–138.

M. J. Ablowitz, G. Biondini, and E. S. Olson, “On the evolution and interaction of dispersion-managed solitons,” Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

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Figures (12)

Fig. 1
Fig. 1

Variation of the rms width of the spectrum in the averaging procedure.

Fig. 2
Fig. 2

DM soliton solution (s=0.56, d0=1.65, θ=0.8, M=0.34, za=0.06) (a) in the spectral domain and (b) in the time domain. The dashed curves represent the initial (Gaussian) waveforms in both (a) and (b).

Fig. 3
Fig. 3

Solid curve is an approximate solution u(t)=u(0)(t)+zau(1)(t) which is calculated from Eqs. (7) and (14). The dashed curve represents a DM soliton obtained from the averaging method on the p-NLS equation; it is indistinguishable from the solid curve. The dotted curve is U0(t) which is the inverse Fourier transform of Uˆ0(ω), which is the leading-order solution of the HO-DMNLS. The waveforms are shown in (a) linear and (b) log scale. In (a) the dashed curve is indistinguishable from the solid curve.

Fig. 4
Fig. 4

Evolution of chirp and peak amplitude of a DM soliton within a DM period. The solid curve and dashed curve denote the approximate solution u=u(0)+zau(1) and leading-order solution u(0), respectively. The circles represent the evolution on the p-NLS equation.

Fig. 5
Fig. 5

θ dependency of single DM solitons that are obtained by using the averaging method on the HO-DMNLS. All of the parameters except θ are the same as those used for Fig. 2.

Fig. 6
Fig. 6

Bi-soliton with τs=3τFWHM solution which is obtained by the averaging method on the HO-DMNLS equation for s=0.56, θ=0.8, d0=1.65, and then M=0.340 (solid curve). The dotted curve shows the same solution which is given by the averaging method on the p-NLS equation.

Fig. 7
Fig. 7

Regions in which a bi-soliton solution with τs=3τFWHM can be found by using the averaging method on (a) the HO-DMNLS and (b) the p-NLS equation. In the bright region in (b) two Gaussian inputs with τs=3τFWHM can propagate without collision or large timing shift over long distances.

Fig. 8
Fig. 8

Antiphase bi-soliton with τs=2τFWHM for s=0.46, θ=0.8, d0=1.65, and M=0.279, which is obtained by the averaging method on the HO-DMNLS equation (solid curve) and on the p-NLS equation (dotted curve).

Fig. 9
Fig. 9

In-phase tri-soliton solution with τs=3τFWHM for s=0.54, θ=0.3, d0=1.65, and M=0.328, which is obtained by the averaging method on the HO-DMNLS equation (solid curve) and on the p-NLS equation (dotted curve).

Fig. 10
Fig. 10

Anti-phase tri-soliton solution with τs=2τFWHM for s=0.37, θ=0.8, d0=1.65, and M=0.225, which is obtained by the averaging method on the HO-DMNLS equation (solid curve) and on the p-NLS equation (dotted curve).

Fig. 11
Fig. 11

(a) In-phase quartic-soliton with τs=3τFWHM for s=0.51, θ=0.6, d0=1.65, and M=0.310 and (b) antiphase quartic-soliton with τs=2τFWHM for s=0.37, θ=0.8, d0=1.65, and M=0.225.

Fig. 12
Fig. 12

(a) Initial waveforms of bi-soliton with weak white noise Un(t) and the pure bi-soliton U0(t) which appears in Fig. 6. (b) Evolution of the energy of the difference |Un-U0| as a function of distance.

Equations (45)

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i uz+d(z)2 2ut2+g(z)|u|2u=0,
u(ζ, Z, t)=u(0)(ζ, Z, t)+zau(1)(ζ, Z, t)+za2u(2)(ζ, Z, t)+O(za3).
O(za-1):i u(0)ζ+Δ(ζ)2 2u(0)t2
=0,
O(1):i u(1)ζ+Δ(ζ)2 2u(1)t2
=-i u(0)Z+d02 2u(0)t2+g(ζ)|u(0)|2u(0),
O(za):i u(2)ζ+Δ(ζ)2 2u(2)t2
=-i u(1)Z+d02 2u(1)t2+g(ζ)[2|u(0)|2u(1)+u(0)2u(1)*].
i uˆ(0)ζ-Δ(ζ)2ω2uˆ(0)=0,
uˆ(0)(ζ, Z, ω)=exp-i ω22C(ζ)Uˆ0(Z, ω),
i uˆ(1)ζ-Δ(ζ)2ω2uˆ(1)
=-exp-i ω22C(ζ)×i Uˆ0Z-d02ω2Uˆ0-g(ζ)Pˆ0(ζ, Z, ω),
i Uˆ0Z-d02ω2Uˆ0+g(ζ)expi ω22C(ζ)Pˆ0(ζ, Z, ω)
=0.
i Uˆ0Z-d02ω2Uˆ0+1(2π)2 -+dω1dω2r0(ω1ω2)
×Uˆ0(ω+ω1)Uˆ0(ω+ω2)Uˆ0*(ω+ω1+ω2)=0,
ζ{iuˆ(1) exp[iC(ζ)ω2/2]}
=g(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω)-g(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω).
iuˆ(1) exp[iC(ζ)ω2/2]
=Uˆ1-0ζg(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω)dζ+ζg(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω),
Uˆ1(Z, ω)=0ζg(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω)dζ-12g(ζ)exp[iC(ζ)ω2/2]Pˆ0(ζ, Z, ω).
uˆ(1)(ζ, Z, ω)=i exp-i ω22C(ζ)0ζ expi ω22C(ζ)×g(ζ)Pˆ0(ζ, Z, ω)dζ-0ζ expi ω22C(ζ)g(ζ)×Pˆ0(ζ, Z, ω)dζ-ζ-12×expi ω22C(ζ)g(ζ)Pˆ0(ζ, Z, ω),
uˆ(1)(ζ, Z, ω)
=i exp-i ω22C(ζ) 1(2π)2 -+dΩ1dΩ2
×Uˆ0(ω+Ω1)Uˆ0(ω+Ω2)Uˆ0*(ω+Ω1+Ω2)
×0ζg(ζ)K(ζ, Ω1Ω2)dζ-0ζg(ζ)K(ζ, Ω1Ω2)dζ-ζ-12g(ζ)K(ζ, Ω1Ω2).
i Uˆ0Z-d02ω2Uˆ0+1(2π)2 -+dω1dω2r0(ω1ω2)×Uˆ0(ω+ω1)Uˆ0(ω+ω2)Uˆ0*(ω+ω1+ω2)
=zanˆ1(Z, ω)+O(za2).
ζ{iuˆ(2) exp[iC(ζ)ω2/2]}+nˆ1+exp[iC(ζ)ω2/2]
×i uˆ(1)Z-d02ω2uˆ(1)+g(ζ)Pˆ1(ζ, Z, ω)=0,
nˆ1=-g(ζ)exp[iC(ζ)ω2/2]Pˆ1(ζ, Z, ω).
nˆ1=-i(2π)4 -+dω1dω2dΩ1dΩ2r1(ω1ω2, Ω1Ω2)×[2Uˆ0(ω+ω1)Uˆ0*(ω+ω1+ω2)×Uˆ0(ω+ω2+Ω1)Uˆ0(ω+ω2+Ω2)Uˆ0*(ω+ω2+Ω1+Ω2)-Uˆ0(ω+ω1)Uˆ0(ω+ω2)Uˆ0*(ω+ω1+ω2+Ω1)×Uˆ0*(ω+ω1+ω2-Ω2)Uˆ0(ω+ω1+ω2+Ω1-Ω2)],
r1(x, y)=g(ζ)K(ζ, x)0ζg(ζ)K(ζ, y)dζ-g(ζ)K(ζ, x)0ζg(ζ)K(ζ, y)dζ-ζ-12g(ζ)K(ζ, x)g(ζ)K(ζ, y).
r0(x)=sin(sx)sx,
r1(x, y)=i(2θ-1)2s3x2y2(x+y){sxy[y cos(sx)sin(sy)-x cos(sy)sin(sx)]+(x2-y2)sin(sx)sin(sy)}.
i Uˆ0Z-ω22Uˆ0+1(2π)2 -+dω1dω2r0(ω1ω2)
×Uˆ0(ω+ω1)Uˆ0(ω+ω2)Uˆ0*(ω+ω1+ω2)=zanˆ1,
nˆ1=-i(2π)4 -+dω1dω2dΩ1dΩ2r1(ω1ω2, Ω1Ω2)×[2Uˆ0(ω+ω1)Uˆ0*(ω+ω1+ω2)Uˆ0(ω+ω2+Ω1)×Uˆ0(ω+ω2+Ω2)Uˆ0*(ω+ω2+Ω1+Ω2)-Uˆ0(ω+ω1)Uˆ0(ω+ω2)Uˆ0*(ω+ω1+ω2+Ω1)×Uˆ0*(ω+ω1+ω2-Ω2)Uˆ0(ω+ω1+ω2+Ω1-Ω2)],
r0(x)=sin(Mx)Mx,
r1(x, y)=i(2θ-1)2M3x2y2(x+y){Mxy[y cos(Mx)sin(My)-x cos(My)sin(Mx)]+(x2-y2)sin(Mx)sin(My)},
Uˆ0(Z, ω)=1|d0|Uˆ0Z,ω|d0|.
i Uˆ0Z-d02ω2Uˆ0+g(ζ)expi ω22C(ζ)Pˆ(ζ, Z, ω)
=0,
Uˆ(ω)=exp(-iϕmax)Uˆmax(ω)+exp(-iϕmin)Uˆmin(ω)2,
Uˆave(ω)=E0E Uˆ(ω),

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