Abstract

We investigate the interactions of dispersion managed (DM) solitons in a stabilized model where the stabilization is provided by coupling a lossy core to the system’s main fiber. It is found that interaction of solitons in this model is quite complex in that they can attract or repel, depending on the initial phase and initial separation of solitons. An important finding is that bound states of DM solitons exist in this model. It is also found that collision distance increases as the net average dispersion increases from normal to anomalous. In the case of D¯=+0.1, a region in the plane (γ0,L) has been identified where periodic bound states of two solitons exist.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).
  2. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
    [CrossRef]
  3. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, 'Enhanced power solitons in optical fibres with periodic dispersion management,' Electron. Lett. 32, 54-55 (1996).
    [CrossRef]
  4. G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, 'Timing-jitter reduction for a dispersion-managed soliton system: experimental evidence,' Opt. Lett. 22, 513-515 (1997).
    [CrossRef] [PubMed]
  5. M. Matsumoto, 'Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,' Electron. Lett. 33, 1718-1720 (1997).
    [CrossRef]
  6. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, 'Optical pulse dynamics in fibre links with dispersion compensation,' Opt. Commun. 134, 317-329 (1997).
    [CrossRef]
  7. Y. Chen and J. Atai, 'Average dark soliton dynamics in periodically dispersion compensated fibre transmission systems,' IEEE Photon. Technol. Lett. 10, 1280-1282 (1998).
    [CrossRef]
  8. 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]
  9. T. Georges, 'Soliton interaction in dispersion-managed links,' J. Opt. Soc. Am. B 15, 1553-1560 (1998).
    [CrossRef]
  10. T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
    [CrossRef]
  11. A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, 'Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,' Opt. Lett. 23, 900-902 (1998).
    [CrossRef]
  12. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, 'Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,' Electron. Lett. 33, 1726-1727 (1997).
    [CrossRef]
  13. D. S. Govan, W. Forysiak, and N. J. Doran, 'Long-distance 40-Gbit/s soliton transmission over standard fibre by use of dispersion management,' Opt. Lett. 23, 1523-1525 (1998).
    [CrossRef]
  14. D. J. Kaup, B. A. Malomed, and J. Yang, 'Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,' Opt. Lett. 23, 1600-1602 (1998).
    [CrossRef]
  15. A. N. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, 'Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,' Opt. Lett. 23, 1354-1356 (1998).
    [CrossRef]
  16. L. F. Mollenauer, J. P. Gordon, and M. N. Islam, 'Soliton propagation in long fibres with periodically compensated loss,' IEEE J. Quantum Electron. QE-22, 157-173 (1986).
    [CrossRef]
  17. J. P. Gordon and H. A. Haus, 'Random walk of coherently amplified solitons in optical fiber transmission,' Opt. Lett. 11, 665-667 (1986).
    [CrossRef] [PubMed]
  18. S. K. Turitsyn and E. G. Shapiro, 'Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,' Opt. Lett. 23, 682-684 (1998).
    [CrossRef]
  19. J. N. Kutz and S. G. Evangelides, Jr., 'Dispersion managed breathers with average normal dispersion,' Opt. Lett. 23, 685-687 (1998).
    [CrossRef]
  20. V. S. Grigoryan and C. R. Menyuk, 'Dispersion-managed solitons at normal average dispersion,' Opt. Lett. 23, 609-611 (1998).
    [CrossRef]
  21. B. A. Malomed, 'Suppression of soliton jitter and interactions by means of dispersion management,' Opt. Commun. 147, 157-162 (1998).
    [CrossRef]
  22. H. A. Haus, Y. Lai, A. Mecozzi, and J. D. Moores, 'Soliton transmission control,' Opt. Lett. 16, 1841-1843 (1991).
    [CrossRef] [PubMed]
  23. Y. Kodama and A. Hasegawa, 'Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect,' Opt. Lett. 17, 31-33 (1992).
    [CrossRef] [PubMed]
  24. M. Matsumoto, 'Analysis of filter control of dispersion-managed soliton transmission,' J. Opt. Soc. Am. B 15, 2831-2837 (1998).
    [CrossRef]
  25. M. Matsumoto, 'Instability of dispersion managed solitons in a system with filtering,' Opt. Lett. 23, 1901-1903 (1998).
    [CrossRef]
  26. L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, 'Effect of guiding filters on the behavior of dispersion-managed solitons,' Opt. Lett. 24, 220-222 (1999).
    [CrossRef]
  27. A. Bernston and B. A. Malomed, 'Dispersion management with filtering,' Opt. Lett. 24, 507-509 (1999).
    [CrossRef]
  28. J. Atai and B. A. Malomed, 'Stabilized scheme for dispersion management,' J. Opt. Soc. Am. B 17, 1134-1139 (2000).
    [CrossRef]
  29. B. A. Malomed and H. G. Winful, 'Stable solitons in two-component active systems,' Phys. Rev. E 53, 5365-5368 (1996).
    [CrossRef]
  30. J. Atai and B. A. Malomed, 'Stability and interactions of solitons in two-component active systems,' Phys. Rev. E 54, 4371-4374 (1996).
    [CrossRef]
  31. J. Atai and B. A. Malomed, 'Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations,' Phys. Lett. A 246, 412-422 (1998).
    [CrossRef]
  32. E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
    [CrossRef]
  33. H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
    [CrossRef]
  34. G. P. Agrawal, Nonlinear Fibre Optics (Academic, 1995).
  35. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).
  36. C. Kurtze, 'Suppression of fiber nonlinearities by appropriate dispersion management,' IEEE Photon. Technol. Lett. 5, 1250-1253 (1993).
    [CrossRef]
  37. J. Atai and B. A. Malomed, 'Bound states of solitary pulses in linearly couples Ginzburg-Landau equations,' Phys. Lett. A 244, 551-556 (1998).
    [CrossRef]
  38. S. Wabnitz and E. Westin, 'Optical fiber soliton bound states and interaction suppression with high-order filtering,' Opt. Lett. 21, 1235-1237 (1996).
    [CrossRef] [PubMed]
  39. N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
    [CrossRef]
  40. B. Feng and B. A. Malomed, 'Bound states of solitons between close wavelength-separated channels in a dispersion-managed fiber-optic link,' Opt. Commun. 219, 143-156 (2003).
    [CrossRef]

2003 (1)

B. Feng and B. A. Malomed, 'Bound states of solitons between close wavelength-separated channels in a dispersion-managed fiber-optic link,' Opt. Commun. 219, 143-156 (2003).
[CrossRef]

2002 (2)

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
[CrossRef]

2000 (2)

1999 (2)

1998 (15)

Y. Chen and J. Atai, 'Average dark soliton dynamics in periodically dispersion compensated fibre transmission systems,' IEEE Photon. Technol. Lett. 10, 1280-1282 (1998).
[CrossRef]

M. Matsumoto, 'Analysis of filter control of dispersion-managed soliton transmission,' J. Opt. Soc. Am. B 15, 2831-2837 (1998).
[CrossRef]

M. Matsumoto, 'Instability of dispersion managed solitons in a system with filtering,' Opt. Lett. 23, 1901-1903 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Bound states of solitary pulses in linearly couples Ginzburg-Landau equations,' Phys. Lett. A 244, 551-556 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations,' Phys. Lett. A 246, 412-422 (1998).
[CrossRef]

T. Georges, 'Soliton interaction in dispersion-managed links,' J. Opt. Soc. Am. B 15, 1553-1560 (1998).
[CrossRef]

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, 'Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,' Opt. Lett. 23, 900-902 (1998).
[CrossRef]

D. S. Govan, W. Forysiak, and N. J. Doran, 'Long-distance 40-Gbit/s soliton transmission over standard fibre by use of dispersion management,' Opt. Lett. 23, 1523-1525 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, 'Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,' Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

A. N. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, 'Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,' Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

S. K. Turitsyn and E. G. Shapiro, 'Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,' Opt. Lett. 23, 682-684 (1998).
[CrossRef]

J. N. Kutz and S. G. Evangelides, Jr., 'Dispersion managed breathers with average normal dispersion,' Opt. Lett. 23, 685-687 (1998).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, 'Dispersion-managed solitons at normal average dispersion,' Opt. Lett. 23, 609-611 (1998).
[CrossRef]

B. A. Malomed, 'Suppression of soliton jitter and interactions by means of dispersion management,' Opt. Commun. 147, 157-162 (1998).
[CrossRef]

1997 (5)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, 'Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,' Electron. Lett. 33, 1726-1727 (1997).
[CrossRef]

G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, 'Timing-jitter reduction for a dispersion-managed soliton system: experimental evidence,' Opt. Lett. 22, 513-515 (1997).
[CrossRef] [PubMed]

M. Matsumoto, 'Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,' Electron. Lett. 33, 1718-1720 (1997).
[CrossRef]

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

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]

1996 (4)

B. A. Malomed and H. G. Winful, 'Stable solitons in two-component active systems,' Phys. Rev. E 53, 5365-5368 (1996).
[CrossRef]

J. Atai and B. A. Malomed, 'Stability and interactions of solitons in two-component active systems,' Phys. Rev. E 54, 4371-4374 (1996).
[CrossRef]

S. Wabnitz and E. Westin, 'Optical fiber soliton bound states and interaction suppression with high-order filtering,' Opt. Lett. 21, 1235-1237 (1996).
[CrossRef] [PubMed]

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

1995 (1)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

1993 (1)

C. Kurtze, 'Suppression of fiber nonlinearities by appropriate dispersion management,' IEEE Photon. Technol. Lett. 5, 1250-1253 (1993).
[CrossRef]

1992 (1)

1991 (1)

1986 (2)

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, 'Soliton propagation in long fibres with periodically compensated loss,' IEEE J. Quantum Electron. QE-22, 157-173 (1986).
[CrossRef]

J. P. Gordon and H. A. Haus, 'Random walk of coherently amplified solitons in optical fiber transmission,' Opt. Lett. 11, 665-667 (1986).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fibre Optics (Academic, 1995).

Akhmediev, N.

N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
[CrossRef]

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Atai, J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

J. Atai and B. A. Malomed, 'Stabilized scheme for dispersion management,' J. Opt. Soc. Am. B 17, 1134-1139 (2000).
[CrossRef]

J. Atai and B. A. Malomed, 'Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations,' Phys. Lett. A 246, 412-422 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Bound states of solitary pulses in linearly couples Ginzburg-Landau equations,' Phys. Lett. A 244, 551-556 (1998).
[CrossRef]

Y. Chen and J. Atai, 'Average dark soliton dynamics in periodically dispersion compensated fibre transmission systems,' IEEE Photon. Technol. Lett. 10, 1280-1282 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Stability and interactions of solitons in two-component active systems,' Phys. Rev. E 54, 4371-4374 (1996).
[CrossRef]

Bennion, I.

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

Bernston, A.

Berntson, A.

Blow, K. J.

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

Carter, G. M.

Chen, Y.

Y. Chen and J. Atai, 'Average dark soliton dynamics in periodically dispersion compensated fibre transmission systems,' IEEE Photon. Technol. Lett. 10, 1280-1282 (1998).
[CrossRef]

Chu, P. L.

N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
[CrossRef]

Doran, N. J.

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Efremidis, E.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
[CrossRef]

Evangelides, S. G.

Feng, B.

B. Feng and B. A. Malomed, 'Bound states of solitons between close wavelength-separated channels in a dispersion-managed fiber-optic link,' Opt. Commun. 219, 143-156 (2003).
[CrossRef]

Forysiak, W.

Frantzeskakis, D. J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
[CrossRef]

Gabitov, I.

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

Georges, T.

Gloag, A. J.

Golovchenko, E. A.

Gordon, J. P.

Govan, D. S.

Grigoryan, V. S.

Haga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Hizanidis, K.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
[CrossRef]

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, 'Soliton propagation in long fibres with periodically compensated loss,' IEEE J. Quantum Electron. QE-22, 157-173 (1986).
[CrossRef]

Jacob, J. M.

Kaup, D. J.

Kaup, D. K.

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, 'Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,' Electron. Lett. 33, 1726-1727 (1997).
[CrossRef]

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

Kodama, Y.

Kurtze, C.

C. Kurtze, 'Suppression of fiber nonlinearities by appropriate dispersion management,' IEEE Photon. Technol. Lett. 5, 1250-1253 (1993).
[CrossRef]

Kutz, J. N.

Lai, Y.

Lakoba, T. I.

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Malomed, B. A.

B. Feng and B. A. Malomed, 'Bound states of solitons between close wavelength-separated channels in a dispersion-managed fiber-optic link,' Opt. Commun. 219, 143-156 (2003).
[CrossRef]

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

J. Atai and B. A. Malomed, 'Stabilized scheme for dispersion management,' J. Opt. Soc. Am. B 17, 1134-1139 (2000).
[CrossRef]

E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
[CrossRef]

A. Bernston and B. A. Malomed, 'Dispersion management with filtering,' Opt. Lett. 24, 507-509 (1999).
[CrossRef]

J. Atai and B. A. Malomed, 'Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations,' Phys. Lett. A 246, 412-422 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Bound states of solitary pulses in linearly couples Ginzburg-Landau equations,' Phys. Lett. A 244, 551-556 (1998).
[CrossRef]

B. A. Malomed, 'Suppression of soliton jitter and interactions by means of dispersion management,' Opt. Commun. 147, 157-162 (1998).
[CrossRef]

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, 'Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,' Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Stability and interactions of solitons in two-component active systems,' Phys. Rev. E 54, 4371-4374 (1996).
[CrossRef]

B. A. Malomed and H. G. Winful, 'Stable solitons in two-component active systems,' Phys. Rev. E 53, 5365-5368 (1996).
[CrossRef]

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Mamyshev, P. V.

Matsumoto, M.

Mecozzi, A.

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, 'Effect of guiding filters on the behavior of dispersion-managed solitons,' Opt. Lett. 24, 220-222 (1999).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, 'Soliton propagation in long fibres with periodically compensated loss,' IEEE J. Quantum Electron. QE-22, 157-173 (1986).
[CrossRef]

Moores, J. D.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Niculae, A. N.

Nijhof, J. H. B.

Nistazakis, H. E.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

E. Efremidis, K. Hizanidis, B. A. Malomed, H. E. Nistazakis, and D. J. Frantzeskakis, 'Stable transmission of solitons in the region of normal dispersion,' J. Opt. Soc. Am. B 17, 952-958 (2000).
[CrossRef]

Pilipetskii, A. N.

Shapiro, E. G.

S. K. Turitsyn and E. G. Shapiro, 'Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,' Opt. Lett. 23, 682-684 (1998).
[CrossRef]

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

Smith, N. J.

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

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn and E. G. Shapiro, 'Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,' Opt. Lett. 23, 682-684 (1998).
[CrossRef]

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

Wabnitz, S.

Westin, E.

Winful, H. G.

B. A. Malomed and H. G. Winful, 'Stable solitons in two-component active systems,' Phys. Rev. E 53, 5365-5368 (1996).
[CrossRef]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

Yang, J.

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, 'Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,' Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

Yu, T.

Zen, F.

N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
[CrossRef]

Electron. Lett. (4)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Haga, and S. Akiba, 'Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,' Electron. Lett. 31, 2027-2029 (1995).
[CrossRef]

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

M. Matsumoto, 'Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,' Electron. Lett. 33, 1718-1720 (1997).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, 'Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,' Electron. Lett. 33, 1726-1727 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, 'Soliton propagation in long fibres with periodically compensated loss,' IEEE J. Quantum Electron. QE-22, 157-173 (1986).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Y. Chen and J. Atai, 'Average dark soliton dynamics in periodically dispersion compensated fibre transmission systems,' IEEE Photon. Technol. Lett. 10, 1280-1282 (1998).
[CrossRef]

C. Kurtze, 'Suppression of fiber nonlinearities by appropriate dispersion management,' IEEE Photon. Technol. Lett. 5, 1250-1253 (1993).
[CrossRef]

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

Opt. Commun. (5)

T. I. Lakoba, J. Yang, D. K. Kaup, and B. A. Malomed, 'Conditions for stationary pulse propagation in the strong dispersion management regime,' Opt. Commun. 149, 366-375 (1998).
[CrossRef]

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

B. A. Malomed, 'Suppression of soliton jitter and interactions by means of dispersion management,' Opt. Commun. 147, 157-162 (1998).
[CrossRef]

N. Akhmediev, F. Zen, and P. L. Chu, 'Pulse-pulse interaction in dispersion managed fiber systems with nonlinear amplifiers,' Opt. Commun. 201, 217-221 (2002).
[CrossRef]

B. Feng and B. A. Malomed, 'Bound states of solitons between close wavelength-separated channels in a dispersion-managed fiber-optic link,' Opt. Commun. 219, 143-156 (2003).
[CrossRef]

Opt. Lett. (16)

S. Wabnitz and E. Westin, 'Optical fiber soliton bound states and interaction suppression with high-order filtering,' Opt. Lett. 21, 1235-1237 (1996).
[CrossRef] [PubMed]

H. A. Haus, Y. Lai, A. Mecozzi, and J. D. Moores, 'Soliton transmission control,' Opt. Lett. 16, 1841-1843 (1991).
[CrossRef] [PubMed]

Y. Kodama and A. Hasegawa, 'Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect,' Opt. Lett. 17, 31-33 (1992).
[CrossRef] [PubMed]

M. Matsumoto, 'Instability of dispersion managed solitons in a system with filtering,' Opt. Lett. 23, 1901-1903 (1998).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, and J. P. Gordon, 'Effect of guiding filters on the behavior of dispersion-managed solitons,' Opt. Lett. 24, 220-222 (1999).
[CrossRef]

A. Bernston and B. A. Malomed, 'Dispersion management with filtering,' Opt. Lett. 24, 507-509 (1999).
[CrossRef]

G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, 'Timing-jitter reduction for a dispersion-managed soliton system: experimental evidence,' Opt. Lett. 22, 513-515 (1997).
[CrossRef] [PubMed]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, 'Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,' Opt. Lett. 23, 900-902 (1998).
[CrossRef]

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]

J. P. Gordon and H. A. Haus, 'Random walk of coherently amplified solitons in optical fiber transmission,' Opt. Lett. 11, 665-667 (1986).
[CrossRef] [PubMed]

S. K. Turitsyn and E. G. Shapiro, 'Dispersion-managed soliton in optical amplifier transmission systems with zero average dispersion,' Opt. Lett. 23, 682-684 (1998).
[CrossRef]

J. N. Kutz and S. G. Evangelides, Jr., 'Dispersion managed breathers with average normal dispersion,' Opt. Lett. 23, 685-687 (1998).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, 'Dispersion-managed solitons at normal average dispersion,' Opt. Lett. 23, 609-611 (1998).
[CrossRef]

D. S. Govan, W. Forysiak, and N. J. Doran, 'Long-distance 40-Gbit/s soliton transmission over standard fibre by use of dispersion management,' Opt. Lett. 23, 1523-1525 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, 'Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,' Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

A. N. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, 'Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,' Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

Phys. Lett. A (2)

J. Atai and B. A. Malomed, 'Bound states of solitary pulses in linearly couples Ginzburg-Landau equations,' Phys. Lett. A 244, 551-556 (1998).
[CrossRef]

J. Atai and B. A. Malomed, 'Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations,' Phys. Lett. A 246, 412-422 (1998).
[CrossRef]

Phys. Rev. E (3)

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, E. Efremidis, and K. Hizanidis, 'Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,' Phys. Rev. E 65, 036605 (2002).
[CrossRef]

B. A. Malomed and H. G. Winful, 'Stable solitons in two-component active systems,' Phys. Rev. E 53, 5365-5368 (1996).
[CrossRef]

J. Atai and B. A. Malomed, 'Stability and interactions of solitons in two-component active systems,' Phys. Rev. E 54, 4371-4374 (1996).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fibre Optics (Academic, 1995).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Region of stable transmission of DM solitons in the model of Eqs. (1, 2) with D ¯ = 0 , L = L + L , γ 1 = 0.3 , and Γ = 1.35 .

Fig. 2
Fig. 2

Interaction of solitons corresponding to D ¯ = 0 , L = 1.5 , γ 0 = 0.68 , γ 1 = 0.3 , Γ = 1.35 , and Δ ϕ = π . In (a) since Δ τ = 6 < Δ τ cr , the solitons initially repel each other until they reach a separation of Δ τ cr = 6.86 and in (b) they attract since Δ τ = 8 > Δ τ cr .

Fig. 3
Fig. 3

Separation of the pulses versus propagation distance for different initial separations. The parameters are D ¯ = 0.05 , L = 1.0 , γ 0 = 0.68 , γ 1 = 0.3 , Γ = 1.35 . (a) Δ ϕ = 0 ; (b) Δ ϕ = π . It is interesting to note that in (b) the pulses with an initial separation of 8 eventually evolve to Δ τ cr = 6.3 .

Fig. 4
Fig. 4

Separation of the pulses versus propagation distance for different initial separations and Δ ϕ = π . The parameters are D ¯ = + 0.05 , L = 1.0 , γ 0 = 0.68 , γ 1 = 0.3 , and Γ = 1.35 .

Fig. 5
Fig. 5

Dependence of z coll on the average dispersion for (a) Δ ϕ = π , L = 2.5 , γ 0 = 0.725 , γ 1 = 0.3 , and Γ = 1.35 ; (b) Δ ϕ = 0 , L = 0.8 , γ 0 = 0.65 , γ 1 = 0.3 , and Γ = 1.35 .

Fig. 6
Fig. 6

(a) Example of periodic attraction and repulsion of solitons for Δ τ = 7 , Δ ϕ = 0 , D ¯ = + 0.1 , L = 2.5 , γ 0 = 0.69 , γ 1 = 0.3 , and Γ = 1.35 ; (b) separation of the pulses versus the propagation distance. (c) shows the region in the plane ( γ 0 , L ) where such periodic behavior has been observed. Other parameters in (c) are Δ τ = 7 , Δ ϕ = 0 , D ¯ = + 0.1 , γ 1 = 0.3 , and Γ = 1.35 .

Equations (15)

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

i u z + ( 1 2 D ( z ) i γ 1 ) u τ τ + u 2 u i γ 0 u + κ v = 0 ,
i v z + i Γ v + κ u = 0 ,
D ( z ) = { D + > 0 , 0 < z < L + , D < 0 , L + < z < L + + L , }
D ¯ ( D + L + + D L ) 2 L .
L D + = L D 1 ,
L D + 1 .
u ( τ , 0 ) = ψ ( τ Δ τ 2 , 0 ) + ψ ( τ + Δ τ 2 , 0 ) exp ( i Δ ϕ ) ,
v ( τ , 0 ) = ξ ( τ Δ τ 2 , 0 ) + ξ ( τ + Δ τ 2 , 0 ) exp ( i Δ ϕ ) ,
ψ ( τ , z ) = A [ sech ( χ τ ) ] 1 + i μ e i k z ,
ξ ( τ , z ) = B [ sech ( χ τ ) ] 1 + i μ e i k z ,
A 2 = 1 2 [ ( 2 μ 2 ) + ( 3 μ 2 γ 1 ) ] χ 2 ,
B = A k i Γ ,
μ = ( 9 + 8 ( 2 γ 1 ) 2 ) 3 4 γ 1 ,
χ 2 = 8 γ 0 γ 1 8 γ 1 2 + 3 9 + 32 γ 1 2 ( 1 Γ γ 0 [ k 2 + Γ 2 ] ) ,
k ( k 2 + Γ 2 ) k = 9 + 32 γ 1 2 2 γ 1 [ γ 0 k 2 Γ ( 1 Γ γ 0 ) ] .

Metrics