Abstract

We develop a perturbation theory to calculate analytically the effects of interchannel collisions on Gaussian pulses in a wavelength-division-multiplexed (WDM) system with moderate and strong dispersion management (DM). The losses are assumed to be balanced by the amplification and are not explicitly included into the model. We show that, for complete collisions, the collision-induced frequency shift of a Gaussian pulse is negligible, whereas for incomplete collisions (those with initially overlapped pulses) this shift is significant. We also show that, as the DM strength increases, the collision-induced position shift becomes more important than the frequency shift produced by the incomplete collision. Another result is that the collisional shifts depend on the DM strength and the path-average dispersion but not on the lengths of the two fiber segments in the DM cell. We check the fully analytical predictions against direct PDE simulations and find satisfactory agreement between them. We also give an estimate of the limit imposed on the transmission distance in the WDM soliton systems by the interchannel collisions.

© 1999 Optical Society of America

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  1. F. M. Knox, W. Forysiak, and N. J. Doran, “10-Gbit/s soliton communication-systems over standard fiber at 1.55-μm and the use of dispersion compensation,” J. Lightwave Technol. 13, 1955–1962 (1995); M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995); N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett. OPLEDP 21, 570–573 (1996); M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. ELLEAK 31, 216–217 (1995); R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear wave guide,” Phys. Scr. PHSTBO 53, 385–393 (1996); 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. ELLEAK 32, 54–55 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “20-GB/s single-channel soliton transmission over 9000 km without in-line filters,” IEEE Photonics Technol. Lett. IPTLEL 8, 1573–1574 (1996); I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. OPLEDP 21, 327–330 (1996).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
    [CrossRef]
  3. N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, “4×SONET OC-192 field installed dispersion managed soliton system over 450km of standard fiber in the 1550nm erbium band,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD19.
  4. S. Wabnitz, “Stabilization of sliding-filtered soliton wavelength-division multiplexing transmissions by dispersion-compensating fibers,” Opt. Lett. 21, 638–641 (1996); S. Kumar, Y. Kodama, and A. Hasegawa, “Optimal dispersion management schemes for WDM soliton systems,” Electron. Lett. 33, 459–461 (1997); H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision-induced frequency-shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. ELLEAK 33, 1065–1066 (1997); J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, “Soliton collisions in dispersion-managed wavelength-division-multiplexed systems,” Opt. Lett. OPLEDP 22, 1695–1698 (1997).
    [CrossRef] [PubMed]
  5. A. M. 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]
  6. Y. Kodama and A. Hasegawa, “Guiding-center soliton in fibers with periodically varying dispersion,” Opt. Lett. 16, 208–210 (1991).
    [CrossRef] [PubMed]
  7. S. K. Turitsyn, “Breathing self-similar dynamics and oscillatory tails of the chirped dispersion-managed soliton,” Phys. Rev. E 58, R1256–R1259 (1998).
    [CrossRef]
  8. M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1671 (1998).
    [CrossRef]
  9. 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, 900–903 (1998).
    [CrossRef]
  10. B. A. Malomed, “Pulse-propagation in a nonlinear-optical fiber with periodically modulated dispersion—variational approach,” Opt. Commun. 136, 313–319 (1997); M. Matsumoto, “Theory of stretched-pulse transmission dispersion-managed fibers,” Opt. Lett. 22, 1238–1241 (1997); J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, “Hamiltonian dynamics of dispersion-managed breathers,” J. Opt. Soc. Am. B JOBPDE 15, 87–96 (1998); S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical propagation in dispersion compensated transmission systems,” Opt. Commun. OPCOB8 151, 117–135 (1998).
    [CrossRef] [PubMed]
  11. 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]
  12. D. K. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1603 (1998).
    [CrossRef]
  13. T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768–771 (1998).
    [CrossRef]
  14. H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
    [CrossRef]
  15. M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
    [CrossRef]
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995); A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).
  17. D. S. Govan, W. Forysiak, and N. J. Doran, “Long-distance 40-Gbit/s soliton transmission over standard fiber by use of dispersion management,” Opt. Lett. 23, 1523–1525 (1998).
    [CrossRef]
  18. M. Wald, B. A. Malomed, and F. Lederer, “Interaction of moderately dispersion-managed solitons,” submitted to Opt. Lett.
  19. 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]
  20. S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998); J. N. Kutz and S. G. Evangelides, “Dispersion-managed breathers with average normal dispersion,” Opt. Lett. 23, 685–687 (1998).
    [CrossRef]
  21. H. Haus and Y. Chen, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. (to be published).
  22. B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
    [CrossRef]
  23. N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion managed systems,” Electron. Lett. 32, 2085–2086 (1996).
    [CrossRef]
  24. B. A. Malomed, “Jitter suppression by fixed-frequency filters in combination with dispersion management,” Opt. Lett. 23, 1250–1252 (1998).
    [CrossRef]
  25. S. S. Orlov, A. Yariv, and S. Van Essen, “Coupled-mode analysis of fiber-optic add–drop filters for dense wavelength-division multiplexing,” Opt. Lett. 22, 688–691 (1997); X. J. Gu, “Wavelength-division multiplexing isolation fiber filter and light source using cascaded long-period fiber gratings,” Opt. Lett. 23, 509–511 (1998).
    [CrossRef] [PubMed]
  26. B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division-multiplexing system with channel-isolating notch filters,” Opt. Lett. (to be published).
  27. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
    [CrossRef]

1998 (11)

S. K. Turitsyn, “Breathing self-similar dynamics and oscillatory tails of the chirped dispersion-managed soliton,” Phys. Rev. E 58, R1256–R1259 (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]

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
[CrossRef]

T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768–771 (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, 900–903 (1998).
[CrossRef]

B. A. Malomed, “Jitter suppression by fixed-frequency filters in combination with dispersion management,” Opt. Lett. 23, 1250–1252 (1998).
[CrossRef]

A. M. 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]

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

D. K. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1603 (1998).
[CrossRef]

M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1671 (1998).
[CrossRef]

1997 (3)

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (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]

B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

1996 (1)

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

1991 (2)

Y. Kodama and A. Hasegawa, “Guiding-center soliton in fibers with periodically varying dispersion,” Opt. Lett. 16, 208–210 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
[CrossRef]

M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1671 (1998).
[CrossRef]

Berntson, A.

Biondini, G.

M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1671 (1998).
[CrossRef]

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
[CrossRef]

Cjakravarty, S.

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
[CrossRef]

Doran, N. J.

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

Forysiak, W.

Gloag, A. J.

Golovchenko, E. A.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

Govan, D. S.

Hasegawa, A.

Hirooka, T.

Horne, R. L.

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (1998).
[CrossRef]

Inoue, T.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

Kaup, D. K.

D. K. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1603 (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]

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]

Kodama, Y.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

Y. Kodama and A. Hasegawa, “Guiding-center soliton in fibers with periodically varying dispersion,” Opt. Lett. 16, 208–210 (1991).
[CrossRef] [PubMed]

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.

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. K. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1603 (1998).
[CrossRef]

B. A. Malomed, “Jitter suppression by fixed-frequency filters in combination with dispersion management,” Opt. Lett. 23, 1250–1252 (1998).
[CrossRef]

B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

Maruta, A.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

Matera, F.

B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

Menyuk, C. R.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

Niculae, A. M.

Nijhof, J. H. B.

Pilipetskii, A. N.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (1997).
[CrossRef]

Settembre, M.

B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

Smith, N. J.

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

Sugahara, H.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, “Breathing self-similar dynamics and oscillatory tails of the chirped dispersion-managed soliton,” Phys. Rev. E 58, R1256–R1259 (1998).
[CrossRef]

Yang, J.

D. K. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600–1603 (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]

Electron. Lett. (4)

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, “Optical dispersion management for wavelength-division-multiplexed RZ optical pulse transmission,” Electron. Lett. 34, 902–904 (1998).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735–737 (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]

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

Opt. Commun. (3)

M. J. Ablowitz, G. Biondini, S. Cjakravarty, and R. L. Horne, “On timing jitter in wavelength-division multiplexed soliton systems,” Opt. Commun. 150, 305–318 (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]

B. A. Malomed, F. Matera, and M. Settembre, “Reduction of the jitter for return-to-zero signals,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. E (1)

S. K. Turitsyn, “Breathing self-similar dynamics and oscillatory tails of the chirped dispersion-managed soliton,” Phys. Rev. E 58, R1256–R1259 (1998).
[CrossRef]

Other (10)

F. M. Knox, W. Forysiak, and N. J. Doran, “10-Gbit/s soliton communication-systems over standard fiber at 1.55-μm and the use of dispersion compensation,” J. Lightwave Technol. 13, 1955–1962 (1995); M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon–Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31, 2027–2029 (1995); N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett. OPLEDP 21, 570–573 (1996); M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. ELLEAK 31, 216–217 (1995); R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear wave guide,” Phys. Scr. PHSTBO 53, 385–393 (1996); 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. ELLEAK 32, 54–55 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “20-GB/s single-channel soliton transmission over 9000 km without in-line filters,” IEEE Photonics Technol. Lett. IPTLEL 8, 1573–1574 (1996); I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. OPLEDP 21, 327–330 (1996).
[CrossRef] [PubMed]

N. Robinson, G. Davis, J. Fee, G. Grasso, P. Franco, A. Zuccala, A. Cavaciuti, M. Macchi, A. Schiffini, L. Bonato, and R. Corsini, “4×SONET OC-192 field installed dispersion managed soliton system over 450km of standard fiber in the 1550nm erbium band,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper PD19.

S. Wabnitz, “Stabilization of sliding-filtered soliton wavelength-division multiplexing transmissions by dispersion-compensating fibers,” Opt. Lett. 21, 638–641 (1996); S. Kumar, Y. Kodama, and A. Hasegawa, “Optimal dispersion management schemes for WDM soliton systems,” Electron. Lett. 33, 459–461 (1997); H. Sugahara, H. Kato, and Y. Kodama, “Maximum reductions of collision-induced frequency-shift in soliton-WDM systems with dispersion compensation,” Electron. Lett. ELLEAK 33, 1065–1066 (1997); J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, “Soliton collisions in dispersion-managed wavelength-division-multiplexed systems,” Opt. Lett. OPLEDP 22, 1695–1698 (1997).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995); A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

M. Wald, B. A. Malomed, and F. Lederer, “Interaction of moderately dispersion-managed solitons,” submitted to Opt. Lett.

S. S. Orlov, A. Yariv, and S. Van Essen, “Coupled-mode analysis of fiber-optic add–drop filters for dense wavelength-division multiplexing,” Opt. Lett. 22, 688–691 (1997); X. J. Gu, “Wavelength-division multiplexing isolation fiber filter and light source using cascaded long-period fiber gratings,” Opt. Lett. 23, 509–511 (1998).
[CrossRef] [PubMed]

B. A. Malomed, G. D. Peng, and P. L. Chu, “Soliton wavelength-division-multiplexing system with channel-isolating notch filters,” Opt. Lett. (to be published).

B. A. Malomed, “Pulse-propagation in a nonlinear-optical fiber with periodically modulated dispersion—variational approach,” Opt. Commun. 136, 313–319 (1997); M. Matsumoto, “Theory of stretched-pulse transmission dispersion-managed fibers,” Opt. Lett. 22, 1238–1241 (1997); J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, “Hamiltonian dynamics of dispersion-managed breathers,” J. Opt. Soc. Am. B JOBPDE 15, 87–96 (1998); S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical propagation in dispersion compensated transmission systems,” Opt. Commun. OPCOB8 151, 117–135 (1998).
[CrossRef] [PubMed]

S. K. Turitsyn and E. G. Shapiro, “Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion,” Opt. Lett. 23, 682–684 (1998); J. N. Kutz and S. G. Evangelides, “Dispersion-managed breathers with average normal dispersion,” Opt. Lett. 23, 685–687 (1998).
[CrossRef]

H. Haus and Y. Chen, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Complete collision of two Gaussian pulses for S=1. The other parameters are specified in the text. The normalizations are the same as in Ref. 11; in particular, τ0=1 corresponds, in the typical case, to the physical pulse’s width τ030 ps. The physical values of the position shift can be rescaled accordingly. (a) Value of |v| versus z at τ=0 (note that the collision takes place at z65). (b) Shapes of the |v| pulse at z=0 and z=150. Note that, after the collision, the v pulse is slightly shifted.

Fig. 2
Fig. 2

Comparison of analytically predicted and numerically found position shifts of the Gaussian pulse induced by the complete collisions. All the parameters but the dispersion management strength S are fixed (see values in text).

Fig. 3
Fig. 3

Incomplete collision of two Gaussian pulses for S=1. Initially the pulses fully overlap. The other parameters are specified in the text. (a) Value of |v| versus z at τ=0. It can be seen that the v pulse experiences a velocity (frequency) shift after the incomplete collision. (b) Shapes of the |v| pulse at z=0 and z=150. Note that, because of a nonzero frequency shift, the total position shift of the v pulse is much larger than in the case of the complete collision (see Fig. 1).

Fig. 4
Fig. 4

Comparison of analytically predicted and numerically obtained frequency shifts generated by the collision of two initially fully overlapped Gaussian pulses in adjacent channels. All the parameters but S are fixed (see values in text).

Equations (32)

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i(uz+cuτ)+½D(z)uττ+[½D¯uuττ
+γ(|u|2+2|v|2)u]=0,
ivz+½D(z)vττ+[½D¯vvττ+γ(|v|2+2|u|2)v]=0,
D(z)=D10<z<L1D2L1<zL1+L2,
u0(z, τ)=τ0Puτ02+2iΔ(z)1/2×exp-(τ-cz)2τ02+2iΔ(z)+iϕu,
u(z, τ)=u0[z,τ-T(z)]exp[-iωτ+iψ(z)],
dω/dz=-(1/2)ω2[D(z)+D¯u],
dT/dz=-ω[D(z)+D¯u].
Δ0=-(1/2)Sτ02,
22D¯u=-Puτ02S[ln(1+S2+S)
-2S(1+S2)-1/2],
S|D1,2|L1,2/τ02.
dωdz=23/2Pvτ04cz[τ04+4Δ2(z)]3/2exp-c2τ02z2[τ04+4Δ2(z)],
c2L-2(τ02+4τ0-2Δ2)
In=-+znF(z)exp[-z2f2(z)]dz,
In=m=-TmznF(z)exp[-z2f2(z)]dz,
InT-1-dZZn0TdzF(z)exp[-Z2f2(z)]dz.
-xne-x2dx=2-n/2πCn,
Cn=0ifnisodd1ifn=0(n-1)!!ifniseven,
In2-n/2πCnF(z)f-(n+1)(z),
δω=-+(dω/dz)dz=0;
δωPvτ03/D2L.
δTu-+dTdzdz=D¯u-+zdωdzdz+-+Δ(z)dωdzdz.
δTu=2π2D¯uPvτ0/c2.
δω=z0+(dω/dz)dz,
δω=2Pvτ02c-1×[τ04+4Δ2(z)]-1/2 exp-τ02(ΔT)2τ04+4Δ2(z),
(δω)max=2Pvτ02c-1[τ04+4Δ2(z)]-1/2.
(δω)max=2Pv(cS)-1 ln(S+1+S2),
δTu(ω)=-δωDu¯z.
δTu(ω)δTumax=1πcz1τ0Sln(S+1+S2),
δTu(ω)δTumax2Sln(S+1+S2).
|D1,2|L1,21,L1+L21.

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