Abstract

A model of a long optical communication line consisting of alternating segments with anomalous and normal dispersion, whose lengths are picked randomly from a certain interval, is considered. As the first stage of the analysis, we calculate small changes in parameters of a quasi-Gaussian pulse passing a double-segment cell by means of the variational approximation (VA) and we approximate the evolution of the pulse passing many cells by smoothed ordinary differential equations with random coefficients, which are solved numerically. Next we perform systematic direct simulations of the model. Simulations reveal slow long-scale dynamics of the pulse, frequently in the form of long-period oscillations of its width. It is thus found that the soliton is most stable in the case of zero path-average dispersion (PAD), less stable in the case of anomalous PAD, and least stable in the case of normal PAD. The soliton’s stability also strongly depends on its energy, the soliton with low energy being much more robust than its high energy counterpart.

© 2001 Optical Society of America

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    [CrossRef]
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    [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. I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
    [CrossRef]
  5. T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
    [CrossRef]
  6. 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 evidenced,” Opt. Lett. 22, 513–515 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. A. Berntson and B. A. Malomed, “Dispersion-management with filtering,” Opt. Lett. 24, 507–509 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  39. F. Kh. Abdullaev and J. C. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
    [CrossRef]
  40. A. Bernston, D. Anderson, M. Lisak, and B. A. Malomed, “Slow-dynamics of dispersion-managed solitons,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), pp. 286–288.

2000

1999

1998

S. Kumar, M. Wald, and F. Lederer, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019–1021 (1998).
[CrossRef]

F. Kh. Abdullaev and J. C. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
[CrossRef]

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

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (1998).
[CrossRef]

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).
[CrossRef]

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

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (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]

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

1997

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]

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]

B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: Variational approach,” Opt. Commun. 136, 313–319 (1997).
[CrossRef]

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]

M. Matsumoto, “Theory of stretched-pulse transmission dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
[CrossRef] [PubMed]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (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 evidenced,” Opt. Lett. 22, 513–515 (1997).
[CrossRef] [PubMed]

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

M. K. Chin and X. Y. Tang, “Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,” IEEE Photonics Technol. Lett. 9, 538–540 (1997).
[CrossRef]

V. S. Grigoryan and C. R. Menyuck, “Dispersion-managed solitons at normal path-average dispersion,” Opt. Lett. 23, 609–611 (1997).
[CrossRef]

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

1996

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
[CrossRef]

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[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]

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

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).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

1993

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev and B. B. Baizakov, “Disintegration of a soliton in a dispersion-managed optical communication line with random parameters,” Opt. Lett. 25, 93–95 (2000).
[CrossRef]

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, “Soliton perturbations and the random Kepler problem,” Physica D 135, 369–386 (1999).
[CrossRef]

F. Kh. Abdullaev and J. C. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
[CrossRef]

Aceves, A. B.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

Agrawal, G. P.

Akiba, S.

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).
[CrossRef]

Anderson, D.

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Baizakov, B. B.

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]

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]

Bronski, J.

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, “Soliton perturbations and the random Kepler problem,” Physica D 135, 369–386 (1999).
[CrossRef]

Caputo, J. C.

F. Kh. Abdullaev and J. C. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
[CrossRef]

Carter, G. M.

Chin, M. K.

M. K. Chin and X. Y. Tang, “Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,” IEEE Photonics Technol. Lett. 9, 538–540 (1997).
[CrossRef]

Doran, N. J.

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]

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]

Edagawa, N.

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).
[CrossRef]

Evangelides, S. G.

Forysiak, W.

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]

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]

Frantzeskakis, D.

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (1998).
[CrossRef]

Gabitov, I.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

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

Golovchenko, E. A.

Gordon, J. P.

Grigoryan, V. S.

Grimshaw, R.

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
[CrossRef]

Hasegawa, A.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

He, J.

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
[CrossRef]

Hizanidis, K.

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (1998).
[CrossRef]

Jacob, J. M.

Jones, C. K. R. T.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

Karlsson, M.

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Kath, W. L.

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.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

Kubota, H.

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

Kumar, S.

Kutz, J. N.

Laedke, E. W.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Lakoba, T. I.

T. I. Lakoba and G. P. Agrawal, “Effects of third-order dispersion on dispersion-managed solitons,” J. Opt. Soc. Am. B 16, 1332–1343 (1999).
[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]

Lederer, F.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

S. Kumar, M. Wald, and F. Lederer, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019–1021 (1998).
[CrossRef]

Lisak, M.

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Malomed, B.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

Malomed, B. A.

A. Berntson and B. A. Malomed, “Dispersion-management with filtering,” Opt. Lett. 24, 507–509 (1999).
[CrossRef]

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

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (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, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: Variational approach,” Opt. Commun. 136, 313–319 (1997).
[CrossRef]

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

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
[CrossRef]

Mamyshev, P. V.

Maruta, A.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

Matera, F.

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

Matsumoto, M.

Menyuck, C. R.

Menyuk, C. R.

Mezentsev, V. K.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Mollenauer, L. F.

Morita, I.

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).
[CrossRef]

Musher, S. L.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Nakazawa, M.

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. 31, 216–217 (1995).
[CrossRef]

Nijhof, J. H. B.

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]

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]

Nistazakis, H. E.

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (1998).
[CrossRef]

Okamawari, T.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

Papanicolaou, G. C.

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, “Soliton perturbations and the random Kepler problem,” Physica D 135, 369–386 (1999).
[CrossRef]

Parker, D. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
[CrossRef]

Pilipetskii, A. N.

Quiroga-Teixeiro, M. L.

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Schäfer, T.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Settembre, M.

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

Shapiro, E. G.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

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).
[CrossRef]

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]

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]

Smyth, N. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
[CrossRef]

Spatschek, K. H.

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Suzuki, M.

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).
[CrossRef]

Taga, H.

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).
[CrossRef]

Tang, X. Y.

M. K. Chin and X. Y. Tang, “Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,” IEEE Photonics Technol. Lett. 9, 538–540 (1997).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

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).
[CrossRef]

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

Ueda, Y.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

Wald, M.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

S. Kumar, M. Wald, and F. Lederer, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019–1021 (1998).
[CrossRef]

Yamamoto, S.

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).
[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]

Yang, T.-S.

Yu, T.

Zharnitsky, V.

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

Electron. Lett

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, “Interaction between guiding centre solitons in a periodically dispersion compensated optical transmission line,” Electron. Lett 33, 1063–1065 (1997).
[CrossRef]

Electron. Lett.

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).
[CrossRef]

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. 31, 216–217 (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]

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 Photonics Technol. Lett.

M. K. Chin and X. Y. Tang, “Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,” IEEE Photonics Technol. Lett. 9, 538–540 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31–36 (1999).
[CrossRef]

A. Berntson, D. Anderson, M. Lisak, M. L. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fibre transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

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]

B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: Variational approach,” Opt. Commun. 136, 313–319 (1997).
[CrossRef]

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 pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (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 signal,” Opt. Commun. 143, 193–198 (1997).
[CrossRef]

Opt. Lett.

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

M. Matsumoto, “Theory of stretched-pulse transmission dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
[CrossRef] [PubMed]

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 evidenced,” Opt. Lett. 22, 513–515 (1997).
[CrossRef] [PubMed]

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

F. Kh. Abdullaev and B. B. Baizakov, “Disintegration of a soliton in a dispersion-managed optical communication line with random parameters,” Opt. Lett. 25, 93–95 (2000).
[CrossRef]

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

A. Berntson and B. A. Malomed, “Dispersion-management with filtering,” Opt. Lett. 24, 507–509 (1999).
[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]

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

S. Kumar, M. Wald, and F. Lederer, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019–1021 (1998).
[CrossRef]

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).
[CrossRef]

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

V. S. Grigoryan and C. R. Menyuck, “Dispersion-managed solitons at normal path-average dispersion,” Opt. Lett. 23, 609–611 (1997).
[CrossRef]

Phys. Rev. E

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).
[CrossRef]

S. K. Turitsyn, A. B. Aceves, C. K. R. T. Jones, and V. Zharnitsky, “Average dynamics of the optical soliton in communication lines with dispersion management: analytical results,” Phys. Rev. E 58, R48–R51 (1998).
[CrossRef]

F. Kh. Abdullaev and J. C. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).
[CrossRef]

Phys. Scr.

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).
[CrossRef]

Physica D

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, “Soliton perturbations and the random Kepler problem,” Physica D 135, 369–386 (1999).
[CrossRef]

Pure Appl. Opt.

D. Frantzeskakis, K. Hizanidis, B. A. Malomed, and H. E. Nistazakis, “Stabilizing soliton transmission by the third-order dispersion in long links with dispersion management,” Pure Appl. Opt. 7, L57–L62 (1998).
[CrossRef]

Other

V. V. Konotop and L. Vázquez, Nonlinear Random Waves (World Scientific, Singapore, 1994).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1995).

G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory (Springer, New York, 1990).

B. A. Malomed and A. Berntson, “Propagation of a pulse in a fiber link with random dispersion management,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999) pp. 289–291.

A. Hasegawa, ed., New Trends in Optical Soliton Transmission Systems (Kluwer Academic, Dordrecht, 1998).

A. Bernston, D. Anderson, M. Lisak, and B. A. Malomed, “Slow-dynamics of dispersion-managed solitons,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), pp. 286–288.

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Figures (9)

Fig. 1
Fig. 1

Normalized power versus map strength for stationary solitons in periodic-DM system: (top) analytical result, Eq. (12), produced by variational approximation; (bottom) direct numerical solution of NLS equation (1). Each curve or line corresponds to a constant value of PAD: from left to right, β0=-0.2, -0.02, 0, and 0.02. Asterisks mark particular cases for which response to random-length variations are further displayed in Figs. 29.

Fig. 2
Fig. 2

Cell-average pulse width (top) and minimum-width parameter τ0 (bottom) versus propagation distance, generated by numerical integration of variational equations (14) and (15) for power P=0.16 and β0=-0.2 (anomalous PAD). Mean values (solid curve) and standard deviations from them (dashed curves) are produced by averaging over 200 different realizations of the random-length set.

Fig. 3
Fig. 3

Same as in Fig. 2, but for higher power, P=0.44.

Fig. 4
Fig. 4

Evolution of cell-average pulse width for zero PAD propagating over 1000 DM cells, in the cases of high power P=0.44 (top) and low power P=0.012 (bottom). Mean values (solid curve) and standard deviations from them (dashed curves) are produced by averaging over 200 different realizations of the random length set.

Fig. 5
Fig. 5

Same as Fig. 2, but with normal PAD, β0=0.02 and P=0.27.

Fig. 6
Fig. 6

Pulse width vs. propagation distance for anomalous PAD, β0=-0.2, and low power, P=0.16, generated by direct simulations of Eq. (1). Shown are both mean values (solid curve) and standard deviations from them (dashed curves) as produced by averaging over 200 different realizations of the random length set, and gray curves corresponding to particular realizations of the random set. Inset, effective PAD corrected with regard to optimal dispersion compensation at the receiving edge (average of 200 simulations).

Fig. 7
Fig. 7

Same as in Fig. 6, but for high power, P=0.44.

Fig. 8
Fig. 8

Results of direct simulations of the NLS equation (1) with anomalous PAD, β0=-0.02. Plot shows the pulse dynamics in the dynamical plane whose coordinates are the chirp at the center of the pulse and its width, evaluated at the midpoint of each anomalous-fiber section. Inset, same quantities but in the absence of the nonlinear term in Eq. (1).

Fig. 9
Fig. 9

Same as in Fig. 6 for the case of zero PAD and P=0.16.

Equations (20)

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

iuz-12β(z)uττ+|u|2u=0,
β1(z)
=β-zn<z<zn+Ln(-)β+zn+Ln(-)<z<zn+Ln(-)+Ln(+)zn+1.
E2/π-+|u(τ)|2dτ.
L(-)+L(+)1,β-|L(-)=β+L(+)1.
0.1<L<0.9.
u0=τ0P0[τ02+2iΔ(z)]1/2 exp-τ2τ02+2iΔ(z)+iϕ.
S=1.443/τ02.
u0=a(z)exp[-τ02/W2(z)+ib(z)τ2+iϕ].
a2(z)=τ02p[τ02+2iΔ(z)]-1,
W(z)=τ0-1[τ04+4Δ2(z)]1/2,
b(z)=2Δ[τ04+4Δ2(z)]-1.
dτ0dz=2Eτ0Δ(z)W3(z),dΔ0dz=-β0+E[4Δ2(z)-τ04]22W3(z).
δτ0= dτ0dz dz,δΔ0= dΔ0dz dz,
Δ0=-12,
β0E=24τ03{ln[(1+τ0-4)1/2+τ0-2]-2(τ04+1)-1/2}.
0β0/E(β0/E)max0.0127.
 dτ0dz=2Eτ048[L(-)+L(+)] 1(τ04+4Δ02)1/2+1{τ04+4[Δ0+2L(-)-2L(+)]2}1/2-2{τ04+4[Δ0+2L(-)]2}1/2,
dΔ0dz=-β0+2Eτ038[L(-)+L(+)] 2Δ0(τ04+4Δ02)1/2+2[Δ0+2L(-)-2L(+)]{τ04+4[Δ0+2L(-)-2L(+)]2}1/2-4[Δ0+2L(-)]{τ04+4[Δ0+2L(-)]2}1/2-12 ln[2Δ0+(τ04+4Δ02)1/2]-12 ln(2[Δ0+2L(-)-2L(+)]+{τ04+4[Δ0+2L(-)-2L(+)]2}1/2)+ln(2[Δ0+2L(-)]+{τ04+4[Δ0+2L(-)]2}1/2).
W¯L-1W(z)dz,

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