Abstract

We demonstrate that a single extra cell composed of normal- and anomalous-dispersion fibers with specially selected lengths is sufficient to cast a standard input pulse (Gaussian, including a chirped one, or a raised-cosine pulse) into a properly shaped dispersion-managed (DM) soliton, which allows its subsequent stable transmission in an indefinitely long DM link. Together with the lengths of the fibers in the shaping cell, the optimization procedure developed in this work selects the peak power and temporal width of the input pulse. The considered systems may or may not include in-line filters, as well as higher-order effects, namely, the third-order dispersion and intrapulse stimulated Raman scattering. It is shown that, while the optimal preprocessing secures stable transmission of the pulses, their “raw” counterparts suffer serious degradation if directly launched into the same system. Robustness of the scheme against deviations of the shaper’s parameters from their optimal values is also investigated. The preprocessing stabilizes multisoliton strings too and helps solitons to withstand effects of optical noise. In addition, the preprocessed solitons, unlike the untreated ones, collide in a nearly elastic fashion.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. B. A. Malomed, "Jitter suppression by guiding filters in combination with dispersion management," Opt. Lett. 23, 1250-1252 (1998).
    [CrossRef]
  9. A. M. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, andN. J. Doran, "Soliton collisions with wavelength-division multiplexed systems with strong dispersion management," Opt. Lett. 23, 1354-1356 (1998).
    [CrossRef]
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  28. M. Matsumoto, "Instability of dispersion-managed solitons in a system with filtering," Opt. Lett. 23, 1901-1903 (1998).
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  29. G. M. Carter and J. M. Jacob, "Dynamics of solitons in filtered dispersion managed system," IEEE Photonics Technol. Lett. 10, 546-548 (1998).
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  30. A. Berntson and B. A. Malomed, "Dispersion-management with filtering," Opt. Lett. 24, 507-509 (1999).
    [CrossRef]
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    [CrossRef]
  32. M. Matsumoto, "Time-domain transmission control of dispersion-managed solitons," Electron. Lett. 34, 2155-2157 (1998).
    [CrossRef]
  33. W. Forysiak W. and N. J. Doran, "Conjugate solitons in amplified optical fibre transmission systems," Electron. Lett. 30, 154-155 (1994).
    [CrossRef]
  34. S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
    [CrossRef]
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    [CrossRef]
  36. D. Anderson, M. Lisak, B. Malomed, and M. Quiroga-Teixeiro, "Tunnelling of an optical soliton through a fiber junction," J. Opt. Soc. Am. B 11, 2380-2384 (1994).
    [CrossRef]
  37. K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
    [CrossRef]
  38. V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (1998).
    [CrossRef]
  39. 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]
  40. 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]
  41. T. Georges, "Soliton interaction in dispersion-managed links," J. Opt. Soc. Am. B 15, 1553-1560 (1998).
    [CrossRef]
  42. S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, "Soliton interaction in strongly dispersion-managed optical fibers," Opt. Lett. 23, 1019-1021 (1998).
    [CrossRef]
  43. M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photonics Technol. Lett. 10, 373-375 (1998).
    [CrossRef]
  44. P. V. Mamyshev and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing," Opt. Lett. 24, 1454-1456 (1999).
    [CrossRef]
  45. M. Wald, B. Malomed, and F. Lederer, "Interaction of moderately dispersion managed solitons," Opt. Commun. 172, 31-36 (1999).
    [CrossRef]
  46. J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
    [CrossRef]

2005

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, "An iterative numerical method for dispersion-managed solitons," Opt. Commun. 245, 425-435 (2005).
[CrossRef]

2004

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[CrossRef]

2003

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

2002

2001

2000

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

J. Pina, B. Abueva, and C. G. Goedde, "Periodically conjugated solitons in dispersion-managed optical," Opt. Commun. 176, 397-407 (2000).
[CrossRef]

R. M. Mu, V. S. Grigoryan, and C. R. Menyuk, "Comparison of theory and experiment for dispersion-managed solitons in a recirculating fiber loop," IEEE J. Sel. Top. Quantum Electron. 6, 248-257 (2000).
[CrossRef]

T. Hirooka and S. Wabnitz, "Nonlinear gain control of dispersion-managed soliton amplitude and collisions," Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

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

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

1999

1998

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (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. Georges, "Soliton interaction in dispersion-managed links," J. Opt. Soc. Am. B 15, 1553-1560 (1998).
[CrossRef]

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

M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

M. Matsumoto, "Time-domain transmission control of dispersion-managed solitons," Electron. Lett. 34, 2155-2157 (1998).
[CrossRef]

S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
[CrossRef]

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

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, "Conditions for stationary pulse propagation in the strong dispersion management regime," Opt. Commun. 149, 366-375 (1998).
[CrossRef]

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

G. M. Carter and J. M. Jacob, "Dynamics of solitons in filtered dispersion managed system," IEEE Photonics Technol. Lett. 10, 546-548 (1998).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, "Analysis of Gordon-Haus jitter in a dispersion-compensated optical transmission system," Opt. Lett. 23, 694-696 (1998).
[CrossRef]

B. A. Malomed, "Jitter suppression by guiding 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, andN. J. Doran, "Soliton collisions with wavelength-division multiplexed systems with strong dispersion management," Opt. Lett. 23, 1354-1356 (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]

S. K. Turitsyn, "Dispersion-managed solitons and optimization the dispersion management," Opt. Fiber Technol. 4, 384-452 (1998).
[CrossRef]

1997

1996

1995

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

K. Suzuki and M. Nakazawa, "Recent progress in optical soliton communication," Opt. Fiber Technol. 1, 289-308 (1995).
[CrossRef]

1994

W. Forysiak W. and N. J. Doran, "Conjugate solitons in amplified optical fibre transmission systems," Electron. Lett. 30, 154-155 (1994).
[CrossRef]

D. Anderson, M. Lisak, B. Malomed, and M. Quiroga-Teixeiro, "Tunnelling of an optical soliton through a fiber junction," J. Opt. Soc. Am. B 11, 2380-2384 (1994).
[CrossRef]

Aakjer, T.

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

Ablowitz, M. J.

Abueva, B.

J. Pina, B. Abueva, and C. G. Goedde, "Periodically conjugated solitons in dispersion-managed optical," Opt. Commun. 176, 397-407 (2000).
[CrossRef]

Afanasjev, V. V.

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (1998).
[CrossRef]

Agrawal, G. P.

Aharon, O.

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[CrossRef]

Anderson, D.

Andrekson, P. A.

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

Band, Y. B.

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[CrossRef]

Bélanger, P. A.

Berntson, A.

Bertilsson, K.

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

Biondini, G.

Biswas, A.

Carter, G. M.

G. M. Carter and J. M. Jacob, "Dynamics of solitons in filtered dispersion managed system," IEEE Photonics Technol. Lett. 10, 546-548 (1998).
[CrossRef]

Chakravarty, S.

Chen, P. Y. P.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, "An iterative numerical method for dispersion-managed solitons," Opt. Commun. 245, 425-435 (2005).
[CrossRef]

Chi, S.

S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
[CrossRef]

Chu, P. L.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, "An iterative numerical method for dispersion-managed solitons," Opt. Commun. 245, 425-435 (2005).
[CrossRef]

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (1998).
[CrossRef]

Docherty, A.

Doran, N. J.

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

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

W. Forysiak W. and N. J. Doran, "Conjugate solitons in amplified optical fibre transmission systems," Electron. Lett. 30, 154-155 (1994).
[CrossRef]

Dung, J. C.

S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
[CrossRef]

Fedoruk, M. P.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

Forysiak, W.

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

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

Forysiak W., W.

W. Forysiak W. and N. J. Doran, "Conjugate solitons in amplified optical fibre transmission systems," Electron. Lett. 30, 154-155 (1994).
[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. R.

Georges, T.

Gloag, A. J.

Goedde, C. G.

J. Pina, B. Abueva, and C. G. Goedde, "Periodically conjugated solitons in dispersion-managed optical," Opt. Commun. 176, 397-407 (2000).
[CrossRef]

Golovchenko, E. A.

Grigoryan, V. S.

R. M. Mu, V. S. Grigoryan, and C. R. Menyuk, "Comparison of theory and experiment for dispersion-managed solitons in a recirculating fiber loop," IEEE J. Sel. Top. Quantum Electron. 6, 248-257 (2000).
[CrossRef]

V. S. Grigoryan, T. Yu., E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, "Dispersion-managed soliton dynamics," Opt. Lett. 22, 1609-1611 (1997).
[CrossRef]

Hasegawa, A.

Hedekvist, P.-O.

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

Hirooka, T.

M. J. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, "Collision-induced timing shifts in dispersion-managed soliton systems," Opt. Lett. 27, 318-320 (2002).
[CrossRef]

T. Hirooka and S. Wabnitz, "Nonlinear gain control of dispersion-managed soliton amplitude and collisions," Opt. Fiber Technol. 6, 109-121 (2000).
[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]

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley,1998).

Islam, M. K.

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (1998).
[CrossRef]

Jacob, J. M.

G. M. Carter and J. M. Jacob, "Dynamics of solitons in filtered dispersion managed system," IEEE Photonics Technol. Lett. 10, 546-548 (1998).
[CrossRef]

Kaup, D. J.

T. Lakoba, J. Yang, D. J. 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]

Kodama, Y.

Kubota, H.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

Kumar, S.

Laedke, E. W.

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Lakoba, T.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, "Conditions for stationary pulse propagation in the strong dispersion management regime," Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Lakoba, T. I.

Lederer, F.

Lin, S. C.

S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
[CrossRef]

Lisak, M.

Mahlab, U.

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[CrossRef]

Malomed, B.

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

D. Anderson, M. Lisak, B. Malomed, and M. Quiroga-Teixeiro, "Tunnelling of an optical soliton through a fiber junction," J. Opt. Soc. Am. B 11, 2380-2384 (1994).
[CrossRef]

Malomed, B. A.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, "An iterative numerical method for dispersion-managed solitons," Opt. Commun. 245, 425-435 (2005).
[CrossRef]

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[CrossRef]

M. Wald, B. A. Malomed, and F. Lederer, "Interaction of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines," Opt. Lett. 26, 965-967 (2001).
[CrossRef]

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

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (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]

B. A. Malomed, "Jitter suppression by guiding filters in combination with dispersion management," Opt. Lett. 23, 1250-1252 (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]

T. Lakoba, J. Yang, D. J. 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, Soliton Management in Periodic Systems (Springer, 2006).

Mamyshev, P. V.

Mamysheva, N. A.

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E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley,1998).

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M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

M. Matsumoto, "Time-domain transmission control of dispersion-managed solitons," Electron. Lett. 34, 2155-2157 (1998).
[CrossRef]

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

McEntee, J.

J. McEntee, "Solitons go the distance for Marconi," Fibre Syst. Eur., pp. 19-23 (2003).

McKinstrie, C. J.

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley,1998).

Medvedev, S. B.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

Menyuk, C. R.

Mezentsev, V. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

Mu, R. M.

R. M. Mu and C. R. Menyuk, "Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems," J. Lightwave Technol. 20, 608-617 (2002).
[CrossRef]

R. M. Mu, V. S. Grigoryan, and C. R. Menyuk, "Comparison of theory and experiment for dispersion-managed solitons in a recirculating fiber loop," IEEE J. Sel. Top. Quantum Electron. 6, 248-257 (2000).
[CrossRef]

Nakazawa, M.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

K. Suzuki and M. Nakazawa, "Recent progress in optical soliton communication," Opt. Fiber Technol. 1, 289-308 (1995).
[CrossRef]

Niculae, A. M.

Nijhof, H. B.

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

Nijhof, J. H. B.

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.

Paré, C.

Pilipetskii, A. N.

Pina, J.

J. Pina, B. Abueva, and C. G. Goedde, "Periodically conjugated solitons in dispersion-managed optical," Opt. Commun. 176, 397-407 (2000).
[CrossRef]

Posth, J. A.

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Quiroga-Teixeiro, M.

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

D. Anderson, M. Lisak, B. Malomed, and M. Quiroga-Teixeiro, "Tunnelling of an optical soliton through a fiber junction," J. Opt. Soc. Am. B 11, 2380-2384 (1994).
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Sahara, A.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

Santhanam, J.

Schafer, T.

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley,1998).

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

Spatschek, K. H.

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Suzuki, K.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

K. Suzuki and M. Nakazawa, "Recent progress in optical soliton communication," Opt. Fiber Technol. 1, 289-308 (1995).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

S. K. Turitsyn, "Dispersion-managed solitons and optimization the dispersion management," Opt. Fiber Technol. 4, 384-452 (1998).
[CrossRef]

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

Wabnitz, S.

T. Hirooka and S. Wabnitz, "Nonlinear gain control of dispersion-managed soliton amplitude and collisions," Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

Wald, M.

Yamada, E.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

Yang, J.

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]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, "Conditions for stationary pulse propagation in the strong dispersion management regime," Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Yu., T.

C. R. Phys.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, "Physics and mathematics of dispersion-managed optical solitons," C. R. Phys. 4, 145-161 (2003).
[CrossRef]

Chaos

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, "Recent progress in soliton transmission technology," Chaos 10, 486-514 (2000).
[CrossRef]

Electron. Lett.

M. Matsumoto, "Time-domain transmission control of dispersion-managed solitons," Electron. Lett. 34, 2155-2157 (1998).
[CrossRef]

W. Forysiak W. and N. J. Doran, "Conjugate solitons in amplified optical fibre transmission systems," Electron. Lett. 30, 154-155 (1994).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

R. M. Mu, V. S. Grigoryan, and C. R. Menyuk, "Comparison of theory and experiment for dispersion-managed solitons in a recirculating fiber loop," IEEE J. Sel. Top. Quantum Electron. 6, 248-257 (2000).
[CrossRef]

IEEE Photonics Technol. Lett.

G. M. Carter and J. M. Jacob, "Dynamics of solitons in filtered dispersion managed system," IEEE Photonics Technol. Lett. 10, 546-548 (1998).
[CrossRef]

M. Matsumoto, "Analysis of interaction between stretched pulses propagating in dispersion-managed fibers," IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

V. V. Afanasjev, B. A. Malomed, P. L. Chu, and M. K. Islam, "Generalized variational approximations for the optical soliton," Opt. Commun. 147, 317-322 (1998).
[CrossRef]

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

J. A. Posth, T. Schafer, E. W. Laedke, and K. H. Spatschek, "Fast optimization procedures for third-order dispersion management," Opt. Commun. 219, 241-249 (2003).
[CrossRef]

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, "An iterative numerical method for dispersion-managed solitons," Opt. Commun. 245, 425-435 (2005).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, "Conditions for stationary pulse propagation in the strong dispersion management regime," Opt. Commun. 149, 366-375 (1998).
[CrossRef]

S. Chi, S. C. Lin, and J. C. Dung, "Improving soliton transmission in a dispersion compensated system by pre-chirping and pre-shaping method," Opt. Commun. 148, 27-30 (1998).
[CrossRef]

J. Pina, B. Abueva, and C. G. Goedde, "Periodically conjugated solitons in dispersion-managed optical," Opt. Commun. 176, 397-407 (2000).
[CrossRef]

Opt. Fiber Technol.

S. K. Turitsyn, "Dispersion-managed solitons and optimization the dispersion management," Opt. Fiber Technol. 4, 384-452 (1998).
[CrossRef]

K. Suzuki and M. Nakazawa, "Recent progress in optical soliton communication," Opt. Fiber Technol. 1, 289-308 (1995).
[CrossRef]

T. Hirooka and S. Wabnitz, "Nonlinear gain control of dispersion-managed soliton amplitude and collisions," Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

K. Bertilsson, T. Aakjer, M. Quiroga-Teixeiro, P. A. Andrekson, and P.-O. Hedekvist, "Investigation of soliton compression by propagation through fiber junctions," Opt. Fiber Technol. 1, 117-124 (1995).
[CrossRef]

Opt. Lett.

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

P. V. Mamyshev and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing," Opt. Lett. 24, 1454-1456 (1999).
[CrossRef]

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

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

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

J. Santhanam, C. J. McKinstrie, T. I. Lakoba, and G. P. Agrawal, "Effects of precompensation and postcompensation on timing jitter in dispersion-managed systems," Opt. Lett. 26, 1131-1133 (2001).
[CrossRef]

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

V. S. Grigoryan, T. Yu., E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, "Dispersion-managed soliton dynamics," Opt. Lett. 22, 1609-1611 (1997).
[CrossRef]

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

S. Kumar and A. Hasegawa, "Quasi-soliton propagation in dispersion-managed optical fibers," Opt. Lett. 22, 372-374 (1997).
[CrossRef] [PubMed]

S. Kumar and F. Lederer, "Gordon-Haus effect in dispersion-managed soliton systems," Opt. Lett. 22, 1870-1872 (1997).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, "Analysis of Gordon-Haus jitter in a dispersion-compensated optical transmission system," Opt. Lett. 23, 694-696 (1998).
[CrossRef]

B. A. Malomed, "Jitter suppression by guiding 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, andN. J. Doran, "Soliton collisions with wavelength-division multiplexed systems with strong dispersion management," Opt. Lett. 23, 1354-1356 (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]

M. Wald, B. A. Malomed, and F. Lederer, "Interaction of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines," Opt. Lett. 26, 965-967 (2001).
[CrossRef]

M. J. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, "Collision-induced timing shifts in dispersion-managed soliton systems," Opt. Lett. 27, 318-320 (2002).
[CrossRef]

Opt. Quantum Electron.

O. Aharon, B. A. Malomed, Y. B. Band, and U. Mahlab, "Minimization of the pulse's timing jitter in a dispersion-compensated WDM system," Opt. Quantum Electron. 36, 349-366 (2004).
[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

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, 1997).

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley,1998).

J. McEntee, "Solitons go the distance for Marconi," Fibre Syst. Eur., pp. 19-23 (2003).

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

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Figures (10)

Fig. 1
Fig. 1

Comparison of the input Gaussian [Eq. (4)] with the pulse released by the shaper (the optimized one), and the target of the shaping, i.e., a numerically found DM soliton (required pulse). (a) absolute values of the fields, (b) their real and imaginary parts. In panel (b), the input Gaussian is not displayed, as it is purely real.

Fig. 2
Fig. 2

(a) Contour plots showing the optimal values of amplitude A (solid curves) and inverse squared width a (dashed curves) of the input Gaussian [Eq. (4)] as functions of D = 1 l (dispersion of normal fiber) and the soliton’s (pulse) energy E sol , whereas D + = l + = 1 ; see the text. (b) The optimal values of the lengths of the normal- and anomalous-GVD fibers in the shaper (solid and dashed curves, respectively), as functions of the same parameters.

Fig. 3
Fig. 3

The same as in Fig. 1a, for the case when the input pulse is the raised cosine [Eq. (8)], and the DM map has D = 6 , D + = + 1 , l = 0.2 , l + = 1 .

Fig. 4
Fig. 4

Transmission of the optimally preshaped pulse in the same case as in Fig. 1, with the difference that the input Gaussian pulse is given chirp c = 0.8 .

Fig. 5
Fig. 5

The same as in Figs. 1a, but in the presence of the third-order GVD, D 3 = 0.001 , which breaks the symmetry of the pulses.

Fig. 6
Fig. 6

(a) Copropagation of a string of preprocessed solitons in the DM system with l = 1 , ( D 2 ) = 1 , D 3 = 0.0002 , and ϵ = 0.0004 [see Eq. (11)]. The solitons were generated from the input pulses with the optimal parameters, taken as per Eq. (13). (b) The same with an arbitrarily altered value of the initial chirp, c = 0.4 .

Fig. 7
Fig. 7

(a) Copropagation of a string of preprocessed pulses in the DM system with l = 1 , ( D 2 ) = 0.98 , ( D 2 ) + = 1 , D 3 = 0 , and without bandpass filters. (b) Transmission of the same array of raw pulses launched into the system without preshaping.

Fig. 8
Fig. 8

Eye diagrams for the same soliton string and in the same system as in Fig. 7, with the addition of noise in the pulse source and at positions of amplifiers (in the real system), at the level of ± 2.5 % of the pulse’s amplitude. The diagrams are shown for the transmission distance z = 100 (i.e., 50 DM periods). (a) The string of preprocessed pulses, (b) the string of raw (unprocessed) Gaussian pulses directly launched into the system.

Fig. 9
Fig. 9

Interchannel collisions between the same pulses as in Fig. 7. Each channel is identical to the DM system that was used to generate Fig. 7, with the inverse-group-velocity shift between them being 0.8 (the value in physical units is given in the text). (a) DM solitons generated from the preprocessed pulses, (b) raw Gaussian pulses directly injected into the DM system.

Fig. 10
Fig. 10

Normalized integral errors, N ̃ r (a) and N ̃ i (b) (sensitivity), defined as per Eqs. (15) and (7), as functions of the relative size of lengths L ± in the preshaper, and amplitude A and inverse squared width a of input pulse [Eq.(4)], with respect to their optimal values (“parameter factor”).

Equations (17)

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i q Z 1 2 β 2 2 q T 2 i 6 β 3 3 q T 3 + γ q 2 q = 0 ,
i u z + 1 2 D 2 2 u τ 2 + i D 3 3 u τ 3 + u 2 u = 0 ,
D ¯ = ( D 2 ) l + ( D 2 ) + l + l + l + .
u in ( τ ) = A exp ( a τ 2 ) , a > 0 ,
L = 1.25 , L + = 1.62 ; A = 1.44 , a = 1.65
S = D L + D + L + T FWHM 2 ,
N r = + [ Re { u DM - soliton ( τ ) u output ( τ ) } ] 2 d τ ,
N i = + [ Im { u DM - soliton ( τ ) u output ( τ ) } ] 2 d τ .
u in ( τ ) = { A [ 1 + cos ( π τ T ) ] , for τ < T 0 , for τ > T } .
u in ( τ ) = A exp [ a ( τ τ 0 ) 2 ] , τ 0 = const .
L 1 = 0.809 , L 2 = 1.26 ;
A = 1.48 , a = 1.82 , τ 0 = 0.415 .
i u z + 1 2 D 2 2 u τ 2 + i D 3 3 u τ 3 + u 2 u = ϵ u τ ( u 2 ) ,
u in ( τ ) = A exp [ ( a + i c ) ( τ τ 0 ) 2 ] .
A = 1.48 , a = 1.39 , c = 0.779 ; L = 1.74 , L + = 1.891 .
L = 1.21 , L + = 1.57 , A = 1.40 , a = 1.52
N ̃ r , i = N r , i N r , i ( 0 ) ,

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