Abstract

We use the moment method to calculate the Gordon–Haus timing jitter of optical pulses in dispersion-managed communication systems designed by use of lumped fiber amplifiers. The use of the Gaussian approximation for the chirped pulses, in combination with variational analysis, allows us to obtain an analytic expression for the timing jitter that is valid for an arbitrary number of amplifiers within each map period. We use this result to discuss how jitter is affected when more than one amplifier is used within each map period. We consider jitter for soliton-based systems as well as for low-power light-wave systems designed by use of the chirped return-to-zero format. In each case, the effects of dispersion compensation on the timing jitter are studied in detail.

© 2002 Optical Society of America

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References

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  1. J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665–667 (1986).
    [CrossRef] [PubMed]
  2. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
  3. R. J. Essiambre and G. P. Agrawal, “Timing jitter of ultrashort solitons in high-speed communication systems: general formulation and application to dispersion-decreasing fibers,” J. Opt. Soc. Am. B 14, 314–322 (1997).
    [CrossRef]
  4. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997), Chap. 10.
  5. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998), Chap. 5.
  6. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).
  7. V. S. Grigoryan, C. R. Menyuk, and R. M. Mu, “Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization,” J. Lightwave Technol. 17, 1347–1356 (1999).
    [CrossRef]
  8. 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]
  9. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
    [CrossRef]
  10. I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
    [CrossRef]
  11. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 23, 1609–1611 (1997).
    [CrossRef]
  12. V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609–611 (1998).
    [CrossRef]
  13. 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]
  14. T. I. 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]
  15. L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Vol. 3A, Chap. 12; see also references therein.
  16. E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
    [CrossRef]
  17. I. S. Penketh, P. Harper, S. B. Alleston, A. M. Niculae, I. Bennion and N. J. Doran, “10-Gbit/s dispersion-managed soliton transmission over 16, 500 km in standard fiber by reduction of soliton interactions,” Opt. Lett. 24, 802–804 (1999).
    [CrossRef]
  18. L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Gruener-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett. 25, 704–706 (2000).
    [CrossRef]
  19. A. Yariv, “Signal-to-noise considerations in fiber links with periodic or distributed optical amplification,” Opt. Lett. 15, 1064–1066 (1990).
    [CrossRef] [PubMed]
  20. W. Forysiak, K. J. Blow, and N. J. Doran, “Reduction of Gordon–Haus jitter by posttransmission dispersion compensation,” Electron. Lett. 29, 1225–1226 (1993).
    [CrossRef]
  21. A. D. Ellis and D. M. Spirit, “Unrepeatered transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
    [CrossRef]
  22. R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
    [CrossRef]
  23. D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
    [CrossRef]
  24. E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
    [CrossRef]

2001 (1)

2000 (2)

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Gruener-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett. 25, 704–706 (2000).
[CrossRef]

1999 (2)

1998 (4)

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609–611 (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]

T. I. 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]

1997 (5)

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 23, 1609–1611 (1997).
[CrossRef]

R. J. Essiambre and G. P. Agrawal, “Timing jitter of ultrashort solitons in high-speed communication systems: general formulation and application to dispersion-decreasing fibers,” J. Opt. Soc. Am. B 14, 314–322 (1997).
[CrossRef]

1994 (1)

A. D. Ellis and D. M. Spirit, “Unrepeatered transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

1993 (1)

W. Forysiak, K. J. Blow, and N. J. Doran, “Reduction of Gordon–Haus jitter by posttransmission dispersion compensation,” Electron. Lett. 29, 1225–1226 (1993).
[CrossRef]

1990 (1)

1986 (1)

1971 (1)

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
[CrossRef]

Agrawal, G. P.

Alleston, S. B.

Bennion, I.

Bergano, N. S.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

Berntson, A.

Blow, K. J.

W. Forysiak, K. J. Blow, and N. J. Doran, “Reduction of Gordon–Haus jitter by posttransmission dispersion compensation,” Electron. Lett. 29, 1225–1226 (1993).
[CrossRef]

Breuer, D.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Davidson, C. R.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

Doran, N. J.

Ehrke, H. J.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

Ellis, A. D.

A. D. Ellis and D. M. Spirit, “Unrepeatered transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

Essiambre, R. J.

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]

W. Forysiak, K. J. Blow, and N. J. Doran, “Reduction of Gordon–Haus jitter by posttransmission dispersion compensation,” Electron. Lett. 29, 1225–1226 (1993).
[CrossRef]

Gabitov, I. R.

I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

Golovchenko, E. A.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 23, 1609–1611 (1997).
[CrossRef]

Gordon, J. P.

Grigoryan, V. S.

Gripp, J.

Gruener-Nielsen, L.

Harper, P.

Haus, H. A.

Kaup, D. J.

T. I. 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]

Khatri, F. I.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

Kimball, R. M.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

Kubota, H.

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

Kueppers, F.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Lakoba, T. I.

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]

T. I. 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]

Ludwig, R.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Malomed, B. A.

T. I. 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]

Mamyshev, P. V.

Mamysheva, N.

Mattheus, A.

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Mazurczyk, V. J.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

McKinstrie, C. J.

Menyuk, C. R.

Mollenauer, L. F.

Mu, R. M.

Nakazawa, M.

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

Neubelt, M. J.

Niculae, A. M.

Nijhof, J. H. B.

Penketh, I. S.

Petermanm, K.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

Petermann, K.

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Petrishchev, V. A.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
[CrossRef]

Pieper, W.

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Pilipetskii, A. N.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 23, 1609–1611 (1997).
[CrossRef]

Sahara, A.

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

Santhanam, J.

Shapiro, E. G.

I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

Spirit, D. M.

A. D. Ellis and D. M. Spirit, “Unrepeatered transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

Talanov, V. I.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
[CrossRef]

Turitsyn, S. K.

I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

Veng, T.

Vlasov, S. N.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
[CrossRef]

Weber, H. G.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

Weich, K.

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

Yamada, E.

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

Yamamoto, T.

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

Yang, J.

T. I. 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]

Yariv, A.

Yu, T.

Electron. Lett. (4)

E. Yamada, H. Kubota, T. Yamamoto, A. Sahara, and M. Nakazawa, “10 Gbit/s, 10600km, dispersion-allocated soliton transmission using conventional 1.3 μm single mode fibres,” Electron. Lett. 33, 602–603 (1997).
[CrossRef]

W. Forysiak, K. J. Blow, and N. J. Doran, “Reduction of Gordon–Haus jitter by posttransmission dispersion compensation,” Electron. Lett. 29, 1225–1226 (1993).
[CrossRef]

A. D. Ellis and D. M. Spirit, “Unrepeatered transmission over 80 km standard fibre at 40 Gbit/s,” Electron. Lett. 30, 72–74 (1994).
[CrossRef]

R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, F. Kueppers, and A. Mattheus, “Unrepeatered 40 Gbit/s RZ single-channel transmission over 150km of standard single-mode fibre at 1.55 μm,” Electron. Lett. 33, 76–77 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball, and V. J. Mazurczyk, “Modeling of transoceanic fiber-optic WDM communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 337–347 (2000).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

I. R. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Optical pulse dynamics in fiber links with dispersion compensation,” Opt. Commun. 134, 317–329 (1997).
[CrossRef]

T. I. 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]

Opt. Lett. (8)

V. S. Grigoryan and C. R. Menyuk, “Dispersion-managed solitons at normal average dispersion,” Opt. Lett. 23, 609–611 (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]

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, “Dispersion-managed soliton dynamics,” Opt. Lett. 23, 1609–1611 (1997).
[CrossRef]

I. S. Penketh, P. Harper, S. B. Alleston, A. M. Niculae, I. Bennion and N. J. Doran, “10-Gbit/s dispersion-managed soliton transmission over 16, 500 km in standard fiber by reduction of soliton interactions,” Opt. Lett. 24, 802–804 (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]

L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Gruener-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett. 25, 704–706 (2000).
[CrossRef]

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

A. Yariv, “Signal-to-noise considerations in fiber links with periodic or distributed optical amplification,” Opt. Lett. 15, 1064–1066 (1990).
[CrossRef] [PubMed]

Photonics Technol. Lett. (1)

D. Breuer, H. J. Ehrke, F. Kueppers, R. Ludwig, K. Petermanm, H. G. Weber, and K. Weich, “Unrepeated 40-Gb/s RZ single-channel transmission at 1.55 μm using various fiber types,” Photonics Technol. Lett. 10, 822–824 (1998).
[CrossRef]

Radiophys. Quantum Electron. (1)

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Radiophys. Quantum Electron. 14, 1062–1070 (1971).
[CrossRef]

Other (5)

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, in Optical Fiber Telecommunications, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Vol. 3A, Chap. 12; see also references therein.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997), Chap. 10.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998), Chap. 5.

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

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

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Figures (7)

Fig. 1
Fig. 1

Timing jitter for a 10-Gbit/s soliton DM system as a function of transmission distance. A single amplifier is placed at the end of each 79-km map period (solid curve), whereas a second amplifier is present at a transmission distance of 35 km for the dashed curve. The map has a strength of 0.62 and an average dispersion of 0.2 ps/(km-nm).

Fig. 2
Fig. 2

Same as Fig. 1, except that here the map consists of 66 km of standard fiber followed by 13 km of dispersion-compensating fiber, resulting in a map strength of 2.33 and an average dispersion of 0.2 ps/(km-nm). The second amplifier is placed at a transmission distance of 24 km.

Fig. 3
Fig. 3

Reduction in timing jitter when several amplifiers are placed at equal distances in each map period.

Fig. 4
Fig. 4

Effect of postcompensation on timing jitter of a 10-Gbit/s DM soliton system for the dispersion map used in Fig. 2 (map strength, S=2.33). Jitter is plotted as a function of transmission distance for four values of y that represent the fraction of postcompensation.

Fig. 5
Fig. 5

Same as Fig. 4, except that a second amplifier is placed at a transmission distance of 24 km.

Fig. 6
Fig. 6

Timing jitter for a 10-Gbit/s quasi-linear CRZ system as a function of transmission distance for the same map used for Fig. 2. The second amplifier, placed at a transmission distance of 24 km, reduces the jitter by a factor of ∼3 (dotted curve).

Fig. 7
Fig. 7

Effects of precompensation and postcompensation on timing jitter of a 10-Gbit/s CRZ system for the same dispersion map used in Fig. 2: (a) No precompensation and complete postcompensation; (b) complete precompensation and no postcompensation; (c) 77% precompensation and 23% postcompensation.

Equations (49)

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iUz-β222Ut2+γ|U|2U=-iα2U,
E=-|U|2dt,
T=1E-t|U|2dt,
W=i2E-(U*Ut-UUt*)dt,
dEdz=-αE,dTdz=β2W,dWdz=0.
dWdz=i δWiδ(z-zi),
dTdz=β2W+i δTiδ(z-zi),
δUi(ti)δUj(tj)=0,
δUi*(ti)δUj(tj)=Siδij(ti-tj),
δW2=(2S/E2)-|Vt|2dt,
δWδT=(iS/2E2)-(t-T)(V*Vt-VVt*)dt,
δT2=(2S/E2)-(t-T)2|V|2dt,
U=a exp[iϕ-iW(t-T)-(1+ic)(t-T)2/2τ2],
δW2=(S/E)[(1+c2)/τ2],
δWδT=(S/E)c,
δT2=(S/E)τ2.
 W2j=W2j-1+δWj2,
WTj=WTj-1+djW2j-1+δWjδTj,
T2j=T2j-1+2djWTj-1+dj2W2j-1+δTj2,
dj=1τm2zj-1zj β2(z)dz
W2i=W2i-1+Ai,
WTi=WTi-1+dsW2i-1+Bi,
T2i=T2i-1+2dsWTi-1+ds2W2i-1+Ci,
Ai=j=1naδWj2,
Bi=j=1naδWjδTj+j=1na-1δWj2k=j+1na dk,
Ci=j=1naδTj2+2 j=1na-1δWjδTjk=j+1na dk+j=1na-1δWj2k=j+1na dk2.
W2ns=Ans,
WTns=Bns+Ads(ns-1)/2,
T2ns=Cns+Bdsns(ns-1)+Ads2ns(ns-1)(2ns-1)/6,
S=|D1L1-D2L2|/TFW2,
T2nsAns(nsds)2/3.
T2nsnsphνβ¯22L33lsτm2j=1naGj-1Ej,
fr(na)=T2naT2na=1=naGt1/na-1Gt-1.
T2distribT2lumped=αlsexp(αls)-1=ln GtGt-1,
T2fAns(nsds)2(y2-y+1/3).
cij=c0+(i-1)ds+k=1jdk,
Ai=j=1naδWj2=Sj/Ej
Bi=A(c0+ids).
Ci=A[1+(c0+ids)2].
W2ns=Ans,
WTns=Ans(nsds+dp),
T2ns=Ans[1+(nsds+dp)2].
W2ns=Ans,
WTns=Ans(nsds+dp+df),
T2ns=Ans[1+(nsds+dp+df)2].
T2nsAns(nsds)2.
F(z, x)=z[+(z-x)2].
zmx/3+/2x.
xm3/4+.

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