Abstract

We analyze the propagation stability of dispersion-managed solitons in long-distance fiber optic links, as it is influenced by in-line control elements such as synchronous intensity modulators and filters. The soliton stability analysis permits us to optimize dispersion map design as well as the input optical pulse’s energy and prechirp in the presence of periodic all-optical regeneration. Substantial agreement is obtained between the predictions of linear stability analysis and beam propagation simulations. Dispersion mapping and control are optimized for amplification, reshaping, and retiming regeneration of long-haul transmissions at a 40-Gbit/s channel rate.

© 2002 Optical Society of America

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  1. A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
    [CrossRef]
  2. P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
    [CrossRef]
  3. E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, “Analysis of synchronous intensity modulation control of 40Gbit/s dispersion-managed soliton transmission,” in Optical Fiber Communication Conference (OFC), Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 45–47.
  4. O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
    [CrossRef]
  5. L. F. Mollenauer and P. V. Mamyshev, “Massive wavelength-division multiplexing with solitons,” IEEE J. Quantum Electron. 34, 2089–2102 (1998).
    [CrossRef]
  6. S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
    [CrossRef]
  7. J. Kumasako, M. Matsumoto, and S. Waiyapot, “Linear stability analysis of dispersion-managed solitons controlled by filters,” J. Lightwave Technol. 18, 1064–1068 (2000).
    [CrossRef]
  8. S. Waiyapot and M. Matsumoto, “Stability analysis of dispersion-managed solitons controlled by synchronous amplitude modulators,” IEEE Photon. Technol. Lett. 11, 1408–1410 (1999).
    [CrossRef]
  9. E. Pincemin, O. Audouin, B. Dany, and S. Wabnitz, “Stabil-ity of synchronous intensity modulation control of 40Gb/s dispersion-managed soliton transmissions,” J. Lightwave Technol. 19, 624–635 (2001).
    [CrossRef]
  10. S. Waiyapot and M. Matsumoto, “Jitter and stability analysis of an actively mode-locked dispersion-managed fiber laser,” Opt. Commun. 188, 167–180 (2001).
    [CrossRef]
  11. Y. Kodama, “Nonlinear pulse propagation in dispersion managed system,” Physica D 123, 255–266 (1998).
    [CrossRef]
  12. S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
    [CrossRef]
  13. E. A. Golovchenko, C. R. Menyuk, A. N. Pilipetskii, V. S. Grigoryan, and T. Yu, “Dispersion-managed soliton dynamics,” Opt. Lett. 22, 1609–1611 (1997).
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    [CrossRef]
  16. H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
    [CrossRef]
  17. M. Matsumoto, “Effects of guiding filters on stretched-pulse transmission in dispersion-managed fibres,” Electron. Lett. 33, 1718–1720 (1997).
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  21. D. Marcuse, C. R. Menyuk, and R. Holzlöhner, “Time shift of pulse due to dispersion slope and nonlinearity,” IEEE Photon. Technol. Lett. 11, 1611–1613 (1999).
    [CrossRef]
  22. S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
    [CrossRef]
  23. M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (1998).
    [CrossRef]
  24. E. Pincemin, F. Neddam, and O. Leclerc, “Efficient reduction of interactions in dispersion-managed links through in-line filtering and synchronous intensity modulation,” Opt. Lett. 25, 287–289 (2000).
    [CrossRef]

2001

E. Pincemin, O. Audouin, B. Dany, and S. Wabnitz, “Stabil-ity of synchronous intensity modulation control of 40Gb/s dispersion-managed soliton transmissions,” J. Lightwave Technol. 19, 624–635 (2001).
[CrossRef]

S. Waiyapot and M. Matsumoto, “Jitter and stability analysis of an actively mode-locked dispersion-managed fiber laser,” Opt. Commun. 188, 167–180 (2001).
[CrossRef]

2000

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

J. Kumasako, M. Matsumoto, and S. Waiyapot, “Linear stability analysis of dispersion-managed solitons controlled by filters,” J. Lightwave Technol. 18, 1064–1068 (2000).
[CrossRef]

E. Pincemin, F. Neddam, and O. Leclerc, “Efficient reduction of interactions in dispersion-managed links through in-line filtering and synchronous intensity modulation,” Opt. Lett. 25, 287–289 (2000).
[CrossRef]

1999

D. Marcuse, C. R. Menyuk, and R. Holzlöhner, “Time shift of pulse due to dispersion slope and nonlinearity,” IEEE Photon. Technol. Lett. 11, 1611–1613 (1999).
[CrossRef]

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. Waiyapot and M. Matsumoto, “Stability analysis of dispersion-managed solitons controlled by synchronous amplitude modulators,” IEEE Photon. Technol. Lett. 11, 1408–1410 (1999).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

1998

L. F. Mollenauer and P. V. Mamyshev, “Massive wavelength-division multiplexing with solitons,” IEEE J. Quantum Electron. 34, 2089–2102 (1998).
[CrossRef]

Y. Kodama, “Nonlinear pulse propagation in dispersion managed system,” Physica D 123, 255–266 (1998).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (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]

1997

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

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

1995

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Aceves, A. B.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Audouin, O.

Boucherez, E.

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Bouchoule, S.

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Brindel, P.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Dany, B.

E. Pincemin, O. Audouin, B. Dany, and S. Wabnitz, “Stabil-ity of synchronous intensity modulation control of 40Gb/s dispersion-managed soliton transmissions,” J. Lightwave Technol. 19, 624–635 (2001).
[CrossRef]

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Desourvire, E.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Duchet, C.

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Gabitov, I.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Golovchenko, E. A.

Grigoryan, V. S.

Hasegawa, A.

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, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (1998).
[CrossRef]

Holzlöhner, R.

D. Marcuse, C. R. Menyuk, and R. Holzlöhner, “Time shift of pulse due to dispersion slope and nonlinearity,” IEEE Photon. Technol. Lett. 11, 1611–1613 (1999).
[CrossRef]

Inoue, T.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Inui, T.

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

Kato, H.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Kodama, Y.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (1998).
[CrossRef]

Y. Kodama, “Nonlinear pulse propagation in dispersion managed system,” Physica D 123, 255–266 (1998).
[CrossRef]

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Komukai, T.

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

Kubota, H.

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

Kumar, S.

Kumasako, J.

Kurokawa, H.

M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (1998).
[CrossRef]

Laedke, E. W.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Leclerc, O.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

E. Pincemin, F. Neddam, and O. Leclerc, “Efficient reduction of interactions in dispersion-managed links through in-line filtering and synchronous intensity modulation,” Opt. Lett. 25, 287–289 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Lederer, F.

Mamyshev, P. V.

L. F. Mollenauer and P. V. Mamyshev, “Massive wavelength-division multiplexing with solitons,” IEEE J. Quantum Electron. 34, 2089–2102 (1998).
[CrossRef]

Marcuse, D.

D. Marcuse, C. R. Menyuk, and R. Holzlöhner, “Time shift of pulse due to dispersion slope and nonlinearity,” IEEE Photon. Technol. Lett. 11, 1611–1613 (1999).
[CrossRef]

Maruta, A.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Matsumoto, M.

S. Waiyapot and M. Matsumoto, “Jitter and stability analysis of an actively mode-locked dispersion-managed fiber laser,” Opt. Commun. 188, 167–180 (2001).
[CrossRef]

J. Kumasako, M. Matsumoto, and S. Waiyapot, “Linear stability analysis of dispersion-managed solitons controlled by filters,” J. Lightwave Technol. 18, 1064–1068 (2000).
[CrossRef]

S. Waiyapot and M. Matsumoto, “Stability analysis of dispersion-managed solitons controlled by synchronous amplitude modulators,” IEEE Photon. Technol. Lett. 11, 1408–1410 (1999).
[CrossRef]

M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, “Effects of filters on pulse-to-pulse interaction between dispersion-managed solitons,” Opt. Commun. 155, 28–32 (1998).
[CrossRef]

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

Menyuk, C. R.

D. Marcuse, C. R. Menyuk, and R. Holzlöhner, “Time shift of pulse due to dispersion slope and nonlinearity,” IEEE Photon. Technol. Lett. 11, 1611–1613 (1999).
[CrossRef]

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

Mezentsev, V. K.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, 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.

L. F. Mollenauer and P. V. Mamyshev, “Massive wavelength-division multiplexing with solitons,” IEEE J. Quantum Electron. 34, 2089–2102 (1998).
[CrossRef]

Musher, S. L.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Nakazawa, M.

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

Neddam, F.

Nouchi, P.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

Pilipetskii, A. N.

Pincemin, E.

Rouvillain, D.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

Sahara, A.

A. Sahara, T. Inui, T. Komukai, H. Kubota, and M. Nakazawa, “40Gb/s RZ transmission over transoceanic distance in a dispersion managed standard fiber using a new inline synchronous modulation method,” IEEE Photon. Technol. Lett. 12, 720–722 (2000).
[CrossRef]

Scäfer, T.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Schäfer, T.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

Shapiro, E. G.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Spatschek, K. H.

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Sugahara, H.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, T. Schäfer, and V. K. Mezentsev, “Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links,” IEEE Photon. Technol. Lett. 11, 203–205 (1999).
[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Scäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).
[CrossRef]

Wabnitz, S.

Waiyapot, S.

S. Waiyapot and M. Matsumoto, “Jitter and stability analysis of an actively mode-locked dispersion-managed fiber laser,” Opt. Commun. 188, 167–180 (2001).
[CrossRef]

J. Kumasako, M. Matsumoto, and S. Waiyapot, “Linear stability analysis of dispersion-managed solitons controlled by filters,” J. Lightwave Technol. 18, 1064–1068 (2000).
[CrossRef]

S. Waiyapot and M. Matsumoto, “Stability analysis of dispersion-managed solitons controlled by synchronous amplitude modulators,” IEEE Photon. Technol. Lett. 11, 1408–1410 (1999).
[CrossRef]

Wald, M.

Yu, T.

Electron. Lett.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desourvire, and P. Nouchi, “Experimental demonstration of new regeneration scheme for 40Gbit/s dispersion managed long-haul transmissions,” Electron. Lett. 36, 61–62 (2000).
[CrossRef]

O. Leclerc, P. Brindel, D. Rouvillain, E. Pincemin, B. Dany, E. Desourvire, C. Duchet, E. Boucherez, and S. Bouchoule, “40 Gbit/s polarization-insensitive and wavelength-independent InP Mach–Zehnder modulator for all-optical regeneration,” Electron. Lett. 35, 730–731 (1999).
[CrossRef]

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

IEEE J. Lightwave Technol.

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” IEEE J. Lightwave Technol. 17, 1547–1559 (1999).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Archetypal system setup with its relative dispersion map profile; IMs are assumed to slide in different positions. EDFAs, erbium-doped fiber amplifiers.

Fig. 2
Fig. 2

LSA results. Left, instability gain G for pulse energies of A, 50; B, 100; C, 200 fJ. D refers to a different map with smaller local dispersion [±0.25 ps/(km nm)] and energy of 50 fJ. Right, gain G of (solid curve) amplitude and (dashed curve) timing instability at 50 fJ. Shaded regions represent unstable configurations.

Fig. 3
Fig. 3

Top, pulse amplitude instability: solid (dashed) curve, positive (negative) weak energy deviation from the DM soliton energy. Bottom, timing instability: pulse center shifts for solid (dashed) curve, positive (negative) initial frequency seed.

Fig. 4
Fig. 4

Energy threshold stability for IMs in units of z (=14 km): top, unstable pulse evolution with energy of 50 fJ; bottom, stable pulse propagation with energy of 200 fJ.

Fig. 5
Fig. 5

Evolution of fractional soliton power deviation ΔP/P for IM at z=A, 10; B, 25; C, 15; D, 17; E, 18; F, 20.5 km. For comparison, the gray scale at the right shows the corresponding LSA gain G [dB/Mm].

Fig. 6
Fig. 6

Eye diagrams after 7000 km of a 512 PRBS in the absence of ASE noise. Top, with IMs at the fiber junctions; bottom, with IMs at the amplifier locations. Sinusoidal modulation depth, 10 dB.

Fig. 7
Fig. 7

Eye diagram after 7000 km of a 512 PRBS in the absence of ASE noise. Top, with IMs at the fiber junctions; bottom, with IMs at the amplifier locations. Sinusoidal modulation depth, 10 dB. The fiber sequence here was NZDF-, NZDF+.

Fig. 8
Fig. 8

Left, LSA gain G versus IMs position for a pulse energy of 200 fJ (shaded regions represent unstable configurations). Right, one-to-one corresponding fiber sequence. Bottom, stable solutions refer to the presence of IMs and filters (126 GHz).

Fig. 9
Fig. 9

Top left, stable pulse propagation controlled by IMs and filters with a dispersion map NZDF+, NZDF-; top right, unstable evolution with only IMs. Bottom: dashed curve, pulse center drift induced by IMs; solid curve, stable evolution with IMs and filters.

Fig. 10
Fig. 10

Stable PRBS transmission after 24 Mm in the presence of ASE noise with a dispersion map of [±0.25 ps/(km·nm)] and a periodic modulation depth of 10 dB and energy of 50 fJ (numerics).

Fig. 11
Fig. 11

Quality factor Q versus transmission distance: A, with IMs at the amplifier location; C, with IMs at z=12 km; G, with IMs at the fiber junction; F, with IMs at z=18.5 (optimal point and asymptotic trend). BER, bit-error rate.

Equations (19)

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L0=i2(qqz*-qzq*)-12[γ(z)exp(-2Γz)|q|4-D(z)|qt|2],
dAdz=-D(z)CA,
dτdz=2τCD(z),
dCdz=-2C2D(z)-γ(z)exp(-2Γz)A222τ2+D(z)2τ4,
dκdz=0,
dξdz=-κD(z),
A+=A-GIMΨ,
τ+=τ-[H]-1/2,C+=C-,
κ+=κ-+4C-ξ-μτ-2H-1,ξ+=ξ-H-1,
A+=A-GFρ-1/4 exp[-βκ-2(1+4βB2)-1],
τ+=(1+4βB2)(2τ-2ρ)-1,C+=C-ρ-1,
κ+=κ-(1+4βB2)-1,
ξ+=ξ-+4βC-κ-τ-2(1+4βB2)-1,
ξrms(z)=-+t|q(t, z)|2dt-+|q(t, z)|2dt.
JL=10-δL1.
JIM=1m20m4,JF=f10f31.
C=a10a31,
JT=10-δ1L111m20m410-δ2L21.
JT=10-δ1L11f10f311m20m4.

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