Abstract

The Gordon–Haus time jitter and the soliton–soliton interactions in a soliton fiber loop memory or in a transmission link may be suppressed by the periodic injection of a weak cw control beam. In the case of a fiber ring cavity cw injection may also permit clock regeneration from a randomly modulated soliton train.

© 1996 Optical Society of America

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References

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  1. A. Hasegawa and Y. Kodama, Opt. Lett. 7, 285 (1982).
    [CrossRef] [PubMed]
  2. M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
    [CrossRef]
  3. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
    [CrossRef]
  4. M. Haelterman, S. Trillo, and S. Wabnitz, Electron. Lett. 29, 119 (1993).
    [CrossRef]
  5. L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  6. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  7. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  8. N. N. Akhmediev and S. Wabnitz, J. Opt. Soc. Am. B 9, 236 (1992).
    [CrossRef]
  9. S. Wabnitz, Opt. Lett. 18, 601 (1993).
    [CrossRef]
  10. A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, Opt. Lett. 16, 1841 (1991); Y. Kodama and A. Hasegawa, ibid. 17, 31 (1992).
    [CrossRef] [PubMed]
  11. L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [CrossRef] [PubMed]
  12. Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
    [CrossRef]
  13. Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [CrossRef]
  14. M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
    [CrossRef]
  15. J. N. Kutz, W. L. Kath, R. D. Li, and P. Kumar, Opt. Lett. 18, 802 (1993).
    [CrossRef] [PubMed]
  16. J. N. Kutz, C. V. Hile, W. L. Kath, R. D. Li, and P. Kumar, J. Opt. Soc. Am. B 11, 2112 (1994).
    [CrossRef]
  17. R. D. Li, P. Kumar, W. L. Kath, and N. J. Kutz, IEEE Photonics Technol. Lett. 5, 669 (1993); R. D. Li, P. Kumar, and W. L. Kath, J. Lightwave Technol. 12, 541 (1994).
    [CrossRef]
  18. A. Mecozzi, W. L. Kath, P. Kumar, and C. G. Goedde, Opt. Lett. 19, 2050 (1994).
    [CrossRef] [PubMed]
  19. A. Niculae and W. L. Kath, Opt. Lett. 20, 557 (1995).
    [CrossRef] [PubMed]
  20. V. S. Grigoryan, A. Hasegawa, and A. Maruta, Opt. Lett. 20, 857 (1995).
    [CrossRef] [PubMed]
  21. V. I. Karpman and E. M. Maslov, Sov. Phys. JETP 46, 281 (1977); Zh. Eksp. Teor. Fiz. 73, 537 (1977).
  22. D. J. Kaup and A. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978).
    [CrossRef]
  23. K. Nozaki and N. Bekki, Physica D 21, 381 (1986).
    [CrossRef]
  24. S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
    [CrossRef]
  25. D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
    [CrossRef]
  26. The method of numerical solution of the Zakharov–Shabat scattering problem is described in G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
    [CrossRef]
  27. A similar discrepancy between the one- and two-soliton dynamics is also observed with other types of dissipative perturbations to the NLS equation, e.g., in the case of bandwidth-limited amplification: V. V. Afanasjev, Opt. Lett. 18, 790 (1993); Y. Kodama and S. Wabnitz, ibid. 18, 1311 (1993).
    [CrossRef] [PubMed]
  28. Y. Kodama and S. Wabnitz, Opt. Lett. 18, 1311 (1993).
    [CrossRef]
  29. V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
    [CrossRef]
  30. The role of the soliton chirp in suppressing the pulse-pair interactions has also been discussed for other types of perturbation, such as bandwidth-limited amplication and nonlinear gain: B. A. Malomed, Phys. Rev. A 44, 6954 (1991); I. M. Uzunov, R. Muschall, M. Golles, F. Lederer, and S. Wabnitz, Opt. Commun. 118, 577 (1995).
    [CrossRef] [PubMed]
  31. D. Marcuse, J. Lightwave Technol. 9, 356 (1991).
    [CrossRef]
  32. Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).
  33. M. Haelterman, Service d’ Optique Appliqué, Université Libre de Bruxelles, Bruxelles, Belgium (personal communication, 1995).
  34. K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
    [CrossRef]

1995 (4)

A. Niculae and W. L. Kath, Opt. Lett. 20, 557 (1995).
[CrossRef] [PubMed]

V. S. Grigoryan, A. Hasegawa, and A. Maruta, Opt. Lett. 20, 857 (1995).
[CrossRef] [PubMed]

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

1994 (4)

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

A. Mecozzi, W. L. Kath, P. Kumar, and C. G. Goedde, Opt. Lett. 19, 2050 (1994).
[CrossRef] [PubMed]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
[CrossRef]

J. N. Kutz, C. V. Hile, W. L. Kath, R. D. Li, and P. Kumar, J. Opt. Soc. Am. B 11, 2112 (1994).
[CrossRef]

1993 (6)

1992 (5)

The method of numerical solution of the Zakharov–Shabat scattering problem is described in G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
[CrossRef]

N. N. Akhmediev and S. Wabnitz, J. Opt. Soc. Am. B 9, 236 (1992).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[CrossRef] [PubMed]

1991 (5)

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, Opt. Lett. 16, 1841 (1991); Y. Kodama and A. Hasegawa, ibid. 17, 31 (1992).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

The role of the soliton chirp in suppressing the pulse-pair interactions has also been discussed for other types of perturbation, such as bandwidth-limited amplication and nonlinear gain: B. A. Malomed, Phys. Rev. A 44, 6954 (1991); I. M. Uzunov, R. Muschall, M. Golles, F. Lederer, and S. Wabnitz, Opt. Commun. 118, 577 (1995).
[CrossRef] [PubMed]

D. Marcuse, J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

1989 (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

1986 (2)

1983 (1)

1982 (1)

1981 (1)

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

1979 (1)

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

1978 (1)

D. J. Kaup and A. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978).
[CrossRef]

1977 (1)

V. I. Karpman and E. M. Maslov, Sov. Phys. JETP 46, 281 (1977); Zh. Eksp. Teor. Fiz. 73, 537 (1977).

Aceves, A. B.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Afanasjev, V. V.

Akhmediev, N. N.

Bekki, N.

K. Nozaki and N. Bekki, Physica D 21, 381 (1986).
[CrossRef]

Bishop, A. R.

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

Boffetta, G.

The method of numerical solution of the Zakharov–Shabat scattering problem is described in G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Cai, D.

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

Chinn, S. R.

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

Goedde, C. G.

Gordon, J. P.

Grigoryan, V. S.

Gronbech-Jensen, N.

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

Haelterman, M.

M. Haelterman, S. Trillo, and S. Wabnitz, Electron. Lett. 29, 119 (1993).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
[CrossRef]

M. Haelterman, Service d’ Optique Appliqué, Université Libre de Bruxelles, Bruxelles, Belgium (personal communication, 1995).

Hall, K. L.

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

Hasegawa, A.

Haus, H. A.

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, Opt. Lett. 16, 1841 (1991); Y. Kodama and A. Hasegawa, ibid. 17, 31 (1992).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

Hile, C. V.

Karpman, V. I.

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

V. I. Karpman and E. M. Maslov, Sov. Phys. JETP 46, 281 (1977); Zh. Eksp. Teor. Fiz. 73, 537 (1977).

Kath, W. L.

Kaup, D. J.

D. J. Kaup and A. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978).
[CrossRef]

Kodama, Y.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
[CrossRef]

Y. Kodama and S. Wabnitz, Opt. Lett. 18, 1311 (1993).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

A. Hasegawa and Y. Kodama, Opt. Lett. 7, 285 (1982).
[CrossRef] [PubMed]

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

Kumar, P.

Kutz, J. N.

Kutz, N. J.

R. D. Li, P. Kumar, W. L. Kath, and N. J. Kutz, IEEE Photonics Technol. Lett. 5, 669 (1993); R. D. Li, P. Kumar, and W. L. Kath, J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

Lai, Y.

Li, R. D.

J. N. Kutz, C. V. Hile, W. L. Kath, R. D. Li, and P. Kumar, J. Opt. Soc. Am. B 11, 2112 (1994).
[CrossRef]

R. D. Li, P. Kumar, W. L. Kath, and N. J. Kutz, IEEE Photonics Technol. Lett. 5, 669 (1993); R. D. Li, P. Kumar, and W. L. Kath, J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

J. N. Kutz, W. L. Kath, R. D. Li, and P. Kumar, Opt. Lett. 18, 802 (1993).
[CrossRef] [PubMed]

Ma, Y. C.

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

Malomed, B.

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

Malomed, B. A.

The role of the soliton chirp in suppressing the pulse-pair interactions has also been discussed for other types of perturbation, such as bandwidth-limited amplication and nonlinear gain: B. A. Malomed, Phys. Rev. A 44, 6954 (1991); I. M. Uzunov, R. Muschall, M. Golles, F. Lederer, and S. Wabnitz, Opt. Commun. 118, 577 (1995).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

Maruta, A.

Maslov, E. M.

V. I. Karpman and E. M. Maslov, Sov. Phys. JETP 46, 281 (1977); Zh. Eksp. Teor. Fiz. 73, 537 (1977).

Mecozzi, A.

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

Moores, J. D.

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Newell, A. C.

D. J. Kaup and A. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978).
[CrossRef]

Niculae, A.

Nozaki, K.

K. Nozaki and N. Bekki, Physica D 21, 381 (1986).
[CrossRef]

Osborne, A. R.

The method of numerical solution of the Zakharov–Shabat scattering problem is described in G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

Rauschenberg, K. A.

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

Raybon, G.

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

Romagnoli, M.

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Solov’ev, V. V.

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Swanson, E. A.

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Electron. Lett. 29, 119 (1993).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
[CrossRef]

Wabnitz, S.

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Electron. Lett. 29, 119 (1993).
[CrossRef]

S. Wabnitz, Opt. Lett. 18, 601 (1993).
[CrossRef]

Y. Kodama and S. Wabnitz, Opt. Lett. 18, 1311 (1993).
[CrossRef]

N. N. Akhmediev and S. Wabnitz, J. Opt. Soc. Am. B 9, 236 (1992).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

Electron. Lett. (4)

M. Haelterman, S. Trillo, and S. Wabnitz, Electron. Lett. 29, 119 (1993).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 30, 261 (1994).
[CrossRef]

Y. Kodama, M. Romagnoli, and S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991); H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

R. D. Li, P. Kumar, W. L. Kath, and N. J. Kutz, IEEE Photonics Technol. Lett. 5, 669 (1993); R. D. Li, P. Kumar, and W. L. Kath, J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

K. L. Hall, K. A. Rauschenberg, E. A. Swanson, S. R. Chinn, and G. Raybon, IEEE Photonics Technol. Lett. 7, 935 (1995).
[CrossRef]

J. Comput. Phys. (1)

The method of numerical solution of the Zakharov–Shabat scattering problem is described in G. Boffetta and A. R. Osborne, J. Comput. Phys. 102, 252 (1992).
[CrossRef]

J. Lightwave Technol. (2)

D. Marcuse, J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991); A. Hasegawa and Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992); Opt. Lett. 17, 745 (1992); Phys. Rev. A 47, 2344 (1993).
[CrossRef]

Opt. Fiber Technol. (1)

S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
[CrossRef]

Opt. Lett. (12)

Phys. Rev. A (1)

The role of the soliton chirp in suppressing the pulse-pair interactions has also been discussed for other types of perturbation, such as bandwidth-limited amplication and nonlinear gain: B. A. Malomed, Phys. Rev. A 44, 6954 (1991); I. M. Uzunov, R. Muschall, M. Golles, F. Lederer, and S. Wabnitz, Opt. Commun. 118, 577 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. Cai, A. R. Bishop, N. Gronbech-Jensen, and B. Malomed, Phys. Rev. E 49, 1677 (1994).
[CrossRef]

Physica D (2)

K. Nozaki and N. Bekki, Physica D 21, 381 (1986).
[CrossRef]

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. J. Kaup and A. C. Newell, Proc. R. Soc. London Ser. A 361, 413 (1978).
[CrossRef]

Sov. Phys. JETP (1)

V. I. Karpman and E. M. Maslov, Sov. Phys. JETP 46, 281 (1977); Zh. Eksp. Teor. Fiz. 73, 537 (1977).

Stud. Appl. Math. (1)

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

Other (1)

M. Haelterman, Service d’ Optique Appliqué, Université Libre de Bruxelles, Bruxelles, Belgium (personal communication, 1995).

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Figures (18)

Fig. 1
Fig. 1

Schematic of soliton storage ring (or transmission cell) with an erbium-doped fiber amplifier (EDFA) and (a) a cw or (b) a synchronously modulated pump.

Fig. 2
Fig. 2

Schematic of cw-activated clock recovery from a randomly modulated soliton train.

Fig. 3
Fig. 3

Two-soliton interactions with D(Z=0)=8 and different injected cw amplitudes: (a) attraction, (b) no interaction, (c) repulsion.

Fig. 4
Fig. 4

Numerically computed evolution of the imaginary part of the two-soliton eigenvalues for different initial pulse separations D and forcing amplitudes S0.

Fig. 5
Fig. 5

Evolution of the imaginary part of the two-soliton eigenvalues from inverse-scattering-transform perturbation theory.

Fig. 6
Fig. 6

Evolution with distance Z of pulse separation Δ, with S0=0.65δ and δ=0 (large dots), 0.05 (solid curve), 0.1 (dashed curve), 0.15 (dotted–dashed curve), and 0.2 (small dots).

Fig. 7
Fig. 7

Dependence of collision distance on injected cw amplitude for different initial pulse separations D. Solid curves: perturbation theory; dots: numerical results.

Fig. 8
Fig. 8

Simulation of (a) 20-Gbit/s and (b) 40-Gbit/s soliton sequences without cw injection.

Fig. 9
Fig. 9

Output pulse sequence (at 20 Mm) for the case of Fig. 8(a).

Fig. 10
Fig. 10

Same as Fig. 8, but with cw injection.

Fig. 11
Fig. 11

Output pulse sequence for the case of Fig. 10(a).

Fig. 12
Fig. 12

Evolution with distance of the total field energy for the cases of Fig. 8(a) (dashed curve) and Fig. 10(a) (solid curve).

Fig. 13
Fig. 13

Simulation of (a) 20-Gbit/s and (b) 40-Gbit/s soliton sequences with cw injection and random amplifier phases.

Fig. 14
Fig. 14

Output pulse sequence for the case of Fig. 13(a) and evolution with distance of the total field energy.

Fig. 15
Fig. 15

Same as Fig. 14, but for the case in Fig. 13(b).

Fig. 16
Fig. 16

Simulation of (a) 40-Gbit/s soliton train storage and (b) clock recovery from the periodic (0, 0, 1, 1, 1, 0, 1, 0) bit sequence.

Fig. 17
Fig. 17

Average soliton amplitudes after 10 Mm in a cw-pumped fiber loop memory.

Fig. 18
Fig. 18

Average soliton amplitudes after 50 km in a cw-pumped fiber loop train regenerator.

Equations (37)

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A(m)(z=0, t)=τA0(t)exp(iΦm)+ϱ exp(iϕ0)
×A(m-1)(z=L, t)+N(m)(t),
iAZ(m)+ik0At(m)-k02Att(m)+γ|A(m)|2A(m)=-iαA(m),
iuZ+12uTT+|u|2u=iR-iδu-iS exp(iΛZ)+Sn,
us(T, Z)=η sech{η[T-ξ(Z)]}exp[-iκ(Z)T+iθ(Z)].
dηdZ=- Re[R(us, us*)exp(-iφ)]sech τ dτ,
dκdZ=-- Im[R(us, us*)exp(-iφ)]sech τ tanh τ dτ,
dξdZ=-κ+1η2- Re[R(us, us*)exp(-iφ)]τ sech τ dτ,
dθdZ=η2-κ22+ξ dκdZ+1η- Im[R(us, us*)exp(-iφ)]×sech τ(1-τ tanh τ)dτ,
L(Z)Ψ=ζΨ,
L=i T-u*u-i T,
dηdZ=-2δη+(sin χ)(S0-S2ξ2)C0-S2η2C1-2ξS2η(cos χ)I0,
dκdZ=-(sin χ)κη(S0-S2ξ2)C0-S2η22I0+κηC1-2ξS2η(cos χ)C0-κηI0,
dξdZ=-κ-cos χη2I0(S2ξ2-S0)-S2η2I1-2ξS2η(sin χ)C1,
dθdZ=η2-κ22+ξκ˙+2ξS2 sin χη2I0+κηC1-cos χηκI0η(S0-S2ξ2)+S2η22C1-κηI1,
dηdZ=-2δη+S0π sech β sin χ,
dκdZ=-πκS0ηsech β sin χ,
dξdZ=-κ+π2S02η2sech β tanh β cos χ,
dθdZ=η2-κ22+ξκ˙-π2κS02η2sech β tanh β cos χ,
dηdZ=-2δη+S0π sin χ,  dχdZ=Λ-η22.
d(δκ)dZ=-π(sin χ*)S0-3π2S24δκ+σκ
-γ11δκ+σκ,
d(δξ)dZ=-π3S2 sin χ*2δξ-1-π3 cos χ*4×S0-5π2S24δκ+σξ
-γ22δξ-γ21δκ+σξ,
u2s(Z=0, T)=sechT-D2exp(iθ0)
+sechT-D2exp(iθ0)+c1,
dηndZ=2γn-(R*ψ1n2-Rψ2n2)dT,
dσndZ=12ηn2+Reγn-R* ψ12ζ-R ψ22ζζ=ζndT,
ζψ12ζ=ζn=2iTψ1n2-8l=12 γl*ψ1nψ2l*(ηl+ηn)2×exp[-i(ηn+ηl)T].
ζψ22ζ=ζn=2iTψ2n2+8l=12 γl*ψ2nψ1l*(ηl+ηn)2×exp[-i(ηn+ηl)T].
u(T, Z)=u1(T, Z)+u2(T, Z),
q˙=-4η3 exp(-η|D|)-qS0πηsin χ,
D˙=2q1-S0π34η3cos χ2q,
(|C|2-Λ)C=-iδC-iS.
R(v)=-δv+i2c|v|2+ic*v2,
dηdZ=-2δη+π2|C|η12 sin χ-2δη+πS0η22Λ,
dχdZ=Λ-η22+π|C|η cos χΛ-η22.

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