Abstract

Dispersion-managed solitons with in-line all-optical regeneration are shown to be subject to amplitude and timing-jitter instabilities. We identify and discuss the different natures of these instabilities by means of a linear stability analysis, which is in good agreement with the full numerical solutions of the governing equations. Stable pulse propagation can be achieved through appropriate choices of dispersion map and pulse energy.

© 2000 Optical Society of America

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References

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  1. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).
  2. M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
    [CrossRef]
  3. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [CrossRef]
  4. P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
    [CrossRef]
  5. O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
    [CrossRef]
  6. F. Merlaud and T. Georges, presented at the European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.
  7. M. Matsumoto, Opt. Lett. 23, 1901 (1998).
    [CrossRef]
  8. E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.
  9. S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999).
    [CrossRef]
  10. T. Hirooka and S. Wabnitz, Opt. Fiber Technol. 6, 109 (2000).
    [CrossRef]
  11. E. A. Coddington and N. Levison, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), pp. 78–81.
  12. A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
    [CrossRef]

2000 (4)

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

T. Hirooka and S. Wabnitz, Opt. Fiber Technol. 6, 109 (2000).
[CrossRef]

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

1999 (1)

S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999).
[CrossRef]

1998 (1)

1995 (1)

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

1991 (1)

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Audouin, O.

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

Blache, F.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Bouchoule, S.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Brindel, P.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

Brindl, P.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Capobianco, A. D.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

Coddington, E. A.

E. A. Coddington and N. Levison, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), pp. 78–81.

Coquelin, A.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Dany, B.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

Desurvire, E.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Duchet, C.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Georges, T.

F. Merlaud and T. Georges, presented at the European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

Goix, M.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Grard, E.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Hasegawa, A.

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

Hirooka, T.

T. Hirooka and S. Wabnitz, Opt. Fiber Technol. 6, 109 (2000).
[CrossRef]

Kodama, Y.

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

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Le Lourec, P.

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

Leclerc, O.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Levison, N.

E. A. Coddington and N. Levison, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), pp. 78–81.

Matsumoto, M.

S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999).
[CrossRef]

M. Matsumoto, Opt. Lett. 23, 1901 (1998).
[CrossRef]

Merlaud, F.

F. Merlaud and T. Georges, presented at the European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Nouchi, P.

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Pincemin, E.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

Rouvillain, D.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

Shen, A.

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Taga, H.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Tonello, A.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

Turitsyn, S. K.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

Wabnitz, S.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

T. Hirooka and S. Wabnitz, Opt. Fiber Technol. 6, 109 (2000).
[CrossRef]

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

Waiyapot, S.

S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999).
[CrossRef]

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

Electron. Lett. (4)

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
[CrossRef]

P. Brindel, O. Leclerc, D. Rouvillain, B. Dany, E. Desurvire, and P. Nouchi, Electron. Lett. 36, 61 (2000).
[CrossRef]

O. Leclerc, P. Brindl, D. Rouvillain, B. Dany, E. Pincemin, E. Desurvire, C. Duchet, A. Shen, F. Blache, E. Grard, A. Coquelin, M. Goix, S. Bouchoule, and P. Nouchi, Electron. Lett. 36, 58 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Waiyapot and M. Matsumoto, IEEE Photon. Technol. Lett. 11, 1408 (1999).
[CrossRef]

Opt. Commun. (1)

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, Opt. Commun. 175, 103 (2000).
[CrossRef]

Opt. Fiber Technol. (1)

T. Hirooka and S. Wabnitz, Opt. Fiber Technol. 6, 109 (2000).
[CrossRef]

Opt. Lett. (1)

Other (4)

E. Pincemin, P. Le Lourec, O. Audouin, B. Dany, and S. Wabnitz, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 45–46.

E. A. Coddington and N. Levison, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), pp. 78–81.

F. Merlaud and T. Georges, presented at the European Conference on Optical Communication, Madrid, Spain, September 20–24, 1998.

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

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Figures (5)

Fig. 1
Fig. 1

Left, instability gain G for pulse energies of A, 25 fJ, B, 50 fJ, and C, 100 fJ; D, for pulse energy of 25 fJ and smaller local dispersions ± 0.25   ps / km   nm . Right, Gain G of (solid curve) amplitude and (dashed curve) timing instability for 25 fJ. The gray regions represent unstable configurations.

Fig. 2
Fig. 2

Top, pulse amplitude instability. Solid (dashed) curve, initial positive (negative) energy fluctuation. Bottom, timing instability: pulse center shifts for (solid curve) positive or (dashed curve) negative initial frequency seed.

Fig. 3
Fig. 3

Evolution of fractional soliton power shift Δ P / P for IM at A, z = 10   km ; B, z = 25   km ; C, z = 15   km ; D, z = 17   km ; E, z = 18   km ; E, z = 18   km ; F, z = 20.5   km . The gray scale at the right represents LSA gain G dB / Mm .

Fig. 4
Fig. 4

LSA gains G versus control device position in the map for pulse energy of 100 fJ (the gray regions represent unstable configurations). Top, with IM and DSF - , DSF + map; middle, with IM and map sequence shift; bottom, with map sequence DSF + , DSF - and both GF (126 GHz) and IM.

Fig. 5
Fig. 5

Left, transmission after 24 Mm with IM’s at z = 18.5   km (stable 1’s and 0’s) and average power of 0 dBm. Right, with IM’s in z = 0 (unstable case).

Equations (1)

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d A / d z = - DbA , d τ / d z = 2 Db τ , d b / d z = - 2 b 2 D - γ exp - 2 Γ z A 2 2 2 τ 2 + D 2 τ 4 , d κ / d z = 0 , d ξ / d z = - κ D .

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