Abstract

Optimal allocation of amplifiers in a dispersion-managed line is theoretically derived by means of minimizing the collision-induced frequency shift in a two-channel wavelength-division-multiplexed soliton transmission system. Almost complete cancellation of the frequency shift can be obtained for such a system with any strength of dispersion management.

© 1999 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  2. H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
    [CrossRef]
  3. J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
    [CrossRef]
  4. H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
    [CrossRef]
  5. A. Hasegawa and Y. Kodama, Opt. Lett. 16, 1385 (1991).
    [CrossRef] [PubMed]
  6. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), pp. 179–183.
  7. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  8. Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
    [CrossRef]
  9. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  10. S. Wabnitz, Y. Kodama, and A. B. Aceves, Opt. Fiber Technol. 1, 187 (1995).
    [CrossRef]

1998 (1)

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

1997 (3)

1996 (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

1995 (1)

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

1991 (2)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

A. Hasegawa and Y. Kodama, Opt. Lett. 16, 1385 (1991).
[CrossRef] [PubMed]

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Aceves, A. B.

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

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Devaney, J. F. L.

Doran, N. J.

J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Forysiak, W.

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Opt. Lett. 16, 1385 (1991).
[CrossRef] [PubMed]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), pp. 179–183.

Inoue, T.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

Kato, H.

H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Kodama, Y.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
[CrossRef]

Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
[CrossRef]

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

A. Hasegawa and Y. Kodama, Opt. Lett. 16, 1385 (1991).
[CrossRef] [PubMed]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), pp. 179–183.

Kumar, S.

Maruta, A.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

Y. Kodama, S. Kumar, and A. Maruta, Opt. Lett. 22, 1689 (1997).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Niculae, A. M.

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Sugahara, H.

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
[CrossRef]

Wabnitz, S.

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

Electron. Lett. (3)

H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
[CrossRef]

H. Sugahara, T. Inoue, A. Maruta, and Y. Kodama, Electron. Lett. 34, 902 (1998).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Opt. Fiber Technol. (1)

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

Opt. Lett. (3)

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Other (1)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995), pp. 179–183.

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Figures (4)

Fig. 1
Fig. 1

Dispersion map and locus of the pulse in a two-step dispersion-managed line.

Fig. 2
Fig. 2

(a) Results of Eqs.  (6) and (7), which yield no residual frequency shift for the lossless case. (b), (c) Typical loci of the pulses for types A and B, respectively, for ΔBZd=4Ts.

Fig. 3
Fig. 3

Loci of pulse and frequency shifts for the lossy case. Solid (dashed) curves, ΔD=10 and Za/Zd=0.167 0.083, respectively, which correspond to type  B (A).

Fig. 4
Fig. 4

Dispersion map in which the residual frequency shift is less than 0.3 for the lossy case. Open circles and crosses, sech and Gaussian ansatzes, respectively.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

iuZ+dZ22uT2+a2Zu2u=0,
dΔκdZ=4a2ZE0-u22u12TdT,dΔTdZ=-ΔB+Δκdα,
TnαZ=-ΔB2dαZ-Za+nZd
ddZΔκ=1ΔBdαddZFΔTZ,
Δκ=1ΔB1d1-1d2F2TlαXα-F2Tmα0,
TlαXα-Tmα0=0dα=2-1αl-m+1/2+1
TlαXα+Tmα0=0ZaZd=l+m2dα--1α4.

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