Abstract

Initial overlap between solitons propagating at different carrier frequencies gives rise to a change in the frequencies of the solitons. The frequency change can have a severe effect on the transmission system because it will result in a time displacement of the solitons that is due to the fiber dispersion. The frequency change caused by initial overlap between two solitons at different carrier frequencies is calculated for a transmission system with periodic gain and loss.

© 1993 Optical Society of America

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References

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  1. L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, L. G. Cohen, Opt. Lett. 15, 1203 (1990).
    [CrossRef] [PubMed]
  2. M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
    [CrossRef]
  3. L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
    [CrossRef]
  4. P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
    [CrossRef]
  5. Y. Kodama, A. Hasegawa, Opt. Lett. 16, 208 (1991).
    [CrossRef] [PubMed]
  6. L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  7. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  8. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
    [CrossRef] [PubMed]

1992

M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
[CrossRef]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

1991

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

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

Y. Kodama, A. Hasegawa, Opt. Lett. 16, 208 (1991).
[CrossRef] [PubMed]

A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
[CrossRef] [PubMed]

1990

1983

Andrekson, P. A.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Cohen, L. G.

Evangelides, S. G.

Gordon, J. P.

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Kodama, Y.

Lai, Y.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Logan, R. A.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Mecozzi, A.

Mollenauer, L. F.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

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

L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, L. G. Cohen, Opt. Lett. 15, 1203 (1990).
[CrossRef] [PubMed]

Moores, J. D.

Nakazawa, M.

M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, L. G. Cohen, Opt. Lett. 15, 1203 (1990).
[CrossRef] [PubMed]

Nyman, B. M.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Olsson, N. A.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Simpson, J. R.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R. Simpson, L. G. Cohen, Opt. Lett. 15, 1203 (1990).
[CrossRef] [PubMed]

Suzuki, K.

M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
[CrossRef]

Tanbun-Ek, T.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Wecht, K. W.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Yamada, E.

M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
[CrossRef]

Electron. Lett.

M. Nakazawa, K. Suzuki, E. Yamada, Electron. Lett. 28, 1046 (1992).
[CrossRef]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

J. Lightwave Technol.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

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

Opt. Lett.

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Figures (1)

Fig. 1
Fig. 1

Frequency change δf caused by the initial overlap between two solitons with τFWHM = 20 ps and Δf = 157 GHz. The distance between amplifiers is LPert = 35 km. δf is calculated for the case of loss α = 0 dB/km and α = 0.25 dB/km for different β″ values as a function of the initial overlap.

Equations (15)

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| φ | = A sech [ a ( t + θ β ω 0 z ) ] , | ψ | = A sech [ a ( t θ + β ω 0 z ) ] ,
δ ω res = 2 a 2 ω 0 [ 2 a θ cosh ( 2 a θ ) sinh ( 2 a θ ) sinh 3 ( 2 a θ ) ] .
φ z = α ( z ) 2 φ i 2 β 2 φ t 2 + i γ | φ | 2 φ ,
φ z = i 2 β 2 φ t 2 + i γ | φ | 2 φ G ( z ) .
φ z = i 2 β 2 φ t 2 + i γ ( | φ | 2 + 2 | ψ | 2 ) φ G ( z ) .
ω z = γ G ( z ) Θ 2 | φ | 2 t | ψ | 2 d t .
| φ | = A sech [ a ( t + θ β ω 0 z ) ] , | ψ | = A sech [ a ( t θ + β ω 0 z ) ] .
ω z = 2 A 2 a 2 γ G ( z ) sech 2 [ a ( t + θ β ω 0 z ) ] × tanh [ a ( t + θ β ω 0 z ) ] × sech 2 [ a ( t θ + β ω 0 z ) ] d t .
δ ω res = 2 A 2 a 2 γ G ( z ) sech 2 [ a ( t + θ β ω 0 z ) ] × tanh [ a ( t + θ β ω 0 z ) ] × sech 2 [ a ( t θ + β ω 0 z ) ] d t d z .
G ( z ) = g ˜ ( k ) exp ( i k z ) d k .
δ ω res = a 2 ω 0 g ˜ ( k ) ξ + 2 a θ exp [ i k a β ω 0 ( ξ η 2 + a θ ) ] × sech 2 ( η ) tanh ( η ) sech 2 ( ξ ) d η d ξ d k .
G ( z ) = n = g ˜ n exp ( i 2 π n z / L Pert ) ,
g ˜ n = 1 L Pert 0 L pert g ( z ) exp ( i 2 π n z / L Pert ) d z .
δ ω res = a 2 ω 0 ξ + 2 a θ { n = g ˜ n × exp [ i 2 π n a β ω 0 L Pert ( ξ η 2 + a θ ) ] } × sech 2 ( η ) tanh ( η ) sech 2 ( ξ ) d η d ξ .
g ˜ n = α L Pert α L Pert + i 2 π n .

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