Abstract

Soliton timing jitter that is due to amplifier noise has been studied extensively. In wavelength-multiplexed soliton systems jitter also results from collisions between solitons on different channels. We derive an expression for the variance in pulse arrival times because of such collisions and predict system performance using this result. Jitter depends not only on perturbations to the fiber but also on the encoding of information. When the expression is applied to a system with loss and amplification, it is shown that extensive wavelength multiplexing may significantly enhance soliton communication systems.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [Crossref]
  2. S. Chakravarty, M. J. Ablowitz, J. R. Sauer, R. B. Jenkins, Opt. Lett. 20, 136 (1995).
    [Crossref] [PubMed]
  3. P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
    [Crossref]
  4. A. Mecozzi, H. A. Haus, Opt. Lett. 17, 988 (1992).
    [Crossref] [PubMed]
  5. B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.
  6. J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).
    [Crossref] [PubMed]
  7. L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
    [Crossref]
  8. G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 1983), Chap. 8, p. 234.
  9. F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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1995 (1)

1993 (1)

1992 (1)

1991 (3)

P. 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]

1986 (2)

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

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

Aakjer, T.

Ablowitz, M. J.

Andrekson, P.

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

Chakravarty, S.

Corbett, P. C.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Evangelides, S. G.

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

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Evankow, J. D.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Ferguson, G. A.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Gordon, J. P.

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

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

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

Harvey, G. T.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Hasegawa, A.

Haus, H. A.

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

Jenkins, R. B.

Keiser, G.

G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 1983), Chap. 8, p. 234.

Kodama, Y.

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

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

Koren, U.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Korotky, S. K.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Logan, R. A.

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

Lucero, A.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Mamyshev, P. V.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Matera, F.

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

Mecozzi, A.

Mills, M. A.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Mizrahi, V.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Mollenauer, L. F.

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

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Nagel, J.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Nyman, B. M.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Olsson, N. A.

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

Povlsen, J. H.

Romagnoli, M.

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

Rottwitt, K.

Sauer, J. R.

Saylors, M. L.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Settembre, M.

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

Simpson, J. R.

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

Stark, H.

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1986), Chap. 2, p. 83.

Strasser, T. A.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Sulhoff, J.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Tanbun-Ek, T.

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

Veselka, J. J.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

Wabnitz, S.

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

Wecht, K. W.

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

Woods, J. W.

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1986), Chap. 2, p. 83.

Zyskind, J.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

IEEE J. Quantum Electron. (1)

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

J. Lightwave Technol. (2)

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

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

Opt. Lett. (5)

Other (4)

H. Stark, J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1986), Chap. 2, p. 83.

G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 1983), Chap. 8, p. 234.

F. Matera, M. Romagnoli, M. Settembre, S. Wabnitz, Y. Kodama, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 133.

B. M. Nyman, S. G. Evangelides, G. T. Harvey, L. F. Mollenauer, P. V. Mamyshev, M. L. Saylors, S. K. Korotky, U. Koren, V. Mizrahi, T. A. Strasser, J. J. Veselka, J. D. Evankow, A. Lucero, J. Nagel, J. Sulhoff, J. Zyskind, P. C. Corbett, M. A. Mills, G. A. Ferguson, in Optical Fiber Communications, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD21.

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Figures (3)

Fig. 1
Fig. 1

(a) Shift in inverse group velocity with and without attenuation and (b) the permanent wavelength shift with amplifiers at zc = 0, 25, 50 km.

Fig. 2
Fig. 2

Timing shifts δt at two collisions and the absence of a shift if no collision occurs.

Fig. 3
Fig. 3

Soliton collision-limited (a) length and (b) through-put for a 10−9 bit-error rate.

Equations (7)

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

Δ λ ( z c ) = m = 1 c m sin { 2 π m z c / L a - tan - 1 [ 2 π m / ( α L a ) ] } ,
δ t res = D ¯ - L δ λ ( z ) d z D ¯ Δ λ ( z c ) ( L - z c ) .
Δ t 1 = j = 1 n Δ b j D ¯ Δ λ j ( L - z j ) ,
Δ t 1 = T Λ j = 1 n j Δ b j Δ λ j ,
Δ t 2 1 = ( T Λ ) 2 j = 1 n j 2 Δ λ 2 2 ( T Λ ) 2 n 3 6 Δ λ 2 ,
Δ t 2 p q = 1 q p N ( T Λ p q ) 2 ( L Z c p q ) 3 Δ λ 2 p q 6 ,
L 1.48 τ max p [ q ( D ¯ p q ) 3 Λ p q Δ λ 2 p q ] 1 / 3

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