Abstract

We show that collision-induced frequency shifts in wavelength-division-multiplexed (WDM) soliton transmission systems are strongly suppressed with increasing dispersion management. We predict new oscillations in the residual frequency shift response, owing to the relative motion induced by the dispersion map, and demonstrate a direct correlation between these oscillations and the modified soliton-collision dynamics. Simple analytical expressions for the oscillation minima are obtained, and implications for WDM soliton system design are discussed.

© 1997 Optical Society of America

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  1. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [Crossref]
  2. R. B. Jenkins, J. R. Sauer, S. Chakravarty, and M. J. Ablowitz, Opt. Lett. 20, 1964 (1995).
    [Crossref] [PubMed]
  3. S. G. Evangelides and J. P. Gordon, J. Lightwave Technol. 14, 1639 (1996).
    [Crossref]
  4. P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 396 (1996).
    [Crossref] [PubMed]
  5. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, Electron. Lett. 31, 2027 (1995).
    [Crossref]
  6. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [Crossref]
  7. J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
    [Crossref]
  8. L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper PD22-2.
  9. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
    [Crossref]
  10. D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.
  11. J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.
  12. E. A. Golovchenko, A. N. Pilipetskii, and G. R. Menyuk, in OFC, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), p. 307.
  13. H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
    [Crossref]
  14. S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
    [Crossref]
  15. S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
    [Crossref]
  16. W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
    [Crossref] [PubMed]
  17. M. K. Chin and X. Y. Tang, IEEE Photon. Technol. Lett. 9, 538 (1997).
    [Crossref]
  18. N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
    [Crossref]

1997 (7)

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[Crossref]

S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
[Crossref]

W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
[Crossref] [PubMed]

M. K. Chin and X. Y. Tang, IEEE Photon. Technol. Lett. 9, 538 (1997).
[Crossref]

1996 (4)

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[Crossref]

S. G. Evangelides and J. P. Gordon, J. Lightwave Technol. 14, 1639 (1996).
[Crossref]

P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 396 (1996).
[Crossref] [PubMed]

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

1995 (2)

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

R. B. Jenkins, J. R. Sauer, S. Chakravarty, and M. J. Ablowitz, Opt. Lett. 20, 1964 (1995).
[Crossref] [PubMed]

1991 (1)

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

Ablowitz, M. J.

Akiba, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

Audouin, O.

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[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]

Cardinal, S.

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[Crossref]

Carter, C. R.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

Carter, G. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

Chakravarty, S.

Charbonnier, B.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Chin, M. K.

M. K. Chin and X. Y. Tang, IEEE Photon. Technol. Lett. 9, 538 (1997).
[Crossref]

Desurvire, E.

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[Crossref]

Devaney, J. F. L.

W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
[Crossref] [PubMed]

J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.

Devaux, F.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Doran, N. J.

W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
[Crossref] [PubMed]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[Crossref]

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

J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.

Edagawa, N.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

Evangelides, S. G.

S. G. Evangelides and J. P. Gordon, J. Lightwave Technol. 14, 1639 (1996).
[Crossref]

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

Favre, F.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Forysiak, W.

W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
[Crossref] [PubMed]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[Crossref]

J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.

Georges, T.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Golovchenko, E. A.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

E. A. Golovchenko, A. N. Pilipetskii, and G. R. Menyuk, in OFC, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), p. 307.

Gordon, J. P.

S. G. Evangelides and J. P. Gordon, J. Lightwave Technol. 14, 1639 (1996).
[Crossref]

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

Hamaide, J. P.

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[Crossref]

Hasegawa, A.

S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
[Crossref]

Henry, M.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Jacob, J. M.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

Jenkins, R. B.

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

S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
[Crossref]

Kumar, S.

S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
[Crossref]

Le Guen, D.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Macé, L.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Mamyshev, P. V.

P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 396 (1996).
[Crossref] [PubMed]

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper PD22-2.

Menyuk, G. R.

E. A. Golovchenko, A. N. Pilipetskii, and G. R. Menyuk, in OFC, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), p. 307.

Michaud, G.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Mollenauer, L. F.

P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 396 (1996).
[Crossref] [PubMed]

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

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper PD22-2.

Morita, I.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

Moulinard, M. L.

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

Neubelt, M. J.

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper PD22-2.

Pilipetskii, A. N.

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

E. A. Golovchenko, A. N. Pilipetskii, and G. R. Menyuk, in OFC, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), p. 307.

Sauer, J. R.

Smith, N. J.

W. Forysiak, J. F. L. Devaney, N. J. Smith, and N. J. Doran, Opt. Lett. 22, 600 (1997).
[Crossref] [PubMed]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[Crossref]

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

J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.

Sugahara, H.

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

Suzuki, M.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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]

Tang, X. Y.

M. K. Chin and X. Y. Tang, IEEE Photon. Technol. Lett. 9, 538 (1997).
[Crossref]

Yamamoto, S.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

Electron. Lett. (7)

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

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

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, and S. Akiba, Electron. Lett. 33, 691 (1997).
[Crossref]

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

S. Cardinal, E. Desurvire, J. P. Hamaide, and O. Audouin, Electron. Lett. 33, 77 (1997).
[Crossref]

S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
[Crossref]

N. J. Smith, W. Forysiak, and N. J. Doran, Electron. Lett. 32, 2085 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (2)

M. K. Chin and X. Y. Tang, IEEE Photon. Technol. Lett. 9, 538 (1997).
[Crossref]

J. M. Jacob, E. A. Golovchenko, A. N. Pilipetskii, G. M. Carter, and C. R. Carter, IEEE Photon. Technol. Lett. 9, 130 (1997).
[Crossref]

J. Lightwave Technol. (2)

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

S. G. Evangelides and J. P. Gordon, J. Lightwave Technol. 14, 1639 (1996).
[Crossref]

Opt. Lett. (3)

Other (4)

D. Le Guen, F. Favre, M. L. Moulinard, M. Henry, G. Michaud, L. Macé, F. Devaux, B. Charbonnier, and T. Georges, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper PD17-1.

J. F. L. Devaney, W. Forysiak, N. J. Smith, and N. J. Doran, in OFC, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 306.

E. A. Golovchenko, A. N. Pilipetskii, and G. R. Menyuk, in OFC, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), p. 307.

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper PD22-2.

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Figures (4)

Fig. 1
Fig. 1

Surface plot of the maximum residual frequency shift of solitons in a two-step dispersion-managed transmission line. The normalized excess dispersion, A1=Δ1-1L1/La, ranges from -5 to 5, and first fiber lengths range from L1/La=0.05 to L1/La=0.95. Parameters: La=50 km, α=0.2 dB/km, τ=20 ps (FWHM), Da=0.5 ps/nmkm, and Δλ=1.6 nm.

Fig. 2
Fig. 2

Slice through surface plot in Fig.  1 for a symmetric map with L1/La=0.5.

Fig. 3
Fig. 3

a, Residual frequency shift as a function of collision center for L1/La=0.5 and A1=1.5. b, Numerical simulations of residual frequency shifts plotted over one cycle of initial pulse separation. Other parameters are as in Fig.  1.

Fig. 4
Fig. 4

Collision mechanism for L1/La=0.5 and a, A1=1.5; b, A1=2.5.

Equations (3)

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

δΔf2=0.1432LaLcτ2 Δfn=1Imgnn3x4sinh2nx,
gn=Λ2 expinϕc1-exp-αL1+inϕ1αLa+i2πnΔ1+exp-αL1+inϕ1-exp-αLaαLa+i2πnΔ2.
ϕ1=2π/LaΔ1L1=2πm.

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