Abstract

We investigate collisions between solitons in a lossless two-channel wavelength-division multiplexed system with strong dispersion management. Numerical results show that the net frequency shift that is due to interchannel collisions is at least 1 order of magnitude smaller than predicted by adiabatic theories. A modified theoretical analysis is presented and shown to be in good agreement with the numerical results.

© 1998 Optical Society of America

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  1. A. Hasegawa and Y. Kodama, Opt. Lett. 16, 1385 (1991).
    [CrossRef] [PubMed]
  2. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
    [CrossRef]
  3. C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
    [CrossRef]
  4. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  5. T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997).
    [CrossRef] [PubMed]
  6. M. Matsumoto, Opt. Lett. 22, 1238 (1997).
    [CrossRef] [PubMed]
  7. S. Wabnitz, Opt. Lett. 21, 638 (1996).
    [CrossRef] [PubMed]
  8. J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
    [CrossRef]
  9. S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
    [CrossRef]
  10. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, IEEE J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  11. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
    [CrossRef]
  12. I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
    [CrossRef]
  13. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]

1997 (6)

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

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 22, 793 (1997).
[CrossRef] [PubMed]

M. Matsumoto, Opt. Lett. 22, 1238 (1997).
[CrossRef] [PubMed]

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

1996 (2)

S. Wabnitz, Opt. Lett. 21, 638 (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 (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

1993 (1)

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

1991 (2)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, IEEE 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]

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]

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[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]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (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, IEEE J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Forysiak, W.

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

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Gabitov, I.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

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

Hasegawa, A.

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

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

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

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

Kodama, Y.

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

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

Kumar, S.

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

Kurtzke, C.

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

Matsumoto, M.

Menyuk, C. R.

Mollenauer, L. F.

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

Niculae, A. M.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

Pilipetskii, A. N.

Shapiro, E. G.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Smith, N. J.

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

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Turitsyn, S. K.

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Wabnitz, S.

Yu, T.

Electron. Lett. (3)

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

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

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1726 (1997).
[CrossRef]

IEEE J. Lightwave Technol. (1)

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

IEEE Photon. Technol. Lett. (1)

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Opt. Commun. (1)

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, Opt. Commun. 134, 317 (1997).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

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

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Figures (4)

Fig. 1
Fig. 1

Symmetric dispersion map used in our analysis (upmost curve) and the evolution of the pulse power and width over several dispersion periods (lower curves). β1=-19.84 ps2/km, β2=18.56 ps2/km, βave=-0.64 ps2/km, L=25 km.

Fig. 2
Fig. 2

Comparison of net frequency shift for adiabatic theory, numerics, and theory using enhanced power solitons for sech input and for Gaussian input. βave=-0.64 ps2/km.

Fig. 3
Fig. 3

Maximum width versus dispersion map strength for the variational method for both sech (dashed curve) and Gaussian (solid curve) inputs compared with numerical results (circles). βave=-0.64 ps2/km, T0=20 ps.

Fig. 4
Fig. 4

Ratio between the net frequency shift obtained theoretically with the inclusion of power and width enhancement and the net frequency shift obtained with the adiabatic theory. Solid curve, Gaussian input; dashed curve, sech input.

Equations (11)

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

S=LΔβ/T02,
u=secht+Ωzexp-iΩt+i1-Ω2z/2,
δΔf2=8Lπ3τz0n=1gnn3x4sinh2nx,
gn=Δβ/nπβave1+Δβ/2βave2sinnπ2Δβ2βave+1sinnπzcollL,
u=amin exp-t+Ωz2/2bmax2
δΔf2enh=amin28Lπ3τz0n=1gnn3xbmax4sinh2nxbmax,
δΔf2enh=amin2bmax2Lπτz0n=1gnnx¯2 exp-nx¯2
a2b=η2,
bz=2βzβavebμ,
μz+2βzβaveμ2=βzC12βaveb4-η2C2b3.
bnon=2C2η2βaveC1β12bl-bl-1+1-1bl21/2×sinh-1bl2-11/2.

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