Abstract

We develop a perturbation theory to analytically calculate the effects of complete and incomplete interchannel collisions of Gaussian pulses in a wavelength-division-multiplexed system with strong dispersion management. We show that, for complete collisions, the collision-induced frequency shift of a Gaussian pulse is negligible, whereas its position shift is significant and can be found in a simple analytical form. For strong dispersion management we find that incomplete collisions can be neglected, whereas for dispersion management of moderate strength the contribution of the incomplete collisions can be significant. The analytical predictions are in satisfactory agreement with numerical results. We also give an estimate of the limit imposed on the transmission distance by such collisions.

© 1998 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. F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef] [PubMed]
  3. S. Wabnitz, Opt. Lett. 21, 638 (1996); S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997); H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997); J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
    [CrossRef] [PubMed]
  4. A. M. Niculae, W. Forysiak, and N. J. Doran, in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 184.
  5. J. N. Kurtz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
    [CrossRef]
  6. T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
    [CrossRef]
  7. T. Hirooka and A. Hasegawa, Opt. Lett. 23, 768 (1998).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  9. A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
    [CrossRef]
  10. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
    [CrossRef]

1998 (4)

1997 (1)

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
[CrossRef]

1996 (1)

1995 (1)

F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef] [PubMed]

1991 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

Berntson, A.

Doran, N. J.

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef] [PubMed]

A. M. Niculae, W. Forysiak, and N. J. Doran, in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 184.

Evangelides, S. G.

J. N. Kurtz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
[CrossRef]

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

Forysiak, W.

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23, 900 (1998).
[CrossRef]

F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef] [PubMed]

A. M. Niculae, W. Forysiak, and N. J. Doran, in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 184.

Golovchenko, E. A.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
[CrossRef]

Gordon, J. P.

J. N. Kurtz, P. Holmes, S. G. Evangelides, and J. P. Gordon, J. Opt. Soc. Am. B 15, 87 (1998).
[CrossRef]

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

Hasegawa, A.

Hirooka, T.

Holmes, P.

Kaup, D. J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Knox, F. M.

F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef] [PubMed]

Kurtz, J. N.

Lakoba, T. I.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Malomed, B. A.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Menyuk, C. R.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (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.

A. M. Niculae, W. Forysiak, and N. J. Doran, in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 184.

Nijhof, J. H. B.

Pilipetskii, A. N.

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
[CrossRef]

Wabnitz, S.

Yang, J.

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Electron. Lett. (1)

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
[CrossRef]

J. Lightwave Technol. (2)

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

F. M. Knox, W. Forysiak, and N. J. Doran, J. Lightwave Technol. 13, 1955 (1995); N. J. Smith and N. J. Doran, Opt. Lett. 21, 570 (1996); M. Nakazawa and H. Kubota, Electron. Lett. 31, 216 (1995); R. Grimshaw, J. He, and B. A. Malomed, Phys. Scr. 53, 385 (1996); N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996); I. Morita, M. Suzuki, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, IEEE Photon. Technol. Lett. 8, 1573 (1996); I. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, Opt. Commun. 149, 366 (1998).
[CrossRef]

Opt. Lett. (3)

Other (2)

A. M. Niculae, W. Forysiak, and N. J. Doran, in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 184.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

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Tables (1)

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Table 1 Comparison between the Analytically Predicted and Numerically Found Collision-Induced PS’s of the Gaussian Pulsea

Equations (14)

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

2iuz+cuτ+Dzuττ+D¯uuττ+2u2+2v2u=0,
2ivz+Dzvττ+D¯vvττ+2v2+2u2v=0,
u0z,τ=τ0Puτ02+2iΔz1/2×exp-τ-cz2τ02+2iΔz+iϕu,
uz,τ=u0z,τ-Tzexp-iωτ-Tz+iψz,
dT/dz=-ωDz+D¯u.
22D¯u=-Puτ02Sln1+S2+S-2S1+S2-1/2,
dωdz=23/2Pvτ04czτ04+4Δ2z3/2exp-c2τ02z2τ04+4Δ2z,
-+2znFzexp-z2f2zdzπCnFzf-n+1z,
δTu-+dTdzdz=D¯u-+zdωdzdz+-+Δzdωdzdz.
δTu=2π2D¯u/c2Pvτ0.
Δωmax=2PvcS lnS+1+S2,
δTuω=-ΔωmaxDu¯z.
δTuωδTu=1πczτ0S lnS+1+S2.
δTuωδTu2S lnS+1+S2.

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