Abstract

We theoretically analyze nonlinear interactions between chirped solitons in dispersion-managed wavelength-division-multiplexing (WDM) systems. We employ the perturbation method to evaluate frequency and chirp shifts caused by collisions among different WDM channels. It is shown that a chirped soliton suffers less frequency shift and time displacement than an ideal soliton, indicating its potential applicability for WDM systems.

© 1998 Optical Society of America

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  1. A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
    [CrossRef]
  2. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
    [CrossRef]
  3. S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
    [CrossRef] [PubMed]
  4. T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
    [CrossRef]
  5. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  6. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Electron. Lett. 33, 735 (1997).
    [CrossRef]
  7. H. Sugahara, H. Kato, and Y. Kodama, Electron. Lett. 33, 1065 (1997).
    [CrossRef]
  8. J. F. L. Devaney, W. Forysiak, A. M. Niculae, and N. J. Doran, Opt. Lett. 22, 1695 (1997).
    [CrossRef]
  9. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  10. Y. Kodama and A. Hasegawa, Opt. Lett. 16, 208 (1991).
    [CrossRef] [PubMed]
  11. T. Hirooka and A. Hasegawa, in Conference on Lasers and Electro-Optics/Pacific Rim (Optical Society of America, Washington, D.C., 1997), p. 86.

1997

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
[CrossRef] [PubMed]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

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

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

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

1991

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

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

1983

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

Anderson, D.

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

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

Evangelides, S. G.

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

Forysiak, W.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

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

Golovchenko, E. A.

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

Gordon, J. P.

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

Hasegawa, A.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

S. Kumar and A. Hasegawa, Opt. Lett. 22, 372 (1997).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

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

T. Hirooka and A. Hasegawa, in Conference on Lasers and Electro-Optics/Pacific Rim (Optical Society of America, Washington, D.C., 1997), p. 86.

Hirooka, T.

T. Hirooka and A. Hasegawa, in Conference on Lasers and Electro-Optics/Pacific Rim (Optical Society of America, Washington, D.C., 1997), p. 86.

Kato, H.

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

Know, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

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

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

Kumar, S.

Maruta, A.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[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.

Okamawari, T.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

Pilipetskii, A. N.

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

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

Sugahara, H.

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

Ueda, Y.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

Electron. Lett.

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 1063 (1997).
[CrossRef]

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

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

J. Lightwave Technol.

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

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Know, J. Lightwave Technol. 15, 1808 (1997).
[CrossRef]

Opt. Fiber Technol.

A. Hasegawa, Y. Kodama, and A. Maruta, Opt. Fiber Technol. 3, 197 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Other

T. Hirooka and A. Hasegawa, in Conference on Lasers and Electro-Optics/Pacific Rim (Optical Society of America, Washington, D.C., 1997), p. 86.

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Figures (3)

Fig. 1
Fig. 1

Residual frequency shift Δκ as a function of ΔD. Solid curve, analytical result calculated from Eq.  (9); circles, result obtained from direct numerical simulations. The initial channel spacing is ΔBκ10-κ20=24, which corresponds to 2.12  GHz for the 20-ps pulse.

Fig. 2
Fig. 2

Averaged value of chirp CZ along a distance Z. The initial channel spacing is the same as in Fig.  1.

Fig. 3
Fig. 3

Collision-induced frequency shift of a chirped soliton and a soliton versus normalized distance. Here the soliton propagates in a fiber with uniform dispersion equivalent to the averaged value of the dispersion profile.

Equations (19)

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

iqZ+dZ22qT2+αZq2q=-iΓq+iGZq+Rq, q*,
iuZ+dZ22uT2+αZa2Zu2u=Ru, u*.
uT, Z=AZfBZT-T0ZexpiCZ×T-T0Z2-iκZT-T0Z+iθ0Z.
dAdZ=-ACd-2ILIC-ImRexp-iφ×ILτ2-3ICfτdτ,
dBdZ=-2BCd-BILICA-ImRexp-iφ×ILτ2-ICfτdτ,
dCdZ=-2C2d-αa2A2B2IN4IC+dB4ID2IC+B22ICA×-ReRexp-iφfτ+2τdfdτdτ,
dκdZ=-2BILA-ReRexp-iφdfdτdτ-4CILAB-ImRexp-iφτfτdτ,
dT0dZ=-κd+2ILAB-ImRexp-iφτfτdτ,
IL=-f2τdτ, IC=-τ2f2τdτ, ID=-dfdτ2dτ, IN=-f4τdτ.
iuiZ+dZ22uiT2+αZa2Zui2ui=-2αZa2Zu3-i2ui,
dAdZ=-ACd,
dBdZ=-2BCd,
dCdZ=-2C2d-αa2A2B2IN4IC+dB4ID2IC-αa2A2B2IC-fτif2τ3-i×fτi+2τidfdτidτi,
dκdZ=4αa2A2BIL-fτif2τ3-idfdτidτi,
dT0dZ=-κd.
dΔκdZ=4αa2A2BIL-fτf2τ+BΔTdfdτdτ,
dΔκdZ=22αa2A2B2ΔTexp-B2ΔT2.
dΔCdZ=-αa2A2B2IC-fτf2τ+BΔT×fτ+2τdfdτdτ.
dΔCdZ=2αa2A2B22B2ΔT2-1exp-B2ΔT2.

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