Abstract

We propose a wavelength-division multiplexing system in which transmission of solitons is stabilized by fixed- or sliding-frequency notch filters (a soliton rail), providing channel isolation. We demonstrate analytically and numerically that a soliton trapped in a channel between two notches is very robust. We also predict an optimum ratio between the channel separation and the soliton’s spectral width. The effects of interchannel collisions are considered, and it is demonstrated that these effects can be largely eliminated by notch filters, which require a compensatory gain that is comparable with the basic gain balancing the fiber loss.

© 1999 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991); P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 1659 (1996).
    [CrossRef]
  2. S. Wabnitz, Opt. Lett. 21, 638 (1996); S. Kumar, Y. Kodama, and A. Hasegawa, Electron. Lett. 33, 459 (1997).
    [CrossRef] [PubMed]
  3. M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
    [CrossRef]
  4. D. J. Kaup, B. A. Malomed, and J. Yang, Opt. Lett. 23, 1600 (1998).
    [CrossRef]
  5. E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, Opt. Lett. 21, 195 (1996).
    [CrossRef] [PubMed]
  6. S. S. Orlov, A. Yariv, and S. Van Essen, Opt. Lett. 22, 688 (1997); X. J. Gu, Opt. Lett. 23, 509 (1998).
    [CrossRef] [PubMed]
  7. B. Luce, Opt. Lett. 23, 765 (1998).
    [CrossRef]
  8. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford Press, New York, 1995).
  9. A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, Opt. Lett. 16, 1841 (1991); Y. Kodama and A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]

1998 (3)

M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
[CrossRef]

B. Luce, Opt. Lett. 23, 765 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, Opt. Lett. 23, 1600 (1998).
[CrossRef]

1997 (1)

1996 (2)

1991 (2)

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991); P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 1659 (1996).
[CrossRef]

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, Opt. Lett. 16, 1841 (1991); Y. Kodama and A. Hasegawa, Opt. Lett. 17, 31 (1992).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
[CrossRef]

Biondini, G.

M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
[CrossRef]

Chakravarty, S.

M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991); P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 1659 (1996).
[CrossRef]

Golovchenko, E. A.

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991); P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 1659 (1996).
[CrossRef]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford Press, New York, 1995).

Haus, H. A.

Horne, R. L.

M. J. Ablowitz, G. Biondini, S. Chakravarty, and R. L. Horne, Opt. Commun. 150, 305 (1998).
[CrossRef]

Kaup, D. J.

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford Press, New York, 1995).

Lai, Y.

Luce, B.

Malomed, B. A.

Mecozzi, A.

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Lightwave Technol. 9, 362 (1991); P. V. Mamyshev and L. F. Mollenauer, Opt. Lett. 21, 1659 (1996).
[CrossRef]

Moores, J. D.

Orlov, S. S.

Pilipetskii, A. N.

Van Essen, S.

Wabnitz, S.

Yang, J.

Yariv, A.

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Figures (3)

Fig. 1
Fig. 1

Maximum normalized frequency-sliding rate versus the relative frequency separation between the notches.

Fig. 2
Fig. 2

Numerical simulations of the model with four narrow notches: (a) notches and the soliton in the frequency domain; (b) example of evolution starting with the soliton predicted by the analytical approximation in the optimum case [relation (7)], with τ0=0.55, the notch-filtering strength Γ=0.1, and the extra gain γ=0.0276, as predicted by Eq. (6).

Fig. 3
Fig. 3

Typical example of the (most dangerous) incomplete collision. The trajectories of the solitons’ centers are shown (a) without the filters and (b) with the NF’s and extra gain, taken from Eq. (6). The dashed lines show the trajectory of each soliton in the absence of collision.

Equations (10)

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iuz+1/2uττ+u2u=iγu-iΓn=1,2exp-iωnt×-+expiωnτuτdτ,
dEdz=2γE-2Γn=1,2-+dτexpiωn-Ωτu0τ2,
EdΩdz=2Γn=1,2Ω-ωn×-+dτ expiωn-Ωτu0τ2.
dτ0dz=-2γτ0+π2Γτ02n=1,2 sech212πτ0Ω-ωn,
dΩdz=π2Γτ0n=1,2Ω-ωnsech212πτ0Ω-ωn.
γ=π2Γτ0sech2 W,   Wπ/4τ0Δω,
W=Wopt2.169,
λ=+,-Wb±1sech2Wb±1.
dδΩ/dz=-αδΩ+Fz, dT/dz=-δΩ,
T=β/αz0Fzdzβ/αΔ0Ω,

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