Abstract

We compare a perturbative analysis with a numerical analysis of the reduction of soliton interactions in a long-distance soliton transmission system with lumped amplifiers and filters. We find that soliton interactions may be suppressed by sliding the center frequency of the filters along the line, as devised by Mollenauer et al. [Opt. Lett. 17, 1575 (1992)].

© 1993 Optical Society of America

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References

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  1. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990); Phys. Rev. Lett. 66, 161 (1991).
    [Crossref] [PubMed]
  2. L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
    [Crossref]
  3. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [Crossref] [PubMed]
  4. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
    [Crossref] [PubMed]
  5. L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [Crossref] [PubMed]
  6. M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
    [Crossref]
  7. L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
    [Crossref]
  8. Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993).
    [Crossref] [PubMed]
  9. M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992); M. Nakazawa, H. Kubota, Electron. Lett. 29, 226 (1993).
    [Crossref] [PubMed]
  10. V. V. Afanasjev, Opt. Lett. 18, 790 (1993).
    [Crossref] [PubMed]
  11. Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [Crossref]
  12. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [Crossref]
  13. M. Romagnoli, S. Wabnitz, M. Midrio, “Bandwidth limits of soliton transmission with sliding filters,” presented at the European Cooperation in the Field of Scientific Research 241 Meeting, Prague, April 14–15, 1993.
  14. A. C. Newell, in Solitons, R. K. Bullough, P. J. Caudrey, eds. (Springer-Verlag, Berlin, 1980), pp. 177–242.
    [Crossref]
  15. T. Yamada, K. Nozaki, J. Phys. Soc. Jpn. 58, 1944 (1989)
    [Crossref]

1993 (1)

1992 (6)

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[Crossref]

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992); M. Nakazawa, H. Kubota, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
[Crossref] [PubMed]

L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[Crossref] [PubMed]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

1991 (4)

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
[Crossref] [PubMed]

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[Crossref]

1990 (1)

1989 (1)

T. Yamada, K. Nozaki, J. Phys. Soc. Jpn. 58, 1944 (1989)
[Crossref]

Afanasjev, V. V.

Evangelides, S. G.

L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[Crossref] [PubMed]

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[Crossref]

Gordon, J. P.

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[Crossref]

A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
[Crossref] [PubMed]

Kodama, Y.

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
[Crossref] [PubMed]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990); Phys. Rev. Lett. 66, 161 (1991).
[Crossref] [PubMed]

Kubota, H.

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992); M. Nakazawa, H. Kubota, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

Lai, Y.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

Mecozzi, A.

Midrio, M.

M. Romagnoli, S. Wabnitz, M. Midrio, “Bandwidth limits of soliton transmission with sliding filters,” presented at the European Cooperation in the Field of Scientific Research 241 Meeting, Prague, April 14–15, 1993.

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[Crossref] [PubMed]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[Crossref]

Moores, J. D.

Nakazawa, M.

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992); M. Nakazawa, H. Kubota, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

Newell, A. C.

A. C. Newell, in Solitons, R. K. Bullough, P. J. Caudrey, eds. (Springer-Verlag, Berlin, 1980), pp. 177–242.
[Crossref]

Nozaki, K.

T. Yamada, K. Nozaki, J. Phys. Soc. Jpn. 58, 1944 (1989)
[Crossref]

Nyman, B. M.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

Romagnoli, M.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

M. Romagnoli, S. Wabnitz, M. Midrio, “Bandwidth limits of soliton transmission with sliding filters,” presented at the European Cooperation in the Field of Scientific Research 241 Meeting, Prague, April 14–15, 1993.

Suzuki, E.

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

Wabnitz, S.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

M. Romagnoli, S. Wabnitz, M. Midrio, “Bandwidth limits of soliton transmission with sliding filters,” presented at the European Cooperation in the Field of Scientific Research 241 Meeting, Prague, April 14–15, 1993.

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

Yamada, T.

T. Yamada, K. Nozaki, J. Phys. Soc. Jpn. 58, 1944 (1989)
[Crossref]

Electron. Lett. (5)

M. Nakazawa, E. Yamada, H. Kubota, E. Suzuki, Electron. Lett. 27, 1270 (1991); M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Tanaka, in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD7.
[Crossref]

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992); in Optical Fiber Communication, Vol. 4 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper PD8.
[Crossref]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992); M. Nakazawa, H. Kubota, Electron. Lett. 29, 226 (1993).
[Crossref] [PubMed]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[Crossref]

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

J. Phys. Soc. Jpn. (1)

T. Yamada, K. Nozaki, J. Phys. Soc. Jpn. 58, 1944 (1989)
[Crossref]

Opt. Lett. (5)

Other (2)

M. Romagnoli, S. Wabnitz, M. Midrio, “Bandwidth limits of soliton transmission with sliding filters,” presented at the European Cooperation in the Field of Scientific Research 241 Meeting, Prague, April 14–15, 1993.

A. C. Newell, in Solitons, R. K. Bullough, P. J. Caudrey, eds. (Springer-Verlag, Berlin, 1980), pp. 177–242.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Evolution of soliton eigenvalues η1,2 and phase difference θ1θ2 from two-soliton perturbation theory for different values of δ = β/3: δ = 0.001 (dotted–dashed curve), δ = 0.01 (dotted curve), δ = 0.02 (dashed curve), and δ = 0.04 (solid curve).

Fig. 2
Fig. 2

Dependence of collision distance on excess gain δ from the numerical solution of Eq. (1) (solid curves) and the two-soliton perturbation theory (dashed curves).

Fig. 3
Fig. 3

(a) Increase of the collision distance with constant center frequency filters and X0 = 8, (b) suppression of interactions with sliding-frequency filters and X0 = 6.

Fig. 4
Fig. 4

Full-width asymptotic output time separation xout versus input separation xin = X0/1.763 for sliding-filter bandwidths B = 18 and B =13.

Equations (8)

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V Z - i 2 V T T - i V 2 V = δ V + β V T T R .
H ( Ω ) = 1 ( 1 + 2 i Ω / B ) ,
h ( Ω ) = ln [ H ( Ω ) ] / Z a [ - i 2 Ω / B - 2 Ω 2 / B 2 + i 8 Ω 3 / ( 3 B 3 ) + O ( Ω 4 ) ] / Z a ,
V ( T , Z = 0 ) = sech ( T - X 0 / 2 ) + sech ( T + X 0 / 2 ) .
V 2 ( T , Z ) = 2 Δ ( η 1 + η 2 η 1 - η 2 ) [ η 1 cosh ( σ 2 ) exp ( - i θ 1 ) + η 2 cosh ( σ 1 ) exp ( - i θ 2 ) ] ,
Δ = cosh ( σ 1 + σ 2 ) + ( η 1 + η 2 η 1 - η 2 ) 2 cosh ( σ 1 - σ 2 ) + 4 η 1 η 2 ( η 1 - η 2 ) 2 cos ( θ 1 - θ 2 ) ,
σ l = η l T ,             θ l = - 1 2 η l 2 Z ,             l = 1 , 2.
d η l d Z = 2 γ l - [ R * ψ 1 2 ( ξ l ) - R ψ 2 2 ( ξ l ) ] d T , d θ l d Z = - η l 2 2 - Re { γ l - [ R * ψ 1 2 ( ξ l ) ξ - R ψ 2 2 ( ξ l ) ξ ] d T } ,             l = 1 , 2 ,

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