Abstract

We analyze the effect of the third-order guiding filter term on soliton transmission in optical fibers. We find that this term causes a significant difference between the regimes of up- and down-sliding of filter frequency. In particular, the use of up-sliding requires less additional amplifier gain than down-sliding does, which is preferable in real systems.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [Crossref] [PubMed]
  2. L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
    [Crossref]
  3. L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Opt. Lett. 19, 704 (1994).
    [Crossref] [PubMed]
  4. Y. Kodama, S. Wabnitz, Opt. Lett. 19, 162 (1994).
    [Crossref] [PubMed]
  5. In Ref. 1 there was an error in determining the preferable direction of sliding. All the experiments on soliton transmission that are now carried out at AT&T Bell Laboratories clearly show that up-sliding is more advantageous.
  6. Y. Kodama, M. Romagnoli, S. Wabnitz, M. Midrio, Opt. Lett. 19, 165 (1994).
    [Crossref] [PubMed]
  7. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), p. 250.

1994 (3)

1993 (1)

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
[Crossref]

1992 (1)

Ablowitz, M. J.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), p. 250.

Evangelides, S. G.

Gordon, J. P.

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
[Crossref]

Kodama, Y.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
[Crossref]

Mamyshev, P. V.

Midrio, M.

Mollenauer, L. F.

Neubelt, M. J.

L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, Opt. Lett. 19, 704 (1994).
[Crossref] [PubMed]

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
[Crossref]

Romagnoli, M.

Segur, H.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), p. 250.

Wabnitz, S.

Electron. Lett. (1)

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electron. Lett. 29, 910 (1993).
[Crossref]

Opt. Lett. (4)

Other (2)

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), p. 250.

In Ref. 1 there was an error in determining the preferable direction of sliding. All the experiments on soliton transmission that are now carried out at AT&T Bell Laboratories clearly show that up-sliding is more advantageous.

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Figures (3)

Fig. 1
Fig. 1

Equilibrium values of (a) soliton amplitude A and (b) mean frequency offset from the filter frequency Δω versus excess gain α, as determined from Eqs. (6) and (7). The filter parameters are η2 = 0.1, η3 = 0.05, and |ωf′| = 0.44η2. The dashed curves represent the equilibrium values (A2, ω) for η3 = 0.

Fig. 2
Fig. 2

(a) Soliton amplitude A (b) mean frequency offset from the filter frequency Δω as a function of distance z given in soliton periods, as determined by numerical solution of Eq. (2) with ωf ′ = −0.44η2, corresponding to down-sliding. The solid curves correspond to the gain value α1 given by Eq. (8), and the dashed curves correspond to α2 given by Eq. (9).

Fig. 3
Fig. 3

(a) Soliton amplitude A and (b) mean frequency offset from the filter frequency Δω as a function of distance z given in soliton periods, as determined by numerical solution of Eq. (2) with ωf ′ = 0.44η2, corresponding to up-sliding. The solid curves correspond to the gain value α1 given by Eq. (8), and the dashed curves correspond to α2 given by Eq. (9).

Equations (10)

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F ( ω ) = 1 l f ln { 1 R 1 R exp [ i ( ω ω f ) 2 d / c ] } ,
u z = i ( 1 2 2 u t 2 + | u | 2 u ) + 1 2 α u η 2 ( i t ω f ) 2 u i η 3 ( i t ω f ) 3 u ,
η 2 = 1 2 R ( 1 R ) 2 8 π D l f c ( d λ ) 2 , η 3 = 2 d c ( 1 + R ) ( 1 R ) 1 3 t 0 η 2 , ω f ' = d ω f d z = 4 π 2 f c t 0 3 λ 2 D , α = α R t 0 2 2 π c λ 2 D .
u = A sech ( A t q z ) × exp [ i 1 2 A 2 z + 3 i η 3 A tanh ( A t q z ) i Ω t ] ,
ω 0 = Im d t u u * / t d t | u | 2 = Ω 2 η 3 A 2 .
d ω 0 d z = 4 3 η 2 A 2 [ ( ω 0 ω f ) 6 5 η 3 A 2 ] ,
d A d z = α A 2 η 2 A [ ( ω 0 ω f ) 2 + 1 3 A 2 ] .
( ω 0 ω f ) = 6 5 η 3 A 2 3 4 η 2 A 2 ω f ' .
α 1 = 2 3 η 2 + 2 η 2 ( 3 4 η 2 ω f ' ) 2 ,
α 2 = 2 3 η 2 + 2 η 2 ( 3 4 η 2 ω f ' + 6 5 η 3 ) 2 ,

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