Abstract

The effect of reduction of soliton interaction by bandwidth-limited amplification is analyzed by numerical solution of the nonlinear Schrödinger equation, by computing the eigenvalues of inverse-scattering transform, and by solving the equation for a soliton center. It is shown that this effect is explained by the influence of the perturbation on soliton central frequency.

© 1993 Optical Society of America

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References

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  1. M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
    [CrossRef]
  2. Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991).
    [CrossRef]
  3. B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
    [CrossRef] [PubMed]
  4. M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
    [CrossRef]
  5. Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [CrossRef]
  6. L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
    [CrossRef]
  7. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  8. L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [CrossRef] [PubMed]
  9. N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977).
    [CrossRef]
  10. C. S. Bretherton, E. A. Spiegel, Phys. Lett. A 96, 152 (1983).
    [CrossRef]
  11. Y. Chen, Electron. Lett. 27, 1985 (1991).
    [CrossRef]
  12. V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981); D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986)J. P. Gordon, Opt. Lett. 8, 596 (1983)
    [CrossRef] [PubMed]
  13. C. Desem, P. L. Chu, in Optical Solitons, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992).
  14. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
    [CrossRef]
  15. K. Smith, L. F. Mollenauer, Opt. Lett. 14, 1284 (1989); E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).
    [CrossRef] [PubMed]
  16. A. Mecozzi, H. A. Haus, Opt. Lett. 17, 988 (1992).
    [CrossRef] [PubMed]

1992 (6)

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

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

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]

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

A. Mecozzi, H. A. Haus, Opt. Lett. 17, 988 (1992).
[CrossRef] [PubMed]

1991 (5)

Y. Chen, Electron. Lett. 27, 1985 (1991).
[CrossRef]

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

1989 (1)

1983 (1)

C. S. Bretherton, E. A. Spiegel, Phys. Lett. A 96, 152 (1983).
[CrossRef]

1981 (1)

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981); D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986)J. P. Gordon, Opt. Lett. 8, 596 (1983)
[CrossRef] [PubMed]

1977 (1)

N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977).
[CrossRef]

Bergano, N. S.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Bretherton, C. S.

C. S. Bretherton, E. A. Spiegel, Phys. Lett. A 96, 152 (1983).
[CrossRef]

Chen, Y.

Y. Chen, Electron. Lett. 27, 1985 (1991).
[CrossRef]

Chu, P. L.

C. Desem, P. L. Chu, in Optical Solitons, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992).

Desem, C.

C. Desem, P. L. Chu, in Optical Solitons, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992).

Evangelides, S. G.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

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

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Gordon, J. P.

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

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Haner, M.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Karpman, V. I.

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981); D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986)J. P. Gordon, Opt. Lett. 8, 596 (1983)
[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).
[CrossRef]

Kubota, H.

Kurokawa, K.

Lichtman, E.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Malomed, B. A.

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

Mecozzi, A.

Mollenauer, L. F.

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

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

K. Smith, L. F. Mollenauer, Opt. Lett. 14, 1284 (1989); E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).
[CrossRef] [PubMed]

Nakazawa, M.

Neubelt, M. J.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Nyman, B. M.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Pereira, N. R.

N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977).
[CrossRef]

Romagnoli, M.

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

Smith, K.

Solov’ev, V. V.

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981); D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986)J. P. Gordon, Opt. Lett. 8, 596 (1983)
[CrossRef] [PubMed]

Spiegel, E. A.

C. S. Bretherton, E. A. Spiegel, Phys. Lett. A 96, 152 (1983).
[CrossRef]

Stenflo, L.

N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977).
[CrossRef]

Wabnitz, S.

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

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991).
[CrossRef]

Yamada, E.

Electron. Lett. (5)

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

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

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991).
[CrossRef]

Y. Chen, Electron. Lett. 27, 1985 (1991).
[CrossRef]

J. Lightwave Technol. (1)

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

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

Opt. Lett. (4)

Phys. Fluids (1)

N. R. Pereira, L. Stenflo, Phys. Fluids 20, 1733 (1977).
[CrossRef]

Phys. Lett. A (1)

C. S. Bretherton, E. A. Spiegel, Phys. Lett. A 96, 152 (1983).
[CrossRef]

Phys. Rev. A (1)

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

Physica D (1)

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981); D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986)J. P. Gordon, Opt. Lett. 8, 596 (1983)
[CrossRef] [PubMed]

Other (1)

C. Desem, P. L. Chu, in Optical Solitons, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992).

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Figures (3)

Fig. 1
Fig. 1

(a) Interaction half-period L for in-phase solitons and (b) separation T at z = 100 for out-of-phase solitons. The circles are the numerical solution of Eq. (1), the curves are the numerical solution to Eq. (4), and the asterisk is the numerical simulation taken from Ref. 4. Here β = 3δ and = 0.

Fig. 2
Fig. 2

Imaginary parts ηi of inverse-scattering-transform eigenvalues for soliton interaction at X0 = 8,δ = 0.04, β= 3δ, and = 0 (solid curves); the peak intensity is also shown (dashed curve).

Fig. 3
Fig. 3

Soliton trajectories from numerical solution of Eq. (4) at X0 = 6, δ = 0 (curve 1); X0 = 6, δ = 0.05(curve 2); X0 = 8, δ = 0 (curve 3); X0= 8, δ = 0.04(curve 4).

Equations (4)

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i ψ z + 1 2 2 ψ τ 2 + ψ 2 ψ = i δ ψ + i β 2 ψ τ 2 + i ψ 2 ψ ,
ψ S ( z , τ ) = U 0 sech ( α τ ) exp ( - i Γ z ) exp { i γ ln [ cosh ( α τ ) ] } .
ψ ( 0 , τ ) = ψ 0 ( 0 , τ - X 0 / 2 ) + exp ( i ϕ ) ψ 0 ( 0 , τ + X 0 / 2 ) ,
q ¨ + 4 δ q ˙ + 4 sgn ( q ) exp ( - 2 q ) cos ( ϕ ) = 0 ,

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