Abstract

Third-order dispersion has a detrimental effect on dark solitons, leading to resonant generation of growing soliton tails and soliton decay. This effect is shown to be much stronger than that for bright solitons.

© 1996 Optical Society of America

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References

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  1. M. Nakazawa, K. Suzuki, Electron. Lett. 31, 1076; 1084 (1995).
    [CrossRef]
  2. Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 19 (1994).
    [CrossRef] [PubMed]
  3. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 11, 464 (1986);P. K. A. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 12, 628 (1987); C. R. Menyuk, P. K. A. Wai, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, 1992), pp. 332–346, 359–369.
    [CrossRef]
  4. P. K. A. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 71, 726 (1990).
  5. J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
    [CrossRef]
  6. C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993).
    [CrossRef]
  7. Yu. S. Kivshar, V. V. Afanasjev, Phys. Rev. A 44, R1446 (1991).
    [CrossRef] [PubMed]
  8. Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
    [CrossRef]
  9. V. I. Karpman, Phys. Lett. A 181, 211 (1993).
    [CrossRef]
  10. Yu. S. Kivshar, B. A. Malomed, Phys. Rev. Lett. 60, 129 (1991).

1995

M. Nakazawa, K. Suzuki, Electron. Lett. 31, 1076; 1084 (1995).
[CrossRef]

J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
[CrossRef]

1994

1993

C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993).
[CrossRef]

Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

1991

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. Lett. 60, 129 (1991).

Yu. S. Kivshar, V. V. Afanasjev, Phys. Rev. A 44, R1446 (1991).
[CrossRef] [PubMed]

1990

P. K. A. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 71, 726 (1990).

1986

Afanasjev, V. V.

Yu. S. Kivshar, V. V. Afanasjev, Phys. Rev. A 44, R1446 (1991).
[CrossRef] [PubMed]

Brabec, T.

J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
[CrossRef]

Chen, H. H.

Elgin, J. N.

J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
[CrossRef]

Emplit, Ph.

Haelterman, M.

Hamaide, J.-P.

Karpman, V. I.

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

Kelly, S. M. J.

J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 19 (1994).
[CrossRef] [PubMed]

Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. Lett. 60, 129 (1991).

Yu. S. Kivshar, V. V. Afanasjev, Phys. Rev. A 44, R1446 (1991).
[CrossRef] [PubMed]

Lee, Y. C.

Malomed, B. A.

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. Lett. 60, 129 (1991).

Menyuk, C. R.

Nakazawa, M.

M. Nakazawa, K. Suzuki, Electron. Lett. 31, 1076; 1084 (1995).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, Electron. Lett. 31, 1076; 1084 (1995).
[CrossRef]

Wai, P. K. A.

Electron. Lett.

M. Nakazawa, K. Suzuki, Electron. Lett. 31, 1076; 1084 (1995).
[CrossRef]

IEEE J. Quantum Electron.

Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. N. Elgin, T. Brabec, S. M. J. Kelly, Opt. Commun. 114, 321 (1995).
[CrossRef]

Opt. Lett.

Phys. Lett. A

V. I. Karpman, Phys. Lett. A 181, 211 (1993).
[CrossRef]

Phys. Rev. A

Yu. S. Kivshar, V. V. Afanasjev, Phys. Rev. A 44, R1446 (1991).
[CrossRef] [PubMed]

P. K. A. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 71, 726 (1990).

Phys. Rev. Lett.

Yu. S. Kivshar, B. A. Malomed, Phys. Rev. Lett. 60, 129 (1991).

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Figures (3)

Fig. 1
Fig. 1

Formation of a nonvanishing oscillating tail for the black soliton (α = u0 = 1) at β = 0.18. (a) Gray-scale plot in which the white lines give the propagation with velocity of sound c and the group velocity Vg. (b) Intensity profile at z = 10.

Fig. 2
Fig. 2

Long-term adiabatic decay of a black soliton in the presence of third-order dispersion. (a) Intensity at the soliton center Imin(z), (b) minimum soliton intensity Imin for β = 0.25, calculated analytically as Imin = u0 2V2/c2 (solid curve) and from numerical simulations at equal distances (filled circles). The arrow shows the direction of the evolution.

Fig. 3
Fig. 3

Comparison of numerical (filled circles) and analytical (solid curves) results for (a) the wavelength and (b) the amplitude of the oscillating tail. Parameters are α = u0 = 1 and β = 0.2. The analytical curve in (a) is given by the resonant wavelength κ + ; that in (b) is given by the expression for A from relation (4) at c = 7000.

Equations (6)

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

i u z - α 2 u t 2 + 2 u 2 u = i β 3 u t 3 ,
i v z - α 2 v t 2 + 2 u 0 2 ( v + v * ) = i β 3 v t 3 .
( V - β κ ) 2 = α ( α κ + 4 u 0 2 ) .
i ξ z - α 2 ξ t 2 - i β 3 ξ t 3 + 2 u s 2 ξ + u s 2 ξ * = i β 3 ( u s ) t 3 .
A ~ C B ( κ + ) csch ( π α u 0 cos  θ κ + ) ,
A ~ exp [ - π α 3 / 2 u 0 β ( 1 - V 2 / c 2 ) 1 / 2 ] ,

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