Abstract

Optical dark solitons described by the generalized nonlinear Schrödinger equation are discussed, and the criterion of soliton instability is presented. This analytical criterion is confirmed numerically for an exactly solvable model of nonlinear saturation.

© 1995 Optical Society of America

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References

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  1. Yu. S. Kivshar, IEEE J. Quantum Electron. 28, 250 (1993).
    [CrossRef]
  2. B. Luther-Davies, X. Yang, Opt. Lett. 17, 496, 1775 (1992).
  3. L. J. Mulder, R. H. Enns, IEEE J. Quantum Electron. 25, 2205 (1989).
    [CrossRef]
  4. W. Królikowski, B. Luther-Davies, Opt. Lett. 18, 188 (1993).
    [CrossRef] [PubMed]
  5. W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
    [CrossRef]
  6. M. G. Vakhitov, A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
    [CrossRef]
  7. D. J. Mitchell, A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
    [CrossRef]
  8. C. K. R. T. Jones, J. V. Moloney, Phys. Lett. A 117, 175 (1986).
    [CrossRef]
  9. D. Hart, E. M. Wright, Opt. Lett. 17, 121 (1992).
    [CrossRef] [PubMed]
  10. E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
    [CrossRef]
  11. Yu. S. Kivshar, W. Królikowski, Opt. Commun. 114, 353 (1995).
    [CrossRef]
  12. Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
    [CrossRef]

1995 (1)

Yu. S. Kivshar, W. Królikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

1994 (1)

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

1993 (4)

Yu. S. Kivshar, IEEE J. Quantum Electron. 28, 250 (1993).
[CrossRef]

W. Królikowski, B. Luther-Davies, Opt. Lett. 18, 188 (1993).
[CrossRef] [PubMed]

W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
[CrossRef]

D. J. Mitchell, A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
[CrossRef]

1992 (2)

D. Hart, E. M. Wright, Opt. Lett. 17, 121 (1992).
[CrossRef] [PubMed]

B. Luther-Davies, X. Yang, Opt. Lett. 17, 496, 1775 (1992).

1989 (1)

L. J. Mulder, R. H. Enns, IEEE J. Quantum Electron. 25, 2205 (1989).
[CrossRef]

1986 (2)

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
[CrossRef]

C. K. R. T. Jones, J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

1973 (1)

M. G. Vakhitov, A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Akhmediev, N. N.

W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
[CrossRef]

Enns, R. H.

L. J. Mulder, R. H. Enns, IEEE J. Quantum Electron. 25, 2205 (1989).
[CrossRef]

Hart, D.

Jones, C. K. R. T.

C. K. R. T. Jones, J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar, W. Królikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

Yu. S. Kivshar, IEEE J. Quantum Electron. 28, 250 (1993).
[CrossRef]

Kolokolov, A. A.

M. G. Vakhitov, A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Królikowski, W.

Yu. S. Kivshar, W. Królikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
[CrossRef]

W. Królikowski, B. Luther-Davies, Opt. Lett. 18, 188 (1993).
[CrossRef] [PubMed]

Kuznetsov, E. A.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
[CrossRef]

Luther-Davies, B.

W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
[CrossRef]

W. Królikowski, B. Luther-Davies, Opt. Lett. 18, 188 (1993).
[CrossRef] [PubMed]

B. Luther-Davies, X. Yang, Opt. Lett. 17, 496, 1775 (1992).

Mitchell, D. J.

Moloney, J. V.

C. K. R. T. Jones, J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

Mulder, L. J.

L. J. Mulder, R. H. Enns, IEEE J. Quantum Electron. 25, 2205 (1989).
[CrossRef]

Rubenchik, A. M.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
[CrossRef]

Snyder, A. W.

Vakhitov, M. G.

M. G. Vakhitov, A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Wright, E. M.

Yang, X.

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

B. Luther-Davies, X. Yang, Opt. Lett. 17, 496, 1775 (1992).

Zakharov, V. E.

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

L. J. Mulder, R. H. Enns, IEEE J. Quantum Electron. 25, 2205 (1989).
[CrossRef]

Yu. S. Kivshar, IEEE J. Quantum Electron. 28, 250 (1993).
[CrossRef]

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

Opt. Commun. (1)

Yu. S. Kivshar, W. Królikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

C. K. R. T. Jones, J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

Phys. Rep. (1)

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov, Phys. Rep. 142, 113 (1986).
[CrossRef]

Phys. Rev. E (2)

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

W. Królikowski, N. N. Akhmediev, B. Luther-Davies, Phys. Rev. E 48, 3980 (1993).
[CrossRef]

Radiophys. Quantum Electron. (1)

M. G. Vakhitov, A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Dependence of the Hamiltonian H versus the renormalized momentum Q calculated for the dark soliton in Eq. (5) for Is = 0.2 and Is = 0.08 (I0 = 1). The dashed curve indicates unstable solutions.

Fig. 2
Fig. 2

Renormalized momentum Q as a function of the soliton velocity V in Eq. (5) for Is = 0.02 and Is = 0.08 (I0 = 1). Notice the appearance of the positive slope in the regime of strong saturation.

Fig. 3
Fig. 3

Characteristic examples of the dark soliton propagation in Eq. (5) for (a) stable propagation, V > Vcr, and (b) the instability-induced breakup of the dark soliton, V < Vcr.

Equations (8)

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i Ψ z + 1 2 2 Ψ x 2 + f ( Ψ 2 ) Ψ = 0 ,
H = 1 2 - + { | Ψ x | 2 + G ( Ψ 2 } d x ,
Q = i 2 - + ( Ψ Ψ * x - Ψ * Ψ x ) ( 1 - Ψ 0 2 Ψ 2 ) d x .
δ ( H - V Q ) = 0 ,
L [ υ w ] = λ [ w - υ ] ,
i 2 - + ( Ψ S x Ψ S * V - Ψ S * x Ψ S V ) d x + O ( λ 2 ) T + O ( λ 2 ) .
d Q 0 d V + i 2 ( Ψ S Ψ S * V - Ψ S * Ψ S V ) | - + = d d V ( Q 0 - Ψ 0 2 Δ ϕ ) ,
F ( I ) = - I s 2 [ 1 - 1 ( 1 + I / I s ) 2 ] ,

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