Abstract

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. R. Allan, S. R. Skinner, D. R. Andersen, A. L. Smirl, Opt. Lett. 16, 156 (1991 ); G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991 ); B. Luther-Davies, X. Yang, Opt. Lett. 17, 496 (1992).
    [CrossRef] [PubMed]
  2. M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
    [CrossRef] [PubMed]
  3. G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef] [PubMed]
  4. B. Luther-Davies, R. Powles, V. Tikhonenko, Opt. Lett. 19, 1816 (1994).
    [CrossRef] [PubMed]
  5. Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
    [CrossRef]
  6. T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
    [CrossRef]
  7. M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef] [PubMed]
  8. M. Karlsson, Phys. Rev. A 46, 2726 (1992).
    [CrossRef] [PubMed]
  9. W. Krolikowski, B. Luther-Davies, Opt. Lett. 18, 188 (1993).
    [CrossRef] [PubMed]
  10. Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
    [CrossRef]
  11. Yu. S. Kivshar, W. Krolikowski, Opt. Lett. 20, 1527 (1995).
    [CrossRef] [PubMed]
  12. The definition of the renormalized momentum [Eq. (5)] differs by the sign in front of the integral from that used in Ref. 11.
  13. D. E. Pelinovsky, Yu. S. Kivshar, V. V. Afanasjev, submitted toPhys. Rev. E.

1995 (2)

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Yu. S. Kivshar, W. Krolikowski, Opt. Lett. 20, 1527 (1995).
[CrossRef] [PubMed]

1994 (3)

B. Luther-Davies, R. Powles, V. Tikhonenko, Opt. Lett. 19, 1816 (1994).
[CrossRef] [PubMed]

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

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

1993 (2)

1992 (2)

M. Karlsson, Phys. Rev. A 46, 2726 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

1991 (1)

1968 (1)

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Afanasjev, V. V.

D. E. Pelinovsky, Yu. S. Kivshar, V. V. Afanasjev, submitted toPhys. Rev. E.

Allan, G. R.

Andersen, D. R.

Bashaw, M. C.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Brewer, R. G.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Chiao, R. Y.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Fejer, M. M.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Gustafson, T. K.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Karlsson, M.

M. Karlsson, Phys. Rev. A 46, 2726 (1992).
[CrossRef] [PubMed]

Kelley, P. L.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar, W. Krolikowski, Opt. Lett. 20, 1527 (1995).
[CrossRef] [PubMed]

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

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

D. E. Pelinovsky, Yu. S. Kivshar, V. V. Afanasjev, submitted toPhys. Rev. E.

Krolikowski, W.

Law, C. T.

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Luther-Davies, B.

Pelinovsky, D. E.

D. E. Pelinovsky, Yu. S. Kivshar, V. V. Afanasjev, submitted toPhys. Rev. E.

Porto, P. D.

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Powles, R.

Segev, M.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Skinner, S. R.

Smirl, A. L.

Swartzlander, G. A.

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Taya, M.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Tikhonenko, V.

Valley, G. C.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Yang, X.

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

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968); J. D. Reichert, W. G. Wagner, IEEE J. Quantum Electron. QE-4, 221 (1968); J. H. Margurger, E. E. Dawes, Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Opt. Lett. (4)

Phys. Rev. A (2)

M. Karlsson, Phys. Rev. A 46, 2726 (1992).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (2)

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef] [PubMed]

Other (2)

The definition of the renormalized momentum [Eq. (5)] differs by the sign in front of the integral from that used in Ref. 11.

D. E. Pelinovsky, Yu. S. Kivshar, V. V. Afanasjev, submitted toPhys. Rev. E.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Dynamics of the unstable black soliton in the model Eqs. (2) and (3) at p = 1 and a = 200. (a) Gray-coded variation of |Ψ(x, z)|2, (b) soliton renormalized momentum Ps(υ) and transition to a (stable) gray soliton, and (c) evolution of the minimum soliton intensity.

Fig. 2
Fig. 2

Dynamics of the unstable gray soliton (at υ0 = 0.08) in the model Eqs. (2) and (3) at p = 1 and a = 200. (a) Soliton renormalized momentum Ps (υ) and transitions corresponding to two types of the instability development, (b) gray-coded variation of |Ψ(x, z)|2 for the second case, (c) change of the minimum soliton intensities, and (d) change of the relative soliton positions. Index 0 indicates an evolution of an unperturbed soliton, whereas indices 1 and 2 indicate two different types of the instability-induced soliton dynamics.

Fig. 3
Fig. 3

Instability threshold of a black soliton for the saturable model Eqs. (2) and (3).

Equations (7)

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

n nl ( I ) = n [ 1 1 ( 1 + I / I sat ) p ] .
i Ψ z + 1 2 2 Ψ x 2 + f ( | Ψ | 2 ) Ψ = 0 ,
f ( | Ψ | 2 ) = [ 1 ( 1 + a | Ψ | 2 ) p 1 ] ,
Ψ s ( ξ , z ) = Φ ( ξ ) exp [ i β z + i θ ( ξ ) ] ,
P s ( υ ) = 2 Im + Ψ s * ξ Ψ s ( 1 q | Ψ s | 2 ) d ξ = υ + ( Φ 2 q ) 2 Φ 2 d ξ ,
λ = 1 M s ( υ 0 ) [ P s ( υ ) υ ] ,
M s ( υ ) = [ 2 c q ( N s υ ) 2 + q 2 c ( Δ θ υ ) 2 ] ,

Metrics