Abstract

The first experimental observation to the authors’ knowledge is reported of the generation of optical vortex solitons from instability and breakup of a dark soliton stripe propagating through a saturable self-defocusing nonlinear medium.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, Cambridge, 1990).
  2. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), Chap. 3.8.
    [CrossRef]
  3. See, for example, Yu. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
    [CrossRef]
  4. G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
    [CrossRef] [PubMed]
  5. E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].
  6. G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
    [CrossRef]
  7. C. T. Law, G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
    [CrossRef] [PubMed]
  8. D. E. Pelinovsky, Yu. A. Stepanyants, Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
    [CrossRef]
  9. A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
    [CrossRef] [PubMed]
  10. G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef] [PubMed]
  11. B. Luther-Davies, R. Powles, V. Tikhonenko, Opt. Lett. 19, 1816 (1994).
    [CrossRef] [PubMed]
  12. Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.
  13. V. Tikhonenko, J. Christou, B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
    [CrossRef]
  14. Yu. S. Kivshar, W. Krolikowksi, Opt. Lett. 20, 1527 (1995).
    [CrossRef] [PubMed]

1995 (3)

1994 (1)

1993 (2)

C. T. Law, G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
[CrossRef] [PubMed]

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

1992 (3)

G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
[CrossRef]

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

A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[CrossRef] [PubMed]

1991 (1)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

1988 (1)

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Ablowitz, M. J.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), Chap. 3.8.
[CrossRef]

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Christou, J.

V. Tikhonenko, J. Christou, B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.

Firth, W. J.

G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
[CrossRef]

Infeld, E.

E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, Cambridge, 1990).

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Kivshar, Yu. S.

D. E. Pelinovsky, Yu. A. Stepanyants, Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[CrossRef]

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

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

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.

Krolikowksi, W.

Kuznetsov, E. A.

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Law, C. T.

C. T. Law, G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
[CrossRef] [PubMed]

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

Luther-Davies, B.

V. Tikhonenko, J. Christou, B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
[CrossRef]

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

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.

McDonald, G. S.

G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
[CrossRef]

Mitchell, D. J.

Pelinovsky, D. E.

D. E. Pelinovsky, Yu. A. Stepanyants, Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.

Poladian, L.

Powles, R.

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Rowlands, G.

E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, Cambridge, 1990).

Segur, H.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), Chap. 3.8.
[CrossRef]

Snyder, A. W.

Stepanyants, Yu. A.

D. E. Pelinovsky, Yu. A. Stepanyants, Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Swartzlander, G. A.

C. T. Law, G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
[CrossRef] [PubMed]

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

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Syed, K. S.

G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
[CrossRef]

Tikhonenko, V.

V. Tikhonenko, J. Christou, B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
[CrossRef]

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

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be submitted toPhys. Rev. E.

Turitsyn, S. K.

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

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

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

Opt. Commun. (1)

G. S. McDonald, K. S. Syed, W. J. Firth, Opt. Commun. 94, 469 (1992).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

D. E. Pelinovsky, Yu. A. Stepanyants, Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

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

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Other (3)

E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, Cambridge, 1990).

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981), Chap. 3.8.
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, J. Christou, B. Luther-Davies, V. Tikhonenko, “Influence of non-linearity saturation on the instabilities of dark solitons,” to be 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 (2)

Fig. 1
Fig. 1

Output beam intensity profiles demonstrating the instability of a dark soliton stripe as the nonlinearity is increased. The vapor concentration increases from vanish-ingly small in (a) to the order of 1013 cm−3 in (f). The cell temperatures (°C) were (a) 40, (b) 72, (c) 82, (d) 90, (e) 112, and (f) 125. The inset shows the intensity distribution along a line through the center of the upper vortex of (f). Laser detuning was held constant at 0.85 GHz, and the power of the beam at the cell input was 240 mW, corresponding to a maximum intensity of approximately 170 W/cm2.

Fig. 2
Fig. 2

Results for numerical simulations of dark soliton instability, as modeled by Eqs. (1) and (2). Output profiles (a)–(f) were obtained after 20 cm of propagation in the nonlinear medium with nonlinear refraction and absorption parameters corresponding to the experimental range in Figs. 1(a)–1(f). Inset (g) shows the experimentally obtained intensity distribution at the input of the medium (2× magnification with respect to other profiles) used as the initial condition for these simulations. Other parameters correspond to the experimental situation of Fig. 1.

Equations (2)

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

i E z + 1 2 k 0 n 0 Δ E + k 0 n NL ( I ) E = i γ ( I ) E ,
n NL ( I ) = n s I s 1 [ 1 1 ( 1 + I / I s 1 ) p ] , γ ( I ) = γ s ( 1 + I / I s 2 ) p ,

Metrics