Abstract

We study the interaction of an optical vortex soliton with a dark-soliton stripe in a bulk nonlinear defocusing medium. We develop a multiscale asymptotic theory to predict the main effect of the interaction and then study it experimentally, observing vortex-induced stripe bending, development of the transverse instability, and stripe breakup.

© 2000 Optical Society of America

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References

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  1. Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. (to be published).
  2. A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 76, 2262 (1996); Europhys. Lett. 35, 25 (1996).
    [CrossRef] [PubMed]
  3. V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, Opt. Lett. 21, 1129 (1996).
    [CrossRef] [PubMed]
  4. R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
    [CrossRef]
  5. Yu. S. Kivshar and V. V. Afanasjev, Opt. Lett. 21, 1135 (1996) ; see also Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef] [PubMed]
  6. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [CrossRef]
  7. L. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, 1999).
  8. J. Christou, V. Tikhonenko, Yu. S. Kivshar, and B. Luther-Davies, Opt. Lett. 21, 1649 (1996).
    [CrossRef] [PubMed]
  9. E. DelRe, S. Trillo, and M. Segev, “Observation of hybrid stripe-needle screening soliton interaction,” submitted to Opt. Lett.
  10. F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
    [CrossRef]

1999

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

1997

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

1996

1959

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Afanasjev, V. V.

Aharonov, Y.

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Baboiu, D. M.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Berry, M. V.

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Bohm, D.

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Christou, J.

Coste, C.

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

DelRe, E.

E. DelRe, S. Trillo, and M. Segev, “Observation of hybrid stripe-needle screening soliton interaction,” submitted to Opt. Lett.

Fuerst, R. A.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Kivshar, Yu. S.

Lawrence, B.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Lund, F.

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

Luther-Davies, B.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 76, 2262 (1996); Europhys. Lett. 35, 25 (1996).
[CrossRef] [PubMed]

Melo, F.

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

Pelinovsky, D. E.

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. (to be published).

Pismen, L.

L. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, 1999).

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 76, 2262 (1996); Europhys. Lett. 35, 25 (1996).
[CrossRef] [PubMed]

Segev, M.

E. DelRe, S. Trillo, and M. Segev, “Observation of hybrid stripe-needle screening soliton interaction,” submitted to Opt. Lett.

Stegeman, G. I.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Tikhonenko, V.

Torruellas, W. E.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Trillo, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

E. DelRe, S. Trillo, and M. Segev, “Observation of hybrid stripe-needle screening soliton interaction,” submitted to Opt. Lett.

Vivanco, F.

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

Wabnitz, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 76, 2262 (1996); Europhys. Lett. 35, 25 (1996).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rep.

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. (to be published).

Phys. Rev.

Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959); M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Phys. Rev. Lett.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 76, 2262 (1996); Europhys. Lett. 35, 25 (1996).
[CrossRef] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 82, 1966 (1999).
[CrossRef]

Other

L. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, 1999).

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Figures (2)

Fig. 1
Fig. 1

Schematic presentation of the vortex–stripe asymptotic interaction (see text for details).

Fig. 2
Fig. 2

Experimental images of a vortex interacting with a dark-soliton stripe. (a) The output position of the vortex without the stripe after nonlinear propagation and (b) the stripe background without a vortex are shown. When the vortex is embedded in the stripe background, their interaction leads to (c) an output profile with a bent stripe and slightly downshifted vortex. When the nonlinearity is increased (d), the stripe breaks up into component vortices.

Equations (9)

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-2ik0n0EZ+2E+2k02n0n2E2E=0,
iuz+122u+u1-u2=0,
zR2+R2ϕ=0, -Rϕz+122R-12Rϕ2+1-R2R=0.
ϕ=σ tan-1yx+-1+Δϕk,
R=tanhx-S.
Rx-1,  R2ϕ-σy11+y12.
x-1R12ϕ0x-1=0,  2Rx-12=R1ϕ0x-12.
R1=v12y1+x-121/2,  ϕ0=tan-1x-1v1y1,
Sy1,z1/z1=v1y1.

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