Abstract

We demonstrate, theoretically and experimentally, that dipole-mode vector solitons created in biased photorefractive media possess a number of anisotropy-driven properties, such as stability of a selected orientation, wobbling, and incomplete rotation, owing to the anisotropic nonlocal response of the photorefractive nonlinearity. Such features are found for higher-order (multipole) vector solitons, and they are carefully verified in an experiment.

© 2001 Optical Society of America

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  1. J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
    [CrossRef] [PubMed]
  2. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
    [CrossRef] [PubMed]
  3. T. Carmon, Ch. Anastassiou, S. Lan, D. Kip, Z. Musslimani, and M. Segev, Opt. Lett. 25, 1113 (2000).
    [CrossRef]
  4. A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, Opt. Lett. 26, 435 (2001).
    [CrossRef]
  5. See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
    [CrossRef] [PubMed]
  6. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
    [CrossRef]
  7. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
    [CrossRef]
  8. For particular beam powers a vertical dipole state is observed at the crystal output, and it may correspond to an intermediate state shown in Fig.  2(b).
  9. A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
    [CrossRef]

2001 (1)

2000 (3)

J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

T. Carmon, Ch. Anastassiou, S. Lan, D. Kip, Z. Musslimani, and M. Segev, Opt. Lett. 25, 1113 (2000).
[CrossRef]

1998 (3)

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

1995 (1)

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Anastassiou, Ch.

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Belic, M. R.

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

Carmon, T.

Denz, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

Desyatnikov, A. S.

García-Ripoll, J. J.

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Kaiser, F.

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

Kip, D.

Kivshar, Yu. S.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, Opt. Lett. 26, 435 (2001).
[CrossRef]

J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Krolikowski, W.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

Lan, S.

Luther-Davies, B.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

McCarthy, G.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Musslimani, Z.

Neshev, D.

Ostrovskaya, E. A.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

Pérez-García, V.

Saffman, M.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

Segev, M.

Stepken, A.

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

Weilnau, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (2)

See, e.g., A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1998).
[CrossRef]

Phys. Rev. E (1)

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, Phys. Rev. E 58, R4112 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, Phys. Rev. Lett. 80, 3240 (1998).
[CrossRef]

Other (1)

For particular beam powers a vertical dipole state is observed at the crystal output, and it may correspond to an intermediate state shown in Fig.  2(b).

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Figures (4)

Fig. 1
Fig. 1

Example of the numerical solution of Eqs.  (1) for a dipole-mode vector soliton γ=0.5,E0=2.5,λ2/λ1=0.5.

Fig. 2
Fig. 2

Numerical results of the dipole-mode soliton propagation for different input orientations. The ratio of the peak intensities is 1:0.28, and the diffraction length is 2  mm.

Fig. 3
Fig. 3

Experimental images of the dipole-mode vector solitons with horizontal and vertical orientations: (a), (c) input beams, (b), (d) output beams after simultaneous propagation. The y axis of the crystal corresponds to vertical direction on the figure. The input powers are 12 μW u1 and 6 μWu2, and the ratio of the peak intensities is 1:0.29.

Fig. 4
Fig. 4

Images of the quadrupole vector solitons for two different orientations. (a), (b) Numerics: input and output after 8  mm of propagation, u1peak2/u2peak2=1.6. (c), (d) Experiment: the beam powers are 5.0 μW u1 and 6.0 μW u2.

Equations (1)

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iE1,2z+122E1,2=-γ2φyE1,2,2φ+φln1+I=E0x0φyln1+I,

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