Abstract

We have produced beams with dark rings and studied their propagation through photovoltaic photorefractive media. We observe that dark rings, instead of forming dark ring solitons, break into vortex–antivortex pairs, forming quadrupoles. The experimental results could be taken as a consequence of modulational instability during beam propagation that is revealed through our numerical analysis.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
    [CrossRef]
  3. D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
    [CrossRef]
  4. G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).
  5. A. M. Kamchatnov and S. V. Korneev, “Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics,” Phys. Lett. A 3744625–4628 (2010).
    [CrossRef]
  6. P. Vaity and R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 362994–2996 (2011).
    [CrossRef]
  7. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [CrossRef]
  8. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
    [CrossRef]
  9. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
    [CrossRef]
  10. P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, “Elliptical solitons in nonconventionally biased photorefractive crystals,” Opt. Express 15, 536–544 (2007).
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    [CrossRef]
  13. R. Passier, F. Devaux, and M. Chauvet, “Impact of tensorial nature of the electro-optic effect on vortex beam propagation in photorefractive media,” Opt. Express 16, 7134–7141 (2008).
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    [CrossRef]
  15. A. Stepken, F. Kaiser, and M. R. Belic, “Anisotropic interaction of three-dimensional spatial screening solitons,” J. Opt. Soc. Am. B 17, 68–77 (2000).
    [CrossRef]
  16. D. N. Christodoulides and M. I. Carvalho, “Bright, dark and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
    [CrossRef]
  17. M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
    [CrossRef]
  18. A. V. Mamaev and M. Saffman, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
    [CrossRef]
  19. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
    [CrossRef]
  20. A. V. Volyar and T. A. Fadeeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 235–244 (2003).
    [CrossRef]
  21. A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006).
    [CrossRef]
  22. Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
    [CrossRef]
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    [CrossRef]

2011 (2)

2010 (1)

A. M. Kamchatnov and S. V. Korneev, “Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics,” Phys. Lett. A 3744625–4628 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (1)

2006 (2)

2003 (2)

A. V. Volyar and T. A. Fadeeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 235–244 (2003).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

2002 (1)

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

2000 (1)

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

1997 (4)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713–R1716 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

1996 (3)

A. V. Mamaev and M. Saffman, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
[CrossRef]

1995 (3)

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef]

1994 (1)

Y. Kivshar and X. Yang, “Ring dark solitons,” Phys. Rev. E 50, R40–R43 (1994).
[CrossRef]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Baluschev, S.

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Belic, M. R.

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

A. Stepken, F. Kaiser, and M. R. Belic, “Anisotropic interaction of three-dimensional spatial screening solitons,” J. Opt. Soc. Am. B 17, 68–77 (2000).
[CrossRef]

Carvalho, M. I.

Chauvet, M.

Chen, Z.

Christodoulides, D. N.

Dennis, M. R.

Desyatnikov, A. S.

Devaux, F.

Dinev, S.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Dreischuh, A.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Fadeeva, T. A.

A. V. Volyar and T. A. Fadeeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 235–244 (2003).
[CrossRef]

Fadeyeva, T.

Flieber, W.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

Frantzeskakis, D. J.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

Gan, X.

Gao, Y.

Kaiser, F.

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

A. Stepken, F. Kaiser, and M. R. Belic, “Anisotropic interaction of three-dimensional spatial screening solitons,” J. Opt. Soc. Am. B 17, 68–77 (2000).
[CrossRef]

Kamchatnov, A. M.

A. M. Kamchatnov and S. V. Korneev, “Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics,” Phys. Lett. A 3744625–4628 (2010).
[CrossRef]

Kamenov, V.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

Kevrekidis, P. G.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

Kivshar, Y.

Y. Kivshar and X. Yang, “Ring dark solitons,” Phys. Rev. E 50, R40–R43 (1994).
[CrossRef]

Kivshar, Y. S.

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

Korneev, S. V.

A. M. Kamchatnov and S. V. Korneev, “Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics,” Phys. Lett. A 3744625–4628 (2010).
[CrossRef]

Krolikowski, W.

Kumar, A.

Liu, Q.

Liu, S.

Lou, C.

Maker, P. D.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Malomed, B. A.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713–R1716 (1997).
[CrossRef]

A. V. Mamaev and M. Saffman, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
[CrossRef]

Marazov, O.

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Muller, R. E.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Neshev, D.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

Neshev, D. N.

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Passier, R.

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713–R1716 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. V. Mamaev and M. Saffman, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef]

Segev, M.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Shvedov, V.

Singh, R. P.

Stefanov, I.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

Stepken, A.

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

A. Stepken, F. Kaiser, and M. R. Belic, “Anisotropic interaction of three-dimensional spatial screening solitons,” J. Opt. Soc. Am. B 17, 68–77 (2000).
[CrossRef]

Tan, X.

Theocharis, G.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

Vaity, P.

Velchev, I.

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Volyar, A.

Volyar, A. V.

A. V. Volyar and T. A. Fadeeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 235–244 (2003).
[CrossRef]

Vujic, D.

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

Wilson, D. W.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Windholz, L.

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

Xu, J.

Yang, D.

Yang, X.

Y. Kivshar and X. Yang, “Ring dark solitons,” Phys. Rev. E 50, R40–R43 (1994).
[CrossRef]

Zhang, P.

Zhao, J.

Zheng, Y.

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713–R1716 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef]

Appl. Phys. B (1)

D. Neshev, A. Dreischuh, V. Kamenov, I. Stefanov, S. Dinev, W. Flieber, and L. Windholz, “Generation and intrinsic dynamics of ring dark solitary waves,” Appl. Phys. B 64, 429–433 (1997).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (5)

Opt. Lett. (2)

Opt. Spectrosc. (1)

A. V. Volyar and T. A. Fadeeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 235–244 (2003).
[CrossRef]

Phys. Lett. A (1)

A. M. Kamchatnov and S. V. Korneev, “Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics,” Phys. Lett. A 3744625–4628 (2010).
[CrossRef]

Phys. Rev. A (3)

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713–R1716 (1997).
[CrossRef]

Phys. Rev. E (3)

M. R. Belic, D. Vujic, A. Stepken, and F. Kaiser, “Isotropic versus anisotropic modeling of photorefractive solitons,” Phys. Rev. E 65, 066610 (2002).
[CrossRef]

Y. Kivshar and X. Yang, “Ring dark solitons,” Phys. Rev. E 50, R40–R43 (1994).
[CrossRef]

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517–5523 (1995).
[CrossRef]

Phys. Rev. Lett. (5)

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, “Ring dark solitons and vortex necklaces in Bose-Einstein condensates,” Phys. Rev. Lett. 52, 2262–2265 (2003).

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544–4547 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

A. V. Mamaev and M. Saffman, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Prog. Opt. (1)

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Numerical intensity distributions (first and second rows) and corresponding interferograms (third and fourth rows) at different propagation distances for an LG beam with p=1.

Fig. 2.
Fig. 2.

Experimental setup. L, laser; BS1, BS2, beam splitter; SLM, spatial light modulator; P, polarizer; L1 and L2, lenses; M1 and M2, mirrors; PR, photorefractive crystal; BI, white-light source; CCD, camera.

Fig. 3.
Fig. 3.

Experimental (first and second columns) and numerical (third and fourth columns) intensity profiles at the back surface of the crystal for an LG beam with p=1 (first row) and corresponding interferograms (second row).

Fig. 4.
Fig. 4.

Experimental (first and second columns) and numerical (third and fourth columns) intensity profiles at the back surface of the crystal for an LG beam with p=2 (first row) and corresponding interferograms (second row).

Fig. 5.
Fig. 5.

Experimental (first and second columns) and numerical (third and fourth columns) intensity profiles at the back surface of the crystal for an LG beam with p=1 and l=2 (first row) and corresponding interferograms (second row).

Equations (6)

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u(x,y)z=i22u(x,y)+inoko2wo2Δnu(x,y),
Δn=12no3reffEsc.
2ϕ+ϕ[ln(1+I)]=Epln(1+I)y,
Esc=ϕ.
Δn=12no3reffϕy.
u(x,y,z=0)=Imexp[(x2+y2)]exp[ilθ]Lpl[2(x2+y2)]

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