Abstract

We study nonlinear propagation of optical vortices in presence of hybrid nonlinearity as established in a nonconventional biased photorefractive crystal. Our results indicate that under hybrid nonlinearity the breakup of a singly-charged vortex along with the loss of its angular momentum is suppressed considerably as compared with that under conventional self-focusing or self-defocusing nonlinearity. Disintegration of a doubly-charged vortex under hybrid nonlinearity is also presented. Our experimental results are in good agreement with the numerical simulations.

© 2009 OSA

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    [CrossRef] [PubMed]
  14. I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
    [CrossRef] [PubMed]
  25. T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
    [CrossRef] [PubMed]
  26. A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
    [CrossRef] [PubMed]
  27. A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
    [CrossRef] [PubMed]
  28. A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Express 14(18), 8317 (2006).
    [CrossRef] [PubMed]

2009 (2)

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, “Saddle solitons: a balance between bi-diffraction and hybrid nonlinearity,” Opt. Lett. 34(21), 3259–3261 (2009).
[CrossRef] [PubMed]

2008 (1)

A. V. Gorbach, D. V. Skryabin, and C. N. Harvey, “Vortex solitons in an off-resonant Raman medium,” Phys. Rev. A 77(6), 063810 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (3)

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13(2), 435–443 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291 (2005).
[CrossRef]

2004 (4)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
[CrossRef] [PubMed]

2003 (2)

2001 (2)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001).
[CrossRef] [PubMed]

2000 (1)

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

Z. Chen, M. F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22(23), 1751–1753 (1997).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[CrossRef]

1996 (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[CrossRef] [PubMed]

1995 (2)

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Daves, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12(11), 2046 (1995).
[CrossRef]

1992 (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221 (1992).
[CrossRef] [PubMed]

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
[CrossRef] [PubMed]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bang, O.

Barnett, S. M.

Bartal, G.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bezryadina, A.

Briedis, D.

Buryak, A. V.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

Chen, Z.

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, and Z. Chen, “Saddle solitons: a balance between bi-diffraction and hybrid nonlinearity,” Opt. Lett. 34(21), 3259–3261 (2009).
[CrossRef] [PubMed]

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(2), 536–544 (2007).
[CrossRef] [PubMed]

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Express 14(18), 8317 (2006).
[CrossRef] [PubMed]

A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Z. Chen, M. F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22(23), 1751–1753 (1997).
[CrossRef] [PubMed]

Christodoulides, D. N.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Christou, J.

Cohen, O.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Courtial, J.

Crasovan, L.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

Crosignani, B.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

de Córdoba, P. F.

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Di Porto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Duree, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Edmundson, D.

Eugenieva, E.

Ferrando, A.

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Franke-Arnold, S.

Gao, Y.

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

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(2), 536–544 (2007).
[CrossRef] [PubMed]

García-March, M. A.

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Gibson, G.

Gorbach, A. V.

A. V. Gorbach, D. V. Skryabin, and C. N. Harvey, “Vortex solitons in an off-resonant Raman medium,” Phys. Rev. A 77(6), 063810 (2008).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Harvey, C. N.

A. V. Gorbach, D. V. Skryabin, and C. N. Harvey, “Vortex solitons in an off-resonant Raman medium,” Phys. Rev. A 77(6), 063810 (2008).
[CrossRef]

Heckenberg, N. R.

Hu, Y.

Hudock, J.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Express 14(18), 8317 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291 (2005).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
[CrossRef] [PubMed]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

V. Tikhonenko, Y. S. Kivshar, V. V. Steblina, and A. A. Zozulya, “Vortex solitons in a saturable optical medium,” J. Opt. Soc. Am. B 15(1), 79 (1998).
[CrossRef]

Krolikowski, W.

Law, C. T.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

Liu, Q.

Liu, S.

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

Lou, C.

Luther-Daves, B.

Makasyuk, I.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Maker, P. D.

Malomed, B. A.

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001).
[CrossRef] [PubMed]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

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(11), 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(22), 4544–4547 (1996).
[CrossRef] [PubMed]

Manela, O.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Martin, H.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

McDuff, R.

Mihalache, D.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

Monsoriu, J. A.

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Morin, M.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Muller, R. E.

Musslimani, Z. H.

Neshev, D. N.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Express 14(18), 8317 (2006).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Padgett, M. J.

Pas’ko, V.

Petersen, D. E.

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 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(22), 4544–4547 (1996).
[CrossRef] [PubMed]

Salamo, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

Segev, M.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

Z. Chen, M. F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22(23), 1751–1753 (1997).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Sharp, E.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Shih, M. F.

Skryabin, D. V.

A. V. Gorbach, D. V. Skryabin, and C. N. Harvey, “Vortex solitons in an off-resonant Raman medium,” Phys. Rev. A 77(6), 063810 (2008).
[CrossRef]

Smith, C. P.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Steblina, V. V.

Sukhorukov, A. A.

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
[CrossRef] [PubMed]

Swartzlander, G. A.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

Tan, X.

Tikhonenko, V.

Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291 (2005).
[CrossRef]

Towers, I.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

Vasnetsov, M.

White, A. G.

Wilson, D. W.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Xu, J.

Yang, D.

Yang, J.

Yariv, A.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

Young, J.

Zacarés, M.

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Zhang, P.

Zhao, J.

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

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(2), 536–544 (2007).
[CrossRef] [PubMed]

Zozulya, A. A.

V. Tikhonenko, Y. S. Kivshar, V. V. Steblina, and A. A. Zozulya, “Vortex solitons in a saturable optical medium,” J. Opt. Soc. Am. B 15(1), 79 (1998).
[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(11), 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(22), 4544–4547 (1996).
[CrossRef] [PubMed]

Appl. Phys. B (1)

P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, and Z. Chen, “Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals,” Appl. Phys. B 95(3), 559–563 (2009).
[CrossRef]

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

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (5)

Phys. Lett. A (1)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. Crasovan, and D. Mihalache, “Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation,” Phys. Lett. A 288(5-6), 292–298 (2001).
[CrossRef]

Phys. Rev. A (2)

A. V. Gorbach, D. V. Skryabin, and C. N. Harvey, “Vortex solitons in an off-resonant Raman medium,” Phys. Rev. A 77(6), 063810 (2008).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 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(22), 4544–4547 (1996).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74(11), 1978–1981 (1995).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93(6), 063901 (2004).
[CrossRef] [PubMed]

A. Ferrando, M. Zacarés, M. A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95(12), 123901 (2005).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291 (2005).
[CrossRef]

Other (1)

L. M. Pismen, Vortices in nonlinear fields: from liquid crystals to superfluids, from non-equilibrium patterns to cosmic strings. (Oxford University Press, New York, 1999).

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Figures (5)

Fig. 1
Fig. 1

Numerical simulations of the refractive index change in a biased photorefractive crystal induced by a vortex beam. (a) Input vortex beam; (b)-(d) Index changes at α=0, π, and π/2, respectively.

Fig. 2
Fig. 2

Nonlinear evolution of the singly-charged vortex beam at α=0 (a), π (b), and π/2 (c). From left to right are the output intensity profiles at different normalized propagation distances z=20, 40, 60, 80, and 100, respectively; (d) OAM versus z.

Fig. 3
Fig. 3

Experimental setup for observation of vortex propagation in a biased photorefractive crystal. BS: Beam splitter; RT: Reversed telescope; M: Mirror; L: Lens; F: Spatial filter; WLS: White light source, Mask: Computer-generated holographic mask.

Fig. 4
Fig. 4

Experimental results of a singly-charged vortex under different bias conditions. (a) Intensity distribution and (b) interferogram of the input vortex beam; (c) Linearly diffracted output beam; (d)-(f) Nonlinear output at α=0, π, and π/2, respectively; where results from top to bottom are obtained at gradually increased voltages.

Fig. 5
Fig. 5

Numerical (a, b) and experimental (c-e) results showing breakup of double-charged vortices. Top and bottom correspond to intensity patterns and interferograms, respectively. (a) and (b) Simulations at z=45 for α=π/2 and α=π, respectively; (c) Input vortex; (d) and (e) Experimental results corresponding to (a) and (b).

Equations (3)

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

B ( r ) = I 0 r exp ( | r | 2 σ 2 ) exp ( i m θ ) ,
( z i 2 2 ) B ( r ) = i ( ϕ x sin α + ϕ y cos α ) B ( r ) ,
2 ϕ + ϕ ln [ 1 + | B ( r ) | 2 ] = y ln [ 1 + | B ( r ) | 2 ] ,

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