Abstract

We study interaction of a discrete vortex with a supporting photonic lattice and analyze how the combined action of the lattice periodicity and the medium nonlinearity can modify the vortex structure. In particular, we describe theoretically and observe in experiment, for the first time to our knowledge, the nontrivial topological transformations of the discrete vortex including the flipping of vortex charge and inversion of its orbital angular momentum. We also demonstrate the stabilizing effect of the interaction with the so-called “mixed” optically-induced photonic lattices on the vortex propagation and topological structure.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
  34. A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
    [CrossRef]
  35. Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
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    [CrossRef]
  38. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
    [CrossRef]

2006

2005

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

A. Ferrando, M. Zacarés, P. Andrées, P. F. de Córdoba, and J. Monsoriu, "Nodal solitons and the nonlinear breaking of discrete symmetry," Opt. Express 13, 1072-1078 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. N. Neshev, Yu. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869-871 (2005).
[CrossRef] [PubMed]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

A. Ferrando, "Discrete-symmetry vortices as angular Bloch modes," Phys. Rev. E 72, 036612 (2005).
[CrossRef]

A. Ferrando, M. Zacarés, and M.-Á. Garćıa-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

2004

J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 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, 123904 (2004).
[CrossRef] [PubMed]

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

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express 12, 817-822 (2004).
[CrossRef] [PubMed]

2003

J. Yang and Z. H. Musslimani, "Fundamental and vortex solitons in a two-dimensional optical lattice," Opt. Lett. 28, 2094-2096 (2003).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
[CrossRef]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810 (2003).
[CrossRef] [PubMed]

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

2002

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Z. Chen and K. McCarthy, "Spatial soliton pixles from partially coherent light," Opt. Lett. 27, 2019-2021 (2002).
[CrossRef]

2001

G. Molina-Terriza, E. M. Wright, and L. Torner, "Propagation and control of noncanonical optical vortices," Opt. Lett. 26, 163-165 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2001).
[CrossRef]

1999

J. W. R. Tabosa and D. V. Petrov "Optical pumping of orbital angular momentum of light in cold Cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

1998

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

1997

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Alexander, T. J.

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

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

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

Andrées, P.

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2001).
[CrossRef]

Bezryadina, A.

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

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

Binosi, D.

Chen, Z.

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

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

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

Z. Chen and K. McCarthy, "Spatial soliton pixles from partially coherent light," Opt. Lett. 27, 2019-2021 (2002).
[CrossRef]

Christodoulides, D. N.

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

de Córdoba, P. F.

Dennis, M. R.

Denz, C.

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, "Two-dimensional self-trapped nonlinear photonic lattices," Opt. Express 14, 2851-2863 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. N. Neshev, Yu. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869-871 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
[CrossRef]

Desyatnikov, A. S.

Dreischuh, A.

Efremidis, N. K.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Eugenieva, E.

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

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

A. Ferrando, "Discrete-symmetry vortices as angular Bloch modes," Phys. Rev. E 72, 036612 (2005).
[CrossRef]

A. Ferrando, M. Zacarés, P. Andrées, P. F. de Córdoba, and J. Monsoriu, "Nodal solitons and the nonlinear breaking of discrete symmetry," Opt. Express 13, 1072-1078 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacarés, and M.-Á. Garćıa-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express 12, 817-822 (2004).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

Fischer, R.

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, 123904 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Garcia-March, M.-A.

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

Garcia-March, M.-Á.

A. Ferrando, M. Zacarés, and M.-Á. Garćıa-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810 (2003).
[CrossRef] [PubMed]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

Jägers, J.

Johansson, M.

M. Öster and M. Johansson, "Stable stationary and quasi-periodic discrete vortex-breathers with topological charge S = 2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

Kartashov, Y. V.

Kivshar, Yu. S.

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, "Two-dimensional self-trapped nonlinear photonic lattices," Opt. Express 14, 2851-2863 (2006).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Observation of light localization in modulated Bessel optical lattices," Opt. Express 14, 2825-2830 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. N. Neshev, Yu. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869-871 (2005).
[CrossRef] [PubMed]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

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

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

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
[CrossRef]

Krolikowski, W.

Lederer, F.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

Lopez-Aguayo, S.

Makasyuk, I.

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

Malomed, B. A.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

Martin, H.

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

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

Mazilu, D.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

McCarthy, K.

Mihalache, D.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

G. Molina-Terriza, E. M. Wright, and L. Torner, "Propagation and control of noncanonical optical vortices," Opt. Lett. 26, 163-165 (2001).
[CrossRef]

Monsoriu, J.

Monsoriu, J. A.

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

Musslimani, Z. H.

Neshev, D.

Neshev, D. N.

Öster, M.

M. Öster and M. Johansson, "Stable stationary and quasi-periodic discrete vortex-breathers with topological charge S = 2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

Ostrovskaya, E. A.

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

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
[CrossRef]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov "Optical pumping of orbital angular momentum of light in cold Cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608 (1997).
[CrossRef]

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

Sagemerten, N.

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

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, 123904 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2001).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Sukhorukov, A. A.

Tabosa, J. W. R.

J. W. R. Tabosa and D. V. Petrov "Optical pumping of orbital angular momentum of light in cold Cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

Terhalle, B.

Torner, L.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, E. M. Wright, and L. Torner, "Propagation and control of noncanonical optical vortices," Opt. Lett. 26, 163-165 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608 (1997).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Träger, D.

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2001).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Wright, E. M.

G. Molina-Terriza, E. M. Wright, and L. Torner, "Propagation and control of noncanonical optical vortices," Opt. Lett. 26, 163-165 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Yang, J.

Zacares, M.

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

Zacarés, M.

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

Electron. Lett.

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608 (1997).
[CrossRef]

Europhys. Lett.

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Nature

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810 (2003).
[CrossRef] [PubMed]

New J. Phys.

J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
[CrossRef]

Opt. Commun.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 (1997).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57,522-534 (1998).
[CrossRef]

Phys. Rev. E

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, "Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media," Phys. Rev. E 71, 026615 (2005).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

M. Öster and M. Johansson, "Stable stationary and quasi-periodic discrete vortex-breathers with topological charge S = 2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

A. Ferrando, "Discrete-symmetry vortices as angular Bloch modes," Phys. Rev. E 72, 036612 (2005).
[CrossRef]

Phys. Rev. Lett.

A. Ferrando, M. Zacarés, and M.-Á. Garćıa-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, M.-A. Garćıa-March, J. A. Monsoriu, and P. F. de Córdoba, "Vortex transmutation," Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 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, 123904 (2004).
[CrossRef] [PubMed]

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

J. W. R. Tabosa and D. V. Petrov "Optical pumping of orbital angular momentum of light in cold Cesium atoms," Phys. Rev. Lett. 83, 4967 (1999).
[CrossRef]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Band-gap solitons in nonlinear opticallyinduced lattices," Phys. Rev. Lett. 91, 0153902 (2003).
[CrossRef]

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner and E. M. Wright, "Observation of the dynamical inversion of the topological chage of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Other

A. A. Sukhorukov, "Soliton dynamics in deformable nonlinear lattices," Phys. Rev. E (2006), in press; preprint available: nlin.PS/0507050.
[CrossRef]

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP Publishing, Bristol, 1999).

A. S. Desyatnikov, Yu. S. Kivhsar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics 47, E. Wolf, ed., (North-Holland, Amsterdam, 2005), pp. 219-319.
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, E. Wolf, ed., (North-Holand, Amstredam, 2001), Vol. 42, pp. 219-276.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical angular momentum (Institute of Physics Publishing, 2003).
[CrossRef]

N. R. Heckenberg, M. E. J. Freise, T. A. Nieminen, and H. Rubinsztein-Dunlop, in Optical Vortices, M. Vasnetsov, K. Staliunas, eds., Horizons in World Physics (Nova Sciences Pub., New York, 1999) Vol. 228 p. 75.

Supplementary Material (7)

» Media 1: AVI (6208 KB)     
» Media 2: AVI (6535 KB)     
» Media 3: AVI (2026 KB)     
» Media 4: AVI (4901 KB)     
» Media 5: AVI (4803 KB)     
» Media 6: AVI (9973 KB)     
» Media 7: AVI (5822 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Comparison between the structural and topological instabilities of optical vortices. (a) Linearly unstable vortex soliton in a saturable bulk medium. (b) Generation of a stable vortex soliton on a square photonic lattice. (c) Topological transformations of the asymmetrically perturbed discrete vortex on the lattice [movie IsoUnfoldings.avi, 2.2MB]. The isosurfaces are plotted at the half-peak intensity (green) and at a small value ~ 10-2 (red). The red “string” in (b) shows the position of the vortex core, while bursts in (a) and (c) indicate the vortex unfoldings. (d) Dynamics of the angular momentum (normalized by the power) for all three cases.

Fig. 2.
Fig. 2.

Experimental setup: λ/2 - half-wave plate, PBS - polarising beam splitter, L - lenses, D - rotating diffuser, AM - amplitude mask of square array, FF - Fourier filtering of the four first diffraction orders, M - mirrors, BS - beam splitter, BSC - beam splitter cube, F - neutral density filter, SBN - Strontium Barium Niobate photorefractive crystal, and CCD - camera. Top left inset: schematic of the linear polarisation state of the lattice wave, forming its flexible and fixed components.

Fig. 3.
Fig. 3.

Topological transformation of an off-site vortex in a fixed lattice (induced by an ordinary polarized lattice wave). Upper row - intensity distribution; bottom row - phase interferogram. (a) Input vortex in the lattice; (b) linear diffraction; (c) nonlinear output with a transformed phase structure. (d) corresponding numerical simulations confirming the nonlinear phase transformation [movie FixedOFF.avi, 6.2MB]. Arrows and circles indicate the position of the vortex dislocations. The total charge of the beam in (c) is -1, i.e., it is inverted with respect to the initial charge +1.

Fig. 4.
Fig. 4.

Topological transformations of an on-site vortex in a mixed lattice with 3% nonlinear component. Upper row – intensity distribution; bottom row – phase interferograms. (a) Input vortex; (b) linear diffraction; (c) nonlinear output with a transformed phase structure; (d) corresponding numerical simulations [movie Mixed3ON.avi (2MB), see the description in the text]. Arrows and circles indicate the position of the vortex dislocations. Dotted oval indicates two closely positioned vortices with the opposite charges. The total beam charge in (c) is +1, i.e., it is preserved with respect to the initial charge +1. [Media 7

Fig. 5.
Fig. 5.

Topological transformation of the off-site vortex on a square flexible lattice. Trajectories of vortices are shown vs. lattice depth (relaxation time t after blocking the lattice beam at t = 0). The red lines (gray projections) correspond to vortex dislocation of charge +1, while the blue lines (black projections) correspond to charge -1.

Fig. 6.
Fig. 6.

Dynamics of the angular momentum for an off-site vortex interacting with a flexible lattice (black), fixed lattice (blue), and mixed (50/50%) photonic lattice (red). The black line is terminated when the flexible lattice loses its symmetry during interaction.

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