Abstract

We reveal the existence of dynamically stable, composite topological solitons in Bessel photonic lattices imprinted in focusing Kerr-type nonlinear media. The new stable, composite solitons are made of a vortex ring with unit topological charge incoherently coupled to a fundamental soliton. The stabilization of the otherwise highly azimuthally unstable vortex rings is provided under suitable conditions, which we study in detail, by cross-phase-modulation coupling with the fundamental soliton companion.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  29. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef]
  30. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Soliton trains in photonic lattices,' Opt. Express 12, 2831-2837 (2004).
    [CrossRef] [PubMed]
  33. Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, 'Stable soliton complexes in two-dimensional photonic lattices,' Opt. Lett. 29, 1918-1920 (2004).
    [CrossRef] [PubMed]
  34. D. N. Christodoulides and R. I. Joseph, 'Discrete self-focusing in nonlinear arrays of coupled waveguides,' Opt. Lett. 13, 794-796 (1988).
    [CrossRef] [PubMed]
  35. D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  36. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary solitons in Bessel optical lattices,' Phys. Rev. Lett. 93, 093940 (2004).
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    [CrossRef]

2005 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Stable ring-profile vortex solitons in Bessel optical lattices,' Phys. Rev. Lett. 94, 043992 (2005).
[CrossRef]

2004 (15)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[CrossRef]

S. K. Adhikari, 'Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length,' Phys. Rev. A 69, 063613 (2004).
[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, 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]

M. S. Bigelow, P. Zerom, and R. W. Boyd, 'Breakup of ring beams carrying orbital angular momentum in sodium vapor,' Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

T. A. Davydova and A. I. Yakimenko, 'Stable multicharged localized optical vortices in cubic-quintic nonlinear media,' J. Opt. A 6, 197-201 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary solitons in Bessel optical lattices,' Phys. Rev. Lett. 93, 093940 (2004).

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary dipole-mode solitons in Bessel optical lattices,' J. Opt. B 6, 444-447 (2004).
[CrossRef]

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

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh 'Spatial soliton switching in quasi-continuous optical arrays,' Opt. Lett. 29, 766-768 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, A. A. Egorov, and A. S. Zelenina, 'Stable periodic waves supported by competing cubic-quintic nonlinearity,' J. Opt. Soc. Am. B 21, 982-988 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Soliton trains in photonic lattices,' Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, 'Stable soliton complexes in two-dimensional photonic lattices,' Opt. Lett. 29, 1918-1920 (2004).
[CrossRef] [PubMed]

2003 (7)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, 'Spatial solitons in optically induced gratings,' Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

I. D. Maleev and G. A. Swartzlander, 'Composite optical vortices,' J. Opt. Soc. Am. B 20, 1169-1176 (2003).
[CrossRef]

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

J. Yang and D. Pelinovsky, 'Stable vortex and dipole vector solitons in a saturable nonlinear medium,' Phys. Rev. E 67, 016608 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

2002 (1)

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 (2002).
[CrossRef]

2001 (1)

2000 (2)

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

1998 (2)

1997 (3)

Z. Chen, M. 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, 1751-1753 (1997).
[CrossRef]

L. Torner and D. V. Petrov, 'Azimuthal instabilities and self-splitting of beams into solitons in bulk second-harmonic generation,' Electron. Lett. 33, 608-610 (1997).
[CrossRef]

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

1995 (1)

1988 (1)

1985 (1)

V. I. Kruglov and R. A. Vlasov, 'Spiral self-trapping propagation of optical beams in media with cubic nonlinearity,' Phys. Lett. 111, 401-404 (1985).
[CrossRef]

Adhikari, S. K.

S. K. Adhikari, 'Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length,' Phys. Rev. A 69, 063613 (2004).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003).

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, 123903 (2004).
[CrossRef] [PubMed]

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]

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, 'Breakup of ring beams carrying orbital angular momentum in sodium vapor,' Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Binosi, D.

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, 'Breakup of ring beams carrying orbital angular momentum in sodium vapor,' Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, Z.

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, 123903 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Z. Chen, M. 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, 1751-1753 (1997).
[CrossRef]

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, 123904 (2004).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, 'Stable soliton complexes in two-dimensional photonic lattices,' Opt. Lett. 29, 1918-1920 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
[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 (2002).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, 'Discrete self-focusing in nonlinear arrays of coupled waveguides,' Opt. Lett. 13, 794-796 (1988).
[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, 123904 (2004).
[CrossRef]

Cojocaru, C.

Davydova, T. A.

T. A. Davydova and A. I. Yakimenko, 'Stable multicharged localized optical vortices in cubic-quintic nonlinear media,' J. Opt. A 6, 197-201 (2004).
[CrossRef]

de Córdoba, P. Fernández

Desyatnikov, A. S.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, 'Optical vortices and vortex solitons,' Prog. Opt. (to be published).

Di Trapani, P.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[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 (2002).
[CrossRef]

Egorov, A. A.

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Ferrando, A.

Firth, W. J.

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

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]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[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 (2002).
[CrossRef]

García-Ripoll, J. J.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

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]

Joseph, R. I.

Kartashov, Y. V.

Kivshar, Y.

Kivshar, Y. S.

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, 123903 (2004).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003).

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, 'Optical vortices and vortex solitons,' Prog. Opt. (to be published).

Krolikowski, W.

Kruglov, V. I.

V. I. Kruglov and R. A. Vlasov, 'Spiral self-trapping propagation of optical beams in media with cubic nonlinearity,' Phys. Lett. 111, 401-404 (1985).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Luther-Davies, 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, 123903 (2004).
[CrossRef] [PubMed]

Maker, P. D.

Maleev, I. D.

Malomed, B. A.

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[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]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[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, 123903 (2004).
[CrossRef] [PubMed]

Martorell, J.

Mazilu, D.

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[CrossRef]

Minardi, S.

Molina-Terriza, G.

Monsoriu, J. A.

Muller, R. E.

Musslimani, Z.

Musslimani, Z. H.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

Neshev, D.

Neshev, D. N.

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, 123903 (2004).
[CrossRef] [PubMed]

Ostrovskaya, E.

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, 123903 (2004).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

Pelinovsky, D.

J. Yang and D. Pelinovsky, 'Stable vortex and dipole vector solitons in a saturable nonlinear medium,' Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Pérez-García, V. M.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

Petrov, D. V.

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 (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]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[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 (2002).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

Z. Chen, M. 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, 1751-1753 (1997).
[CrossRef]

Shih, M.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Skryabin, D. V.

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

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

Swartzlander, G. A.

Tikhonenko, V.

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Stable ring-profile vortex solitons in Bessel optical lattices,' Phys. Rev. Lett. 94, 043992 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary solitons in Bessel optical lattices,' Phys. Rev. Lett. 93, 093940 (2004).

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, 'Stable soliton complexes in two-dimensional photonic lattices,' Opt. Lett. 29, 1918-1920 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary dipole-mode solitons in Bessel optical lattices,' J. Opt. B 6, 444-447 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Soliton trains in photonic lattices,' Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh 'Spatial soliton switching in quasi-continuous optical arrays,' Opt. Lett. 29, 766-768 (2004).
[CrossRef] [PubMed]

S. Minardi, G. Molina-Terriza, P. Di Trapani, J. P. Torres, and L. Torner, 'Soliton algebra by vortex-beam splitting,' Opt. Lett. 26, 1004-1006 (2001).
[CrossRef]

J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, 'Solitary wave vortices in quadratic nonlinear media,' J. Opt. Soc. Am. B 15, 625-627 (1998).
[CrossRef]

D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, 'Observation of azimuthal modulation instability and formation of patterns of optical solitons in a quadratic nonlinear crystal,' Opt. Lett. 23, 1444-1446 (1998).
[CrossRef]

L. Torner and D. V. Petrov, 'Azimuthal instabilities and self-splitting of beams into solitons in bulk second-harmonic generation,' Electron. Lett. 33, 608-610 (1997).
[CrossRef]

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, 'Optical vortices and vortex solitons,' Prog. Opt. (to be published).

Torres, J. P.

Vilaseca, R.

Vlasov, R. A.

V. I. Kruglov and R. A. Vlasov, 'Spiral self-trapping propagation of optical beams in media with cubic nonlinearity,' Phys. Lett. 111, 401-404 (1985).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Stable ring-profile vortex solitons in Bessel optical lattices,' Phys. Rev. Lett. 94, 043992 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, A. A. Egorov, and A. S. Zelenina, 'Stable periodic waves supported by competing cubic-quintic nonlinearity,' J. Opt. Soc. Am. B 21, 982-988 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary solitons in Bessel optical lattices,' Phys. Rev. Lett. 93, 093940 (2004).

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary dipole-mode solitons in Bessel optical lattices,' J. Opt. B 6, 444-447 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Soliton trains in photonic lattices,' Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh 'Spatial soliton switching in quasi-continuous optical arrays,' Opt. Lett. 29, 766-768 (2004).
[CrossRef] [PubMed]

Wilson, D. W.

Yakimenko, A. I.

T. A. Davydova and A. I. Yakimenko, 'Stable multicharged localized optical vortices in cubic-quintic nonlinear media,' J. Opt. A 6, 197-201 (2004).
[CrossRef]

Yang, J.

J. Yang and D. Pelinovsky, 'Stable vortex and dipole vector solitons in a saturable nonlinear medium,' Phys. Rev. E 67, 016608 (2003).
[CrossRef]

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

Zacarés, M.

Zelenina, A. S.

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, 'Breakup of ring beams carrying orbital angular momentum in sodium vapor,' Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Electron. Lett. (1)

L. Torner and D. V. Petrov, 'Azimuthal instabilities and self-splitting of beams into solitons in bulk second-harmonic generation,' Electron. Lett. 33, 608-610 (1997).
[CrossRef]

J. Opt. A (1)

T. A. Davydova and A. I. Yakimenko, 'Stable multicharged localized optical vortices in cubic-quintic nonlinear media,' J. Opt. A 6, 197-201 (2004).
[CrossRef]

J. Opt. B (2)

D. Mihalache, D. Mazilu, B. A. Malomed and F. Lederer, 'Stable vortex solitons in a vectorial cubic-quintic model,' J. Opt. B 6, S341-S350 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary dipole-mode solitons in Bessel optical lattices,' J. Opt. B 6, 444-447 (2004).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, 'Discretizing light behavior in linear and nonlinear waveguide lattices,' Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,' Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (8)

Phys. Lett. (1)

V. I. Kruglov and R. A. Vlasov, 'Spiral self-trapping propagation of optical beams in media with cubic nonlinearity,' Phys. Lett. 111, 401-404 (1985).
[CrossRef]

Phys. Rev. A (1)

S. K. Adhikari, 'Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length,' Phys. Rev. A 69, 063613 (2004).
[CrossRef]

Phys. Rev. E (3)

J. Yang and D. Pelinovsky, 'Stable vortex and dipole vector solitons in a saturable nonlinear medium,' Phys. Rev. E 67, 016608 (2003).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, 'Stable vortex solitons supported by competing quadratic and cubic nonlinearities,' Phys. Rev. E 69, 066614 (2004).
[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 (2002).
[CrossRef]

Phys. Rev. Lett. (10)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Rotary solitons in Bessel optical lattices,' Phys. Rev. Lett. 93, 093940 (2004).

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, 'Discrete solitons and solitons-induced dislocations in partially coherent photonic lattices,' Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, 'Observation of discrete solitons in optically induced real time waveguide arrays,' Phys. Rev. Lett. 90, 023902 (2003).
[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, 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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, 'Stable ring-profile vortex solitons in Bessel optical lattices,' Phys. Rev. Lett. 94, 043992 (2005).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, 'Composite multihump vector solitons carrying topological charge,' Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, 'Dipole-mode vector solitons,' Phys. Rev. Lett. 85, 82-85 (2000).
[CrossRef] [PubMed]

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

M. S. Bigelow, P. Zerom, and R. W. Boyd, 'Breakup of ring beams carrying orbital angular momentum in sodium vapor,' Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, 'Optical vortices and vortex solitons,' Prog. Opt. (to be published).

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003).

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Figures (3)

Fig. 1
Fig. 1

(a) Zeroth-order Bessel photonic lattice. (b) Soliton profile corresponding to a point marked by a circle in (c) a dispersion diagram. (d) Energy sharing versus propagation constant b 1 at b 2 = 7 , lattice depth p = 8 .

Fig. 2
Fig. 2

(a) Real part of the growth rate of a perturbation with azimuthal index n = 1 at b 2 = 7 , p = 8 . (b) Real parts of perturbation components corresponding to n = 1 , b 1 = 2 , b 2 = 7 , p = 8 . (c) Areas of stability and instability (shaded) on ( b 1 , b 2 ) plane at p = 8 . (d) Areas of stability and instability (shaded) on ( b 1 , p ) plane at b 2 = 7 .

Fig. 3
Fig. 3

(a) Decay of the unstable vector soliton at b 1 = 2 , and (b) its stable propagation at b 1 = 1.2 in the presence of white input noise with the variance σ noise 2 = 0.01 . Intensity distribution of the first component is shown at three different propagation distances; lattice depth p = 8 and propagation constant b 2 = 7 .

Equations (9)

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

i q 1 ξ = 1 2 ( 2 q 1 η 2 + 2 q 1 ζ 2 ) q 1 ( q 1 2 + q 2 2 ) p R ( η , ζ ) q 1 ,
i q 2 ξ = 1 2 ( 2 q 2 η 2 + 2 q 2 ζ 2 ) q 2 ( q 1 2 + q 2 2 ) p R ( η , ζ ) q 2 .
U = U 1 + U 2 = ( q 1 2 + q 2 2 ) d η d ζ .
q 1 ( η , ζ , ξ ) = w 1 ( r ) exp ( i m 1 ϕ ) exp ( i b 1 ξ )
q 2 ( η , ζ , ξ ) = w 2 ( r ) exp ( i m 2 ϕ ) exp ( i b 2 ξ ) ,
d 2 w 1 , 2 d r 2 + 1 r d w 1 , 2 d r m 1 , 2 2 w 1 , 2 r 2 2 b 1 , 2 w 1 , 2 + 2 w 1 , 2 ( w 1 2 + w 2 2 ) + 2 p R w 1 , 2 = 0
q 1 , 2 ( η , ζ , ξ , p ) χ q 1 , 2 ( χ η , χ ζ , χ 2 ξ , χ 2 p )
q 1 , 2 = [ w 1 , 2 ( r ) + u 1 , 2 ( r , ξ ) exp ( i n ϕ ) + v 1 , 2 * ( r , ξ ) exp ( i n ϕ ) ] exp ( i b 1 , 2 ξ + i m 1 , 2 ϕ )
q 1 , 2 ( r , ϕ , ξ = 0 ) = w 1 , 2 ( r ) exp ( i m 1 , 2 ϕ ) [ 1 + ρ 1 , 2 ( r , ϕ ) ] ,

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