Abstract

We demonstrate the existence of multipeaked fundamental and vortex solitons in defocusing Kerr media with an imprinted azimuthally modulated Bessel lattice. Multipeaked solitons emanating from the fundamental linear lattice modes are stable in their entire existence domains. The number of soliton peaks is determined by the azimuthal index. Multipeaked vortex solitons with high topological charges in lattices exhibit special amplitude and phase distributions that resemble those of azimuthons. We reveal that the “stability rule” for vortex solitons in defocusing Kerr media is exactly opposite to that in focusing media. Multipeaked vortex solitons we obtained may provide a missing link between the radially symmetric vortices and nonrotating soliton clusters.

© 2011 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibres to Photonic Crystals (Academic, 2003).
  2. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [CrossRef]
  3. 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]
  4. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094–2096(2003).
    [CrossRef] [PubMed]
  5. J. Yang, I. Makasyuk, A. Beza, and Z. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29, 1662–1664 (2004).
    [CrossRef] [PubMed]
  6. J. Yang, “Stability of vortex solitons in a photorefractive optical lattice,” New J. Phys. 6, 47 (2004).
    [CrossRef]
  7. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
    [CrossRef]
  8. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
    [CrossRef] [PubMed]
  9. G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
    [CrossRef] [PubMed]
  10. Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
    [CrossRef] [PubMed]
  11. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
    [CrossRef] [PubMed]
  12. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef] [PubMed]
  13. L. Dong, H. Wang, W. Zhou, X. Yang, X. Lv, and H. Chen, “Necklace solitons and ring solitons in Bessel optical lattices,” Opt. Express 16, 5649–5655 (2008).
    [CrossRef] [PubMed]
  14. L. Dong, J. Wang, H. Wang, and G. Yin, “Broken ring solitons in Bessel optical lattices,” Opt. Lett. 33, 2989–2991 (2008).
    [CrossRef] [PubMed]
  15. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
    [CrossRef] [PubMed]
  16. Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B 6, 444–447 (2004).
    [CrossRef]
  17. X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
    [CrossRef] [PubMed]
  18. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
    [CrossRef]
  19. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
    [CrossRef]
  20. 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]
  21. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
    [CrossRef]
  22. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825–2830 (2006).
    [CrossRef] [PubMed]
  23. A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]
  24. A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  25. S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
    [CrossRef] [PubMed]
  26. S. Lopez-Aguayo, A. S. Desyatnikov, and Y. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006).
    [CrossRef] [PubMed]
  27. F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
    [CrossRef]
  28. V. M. Lashkin, “Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates,” Phys. Rev. A 77, 025602 (2008).
    [CrossRef]
  29. V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
    [CrossRef]
  30. B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
    [CrossRef]
  31. K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
    [CrossRef]
  32. L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026(2009).
    [CrossRef]

2009 (6)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
[CrossRef]

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026(2009).
[CrossRef]

2008 (4)

V. M. Lashkin, “Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates,” Phys. Rev. A 77, 025602 (2008).
[CrossRef]

L. Dong, H. Wang, W. Zhou, X. Yang, X. Lv, and H. Chen, “Necklace solitons and ring solitons in Bessel optical lattices,” Opt. Express 16, 5649–5655 (2008).
[CrossRef] [PubMed]

L. Dong, J. Wang, H. Wang, and G. Yin, “Broken ring solitons in Bessel optical lattices,” Opt. Lett. 33, 2989–2991 (2008).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

2007 (1)

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

2006 (4)

2005 (8)

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. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

2004 (5)

J. Yang, I. Makasyuk, A. Beza, and Z. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29, 1662–1664 (2004).
[CrossRef] [PubMed]

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

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

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

2003 (2)

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

2002 (1)

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibres to Photonic Crystals (Academic, 2003).

Alexander, T. J.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Bang, O.

Bartal, G.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

Beza, A.

Buccoliero, D.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

Carretero-Gonzalez, R.

Chen, H.

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Beza, and Z. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29, 1662–1664 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[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]

Cohen, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Denz, C.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Desyatnikov, A. S.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

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

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, and Y. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Dong, L.

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]

Egorov, A.

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

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[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]

Fischer, R.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

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

Fleischer, J. W.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[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]

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

Göries, D.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Grech, M.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

Kaiser, F.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
[CrossRef]

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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[CrossRef]

Y. V. Kartashov, A. Egorov, V. 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, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

Kivshar, Y. S.

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, and Y. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006).
[CrossRef] [PubMed]

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

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibres to Photonic Crystals (Academic, 2003).

Krolikowski, W.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

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

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

Królikowski, W.

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

Lashkin, V. M.

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

V. M. Lashkin, “Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates,” Phys. Rev. A 77, 025602 (2008).
[CrossRef]

Law, K. J. H.

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Lopez-Aguayo, S.

Lv, X.

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Beza, and Z. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29, 1662–1664 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Manela, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

Maucher, F.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Musslimani, Z. H.

Neshev, D. N.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

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

Ostrovskaya, E. A.

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

Richter, T.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Rose, P.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[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]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Skupin, S.

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Sukhorukov, A. A.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

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

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

Terhalle, B.

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
[CrossRef]

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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

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

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[CrossRef]

Vysloukh, V.

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

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Wang, H.

Wang, J.

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Yang, J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

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

J. Yang, I. Makasyuk, A. Beza, and Z. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29, 1662–1664 (2004).
[CrossRef] [PubMed]

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

Yang, X.

Ye, F.

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026(2009).
[CrossRef]

Yin, G.

Zhou, W.

Eur. Phys. J. Special Top. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Solitons in complex optical lattices,” Eur. Phys. J. Special Top. 173, 87–105 (2009).
[CrossRef]

J. Mater. Sci. Mater. Electron. (1)

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Light localization in azimuthally modulated Bessel photonic lattices,” J. Mater. Sci. Mater. Electron. 18, S277–S283 (2007).
[CrossRef]

J. Opt. B (1)

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

Nature (1)

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]

New J. Phys. (2)

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

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026(2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

F. Maucher, D. Buccoliero, S. Skupin, M. Grech, A. S. Desyatnikov, and W. Krolikowski, “Tracking azimuthons in nonlocal nonlinear media,” Opt. Quantum Electron. 41, 337–348 (2009).
[CrossRef]

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Phys. Rev. A (4)

V. M. Lashkin, “Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates,” Phys. Rev. A 77, 025602 (2008).
[CrossRef]

V. M. Lashkin, E. A. Ostrovskaya, A. S. Desyatnikov, and Y. S. Kivshar, “Vector azimuthons in two-component Bose-Einstein condensates,” Phys. Rev. A 80, 013615 (2009).
[CrossRef]

B. Terhalle, T. Richter, K. J. H. Law, D. Göries, P. Rose, T. J. Alexander, P. G. Kevrekidis, A. S. Desyatnikov, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of double-charge discrete vortex solitons in hexagonal photonic lattices,” Phys. Rev. A 79, 043821 (2009).
[CrossRef]

K. J. H. Law, P. G. Kevrekidis, T. J. Alexander, W. Królikowski, and Y. S. Kivshar, “Stable higher-charge discrete vortices in hexagonal optical lattices,” Phys. Rev. A 79, 025801 (2009).
[CrossRef]

Phys. Rev. E (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[CrossRef]

Phys. Rev. Lett. (9)

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]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902(2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibres to Photonic Crystals (Academic, 2003).

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Figures (5)

Fig. 1
Fig. 1

First-order Bessel lattices with azimuthal index (a)  n = 2 and (b)  n = 5 . Profiles of the first linear modes with (c)  n = 2 and (d)  n = 5 . All quantities are plotted in dimensionless units.

Fig. 2
Fig. 2

Properties of multipeaked fundamental solitons in the first-order Bessel lattices with azimuthal index n = 2 . (a) Power versus propagation constant. (b) Propagation constant cutoff b co versus lattice depth p. (c) Profile of soliton marked by circle in (a). (d) Stable propagation of (c), cut of intensity distribution at y = 0 is shown. White noise σ noise 2 = 0.01 was added into the initial input.

Fig. 3
Fig. 3

Stable propagation results of multipeaked solitons in the first-order Bessel lattices with odd azimuthal index. (a)  n = 1.5 , p = 25 , b = 0.9 . (b)  n = 3.5 , p = 25 , b = 0.9 . (c)  n = 7.5 , p = 35 , b = 2 . The propagation distance is 512 and white noise was added into the initial inputs.

Fig. 4
Fig. 4

Amplitude distributions of multipeaked vortex solitons with (a)  m = 1 , (b) 2, and (c), (d) 3. Parameters n = 4 , p = 30 , and b = 0.5 in (a)–(c) and n = 6 , p = 45 , and b = 0.5 in (d). Bottom row: the corresponding phase structures.

Fig. 5
Fig. 5

(a) Power of multipeaked vortex solitons with m = 1 , 2, and 3 versus propagation constant, n = 4 , p = 30 . Propagation constant cutoff b co versus lattice depth p for vortex solitons with (b)  m = 1 and (c) 3. Real parts of instability growth rate λ versus propagation constant for vortex solitons supported by the (d) fourth-, (e) fifth-, and (f) sixth-order lattices with p = 30 , m = 3 ; p = 35 , m = 3 ; and p = 35 , m = 5 , respectively. Azimuthal index n = 4 in (a)–(d), 5 in (e), and 6 in (f).

Tables (1)

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Table 1 Stability Status of Vortex Solitons for Different Lattice Orders

Equations (4)

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i q z + 1 2 ( 2 q x 2 + 2 q y 2 ) | q | 2 q + p R ( x , y ) q = 0.
1 2 ( 2 x 2 + 2 y 2 ) w r , i b w r , i ( w r 2 + w i 2 ) w r , i + p R w r , i = 0.
± λ u i , r = 1 2 ( 2 x 2 + 2 y 2 ) u r , i b u r , i + p R u r , i ( 3 w r , i 2 + w i , r 2 ) u r , i 2 w r w i u i , r ,
0 < m n / 2 ,

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