Abstract

On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.

© 2007 Optical Society of America

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  1. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 219 (2005).
  2. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [Crossref]
  3. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [Crossref] [PubMed]
  4. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
    [Crossref]
  5. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 92, 123903 (2004).
    [Crossref] [PubMed]
  6. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
    [Crossref] [PubMed]
  7. G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
    [Crossref] [PubMed]
  8. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
    [Crossref] [PubMed]
  9. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
    [Crossref] [PubMed]
  10. A. Ferrando, Phys. Rev. E 72, 036612 (2005).
    [Crossref]
  11. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [Crossref] [PubMed]
  12. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [Crossref] [PubMed]
  13. D. Neshev, E. Ostrovskaya, Yu. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [Crossref] [PubMed]
  14. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [Crossref] [PubMed]
  15. X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
    [Crossref] [PubMed]
  16. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, Opt. Express 14, 2825 (2006).
    [Crossref] [PubMed]
  17. F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
    [Crossref] [PubMed]
  18. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, Opt. Lett. 29, 468 (2004).
    [Crossref] [PubMed]
  19. A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
    [Crossref] [PubMed]

2006 (2)

2005 (7)

A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[Crossref] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[Crossref]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 219 (2005).

2004 (4)

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, 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, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tuennermann, Opt. Lett. 29, 468 (2004).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

2003 (5)

B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
[Crossref]

D. Neshev, E. Ostrovskaya, Yu. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[Crossref] [PubMed]

J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

2001 (1)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[Crossref]

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 92, 123903 (2004).
[Crossref] [PubMed]

Baizakov, B.

B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
[Crossref]

Bartal, G.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

Burghoff, J.

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

Chen, F.

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

Cohen, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

Desyatnikov, A. S.

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Ferrando, A.

A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[Crossref]

Fischer, R.

Fleischer, J. W.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

García-March, M. A.

A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
[Crossref] [PubMed]

Hudock, J.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[Crossref]

Kip, D.

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 219 (2005).

Kivshar, Yu.

Kivshar, Yu. S.

Krolikowski, W.

Lederer, F.

Lopez-Aguayo, S.

Malomed, B. A.

B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
[Crossref]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[Crossref]

Manela, O.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[Crossref] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

Musslimani, Z. H.

Neshev, D.

Neshev, D. N.

Nolte, S.

Ostrovskaya, E.

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 92, 123903 (2004).
[Crossref] [PubMed]

Pertsch, T.

Peschel, U.

Runde, D.

Ruter, C. E.

Salerno, M.

B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
[Crossref]

Segev, M.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

Shandarov, V.

Stepic, M.

Sukhorukov, A. A.

Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 219 (2005).

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

Tuennermann, A.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

Will, M.

Yang, J.

Zacarés, M.

A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
[Crossref] [PubMed]

Europhys. Lett. (1)

B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
[Crossref]

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (2)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[Crossref]

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[Crossref]

Phys. Rev. Lett. (9)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[Crossref] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, 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, Phys. Rev. Lett. 92, 123904 (2004).
[Crossref] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, Phys. Rev. Lett. 95, 053904 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[Crossref] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

A. Ferrando, M. Zacarés, and M. A. García-March, Phys. Rev. Lett. 95, 043901 (2005).
[Crossref] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 219 (2005).

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Figures (3)

Fig. 1
Fig. 1

(Left) Field modulus and (right) phase for dipole soliton-vortex at propagation constant b = 10 , lattice depth p = 70 , and saturation parameter S = 0.1 .

Fig. 2
Fig. 2

(a) Cutoff versus lattice depth at S = 0.1 . (b) Energy flow versus propagation constant at p = 70 . (c) Real part of perturbation growth rate versus b at p = 70 , S = 0.1 .

Fig. 3
Fig. 3

(a) Decay of an unstable dipole soliton-vortex with b = 6 and (b) its stable propagation at b = 10 in the presence of broadband input noise with variance σ noise 2 = 0.01 at p = 70 , S = 0.1 .

Equations (2)

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q m β ( r , θ ) = j = 0 N 1 e i 2 π N m j W m β ( r , θ 2 π N j ) .
i q ξ = 1 2 ( 2 η 2 + 2 ζ 2 ) q N ( q 2 ) q R ( η , ζ ) q .

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