Abstract

We study discrete vector solitons and vortices in two-dimensional photonic lattices with Kerr nonlinearity and demonstrate novel types of stable, incoherently coupled dipoles and vortex–soliton complexes that can be excited by Gaussian beams. We also discuss what we believe to be novel scenarios of the charge-flipping instability of incoherently coupled discrete vortices.

© 2006 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  3. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  4. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  5. D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  6. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  7. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  8. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  9. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  10. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  11. 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]
  12. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
    [CrossRef] [PubMed]
  13. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Stud. Appl. Math. 113, 389 (2004).
    [CrossRef]
  14. Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (2004).
    [CrossRef] [PubMed]
  15. Z. Chen, A. Bezryadina, I. Makasyuk, and Y. Yang, Opt. Lett. 29, 1656 (2004).
    [CrossRef] [PubMed]
  16. T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
    [CrossRef] [PubMed]
  17. O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
    [CrossRef] [PubMed]
  18. A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
    [CrossRef]
  19. G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
    [CrossRef]
  20. A. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001).
    [CrossRef] [PubMed]
  21. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
    [CrossRef]

2005 (1)

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

2004 (9)

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

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, 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]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (2004).
[CrossRef] [PubMed]

Z. Chen, A. Bezryadina, I. Makasyuk, and Y. Yang, Opt. Lett. 29, 1656 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

2003 (6)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (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]

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

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

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

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

2001 (2)

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

A. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef] [PubMed]

1999 (1)

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

1988 (1)

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Alexander, T. J.

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

T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Bartal, G.

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]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Bezryadina, A.

Buryak, A. V.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

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, Z.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Z. Chen, A. Bezryadina, I. Makasyuk, and Y. Yang, Opt. Lett. 29, 1656 (2004).
[CrossRef] [PubMed]

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

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

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (2004).
[CrossRef] [PubMed]

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]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Cohen, O.

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]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Desyatnikov, A.

A. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef] [PubMed]

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.

Eugenieva, E. D.

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

Fleischer, J. W.

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]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (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]

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]

Joseph, R. I.

Kartashov, Y. V.

Kevrekidis, P. G.

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

Kivshar, Yu. S.

T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

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

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

A. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef] [PubMed]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Krolikowski, W.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Makasyuk, I.

Malomed, B. A.

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

Manela, O.

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (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]

Martin, H.

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

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

Michinel, H.

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

Montesinos, G. D.

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

Musslimani, Z. H.

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

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

Neshev, D.

Neshev, D. N.

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

Ostrovskaya, E. A.

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

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

Pérez-García, V. M.

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

Rodas-Verde, M. I.

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

Segev, M.

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]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (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]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

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

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Shih, M.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

Sukhorukov, A. A.

T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Torner, L.

Yang, J.

Yang, Y.

Chaos (1)

G. D. Montesinos, M. I. Rodas-Verde, V. M. Pérez-García, and H. Michinel, Chaos 15, 033501 (2005).
[CrossRef]

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

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

Opt. Lett. (7)

Phys. Rev. E (1)

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

Phys. Rev. Lett. (8)

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, and Z. Chen, 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]

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

A. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2003).
[CrossRef]

T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (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]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Stud. Appl. Math. (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

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Figures (5)

Fig. 1
Fig. 1

Internal oscillations of the discrete vector solitons. Top: intensity of one component at three distances. Bottom: evolution of the normalized peak amplitude at one of the sites (solid curve, numerical; dashed curve, variational).

Fig. 2
Fig. 2

Comparison between the cross-coupled vector dipoles and scalar quadrupoles of the same intensity for the off-site (top) and on-site (bottom) configurations.

Fig. 3
Fig. 3

Dynamics of off-site and on-site discrete scalar and vector vortices. (a)–(f) Change of the peak amplitude versus z for (a) and (b) scalar vortices, (c) and (d) equal-charge vortices, and (e) and (f) opposite-charge vector vortices. Arrows indicate the destruction of the vortex phase structure with the charge completely flipped marked by squares.

Fig. 4
Fig. 4

Coherent vortex–soliton (top) and vortex–vortex (bottom) interaction when the neighboring solitons (indicated by + and −) are out of phase. Shown is the peak amplitude for the right soliton of the vortex (solid curve) and the soliton or the left soliton of the right vortex (dashed curve). Arrows indicate the destruction of the vortex phase.

Fig. 5
Fig. 5

Incoherent interaction of a vortex (top row) and soliton ring (bottom row) of three different charges.

Equations (1)

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i ψ j z + Δ ψ j + [ V ( x , y ) + F ( I ) ] ψ j = 0 ,

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