Abstract

We introduce a novel class of stable lattice solitons with a complex phase structure composed of many single-charge discrete vortices in a triangular photonic lattice. We demonstrate that such nonlinear self-trapped states are linked to the resonant Bloch modes, which bear a honeycomb pattern of phase dislocations.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  2. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  3. P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
    [CrossRef]
  4. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  5. B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. 63, 642 (2003).
    [CrossRef]
  6. J. Yang, New J. Phys. 6, 47 (2004).
    [CrossRef]
  7. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  8. 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]
  9. A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Traeger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, Opt. Express 14, 2851 (2006).
    [CrossRef] [PubMed]
  10. T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
    [CrossRef] [PubMed]
  11. T. J. Alexander and Yu. S. Kivshar, Appl. Phys. B 82, 203 (2006).
    [CrossRef]
  12. A. Bezryadina, D. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Yu. S. Kivshar, Opt. Express 14, 8317 (2006).
    [CrossRef] [PubMed]
  13. J. J. García-Ripoll and V. Perez-García, SIAM J. Sci. Comput. 23, 1316 (2001).
    [CrossRef]
  14. R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
    [CrossRef] [PubMed]
  15. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  16. D. Neshev, E. Ostrovskaya, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 28, 210 (2003).
    [CrossRef]
  17. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 32, 397 (2007).
    [CrossRef] [PubMed]
  18. A. S. Desyatnikov, Yu. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, Opt. Lett. 32, 325 (2007).
    [CrossRef] [PubMed]
  19. Ya. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (2004).
    [CrossRef] [PubMed]
  20. T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
    [CrossRef] [PubMed]
  21. A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  22. A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]

2007 (2)

2006 (5)

T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
[CrossRef] [PubMed]

T. J. Alexander and Yu. S. Kivshar, Appl. Phys. B 82, 203 (2006).
[CrossRef]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Traeger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, Opt. Express 14, 2851 (2006).
[CrossRef] [PubMed]

A. Bezryadina, D. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Yu. S. Kivshar, Opt. Express 14, 8317 (2006).
[CrossRef] [PubMed]

2005 (2)

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

2004 (5)

J. Yang, New J. Phys. 6, 47 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, 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. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

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

2003 (3)

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

D. Neshev, E. Ostrovskaya, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 28, 210 (2003).
[CrossRef]

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

2002 (3)

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2001 (1)

J. J. García-Ripoll and V. Perez-García, SIAM J. Sci. Comput. 23, 1316 (2001).
[CrossRef]

Agrawal, G. P.

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

Alexander, T. J.

T. J. Alexander and Yu. S. Kivshar, Appl. Phys. B 82, 203 (2006).
[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
[CrossRef] [PubMed]

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, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Baizakov, B. B.

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

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]

Bezryadina, A.

Cavalcanti, S. B.

Chen, Z.

A. Bezryadina, D. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Yu. S. Kivshar, Opt. Express 14, 8317 (2006).
[CrossRef] [PubMed]

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

Christodoulides, D. N.

Ya. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

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]

Denz, C.

Desyatnikov, A. S.

Dreischuh, A.

Efremidis, N. K.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Egorov, A. A.

Fischer, R.

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]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Gaididei, Yu. B.

P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
[CrossRef]

García-Ripoll, J. J.

J. J. García-Ripoll and V. Perez-García, SIAM J. Sci. Comput. 23, 1316 (2001).
[CrossRef]

Hickmann, J. M.

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, Ya. V.

Kevrekidis, P. G.

P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
[CrossRef]

Kivshar, Yu. S.

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 32, 397 (2007).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, and J. M. Hickmann, Opt. Lett. 32, 325 (2007).
[CrossRef] [PubMed]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Traeger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, Opt. Express 14, 2851 (2006).
[CrossRef] [PubMed]

T. J. Alexander and Yu. S. Kivshar, Appl. Phys. B 82, 203 (2006).
[CrossRef]

A. Bezryadina, D. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Yu. S. Kivshar, Opt. Express 14, 8317 (2006).
[CrossRef] [PubMed]

T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, 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]

D. Neshev, E. Ostrovskaya, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 28, 210 (2003).
[CrossRef]

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

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

Krolikowski, W.

Makasyuk, I.

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

Malomed, B. A.

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

P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
[CrossRef]

Manela, 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]

Martin, H.

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

Musslimani, Z. H.

Neshev, D.

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 32, 397 (2007).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Traeger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, Opt. Express 14, 2851 (2006).
[CrossRef] [PubMed]

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

Ostrovskaya, E.

D. Neshev, E. Ostrovskaya, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 28, 210 (2003).
[CrossRef]

Ostrovskaya, E. A.

T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
[CrossRef] [PubMed]

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

Perez-García, V.

J. J. García-Ripoll and V. Perez-García, SIAM J. Sci. Comput. 23, 1316 (2001).
[CrossRef]

Rosberg, C. R.

Sagemerten, N.

Salerno, M.

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

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, 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, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Shchesnovich, V. S.

Sukhoroukov, A. A.

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

Sukhorukov, A. A.

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, Opt. Lett. 32, 397 (2007).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

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

Terhalle, B.

Torner, L.

Traeger, D.

Träger, D.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Yang, J.

Young, J.

Appl. Phys. B (1)

T. J. Alexander and Yu. S. Kivshar, Appl. Phys. B 82, 203 (2006).
[CrossRef]

Europhys. Lett. (1)

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

New J. Phys. (1)

J. Yang, New J. Phys. 6, 47 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. E (2)

P. G. Kevrekidis, B. A. Malomed, and Yu. B. Gaididei, Phys. Rev. E 66, 016609 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett. (7)

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, 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]

T. J. Alexander, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 040401 (2006).
[CrossRef] [PubMed]

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

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

SIAM J. Sci. Comput. (1)

J. J. García-Ripoll and V. Perez-García, SIAM J. Sci. Comput. 23, 1316 (2001).
[CrossRef]

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) First Brillouin zone, (b) intensity, and (c) bandgap spectrum for a triangular lattice (gaps are shaded) for V 0 = 0.6 . (d) Intensity and (e) phase of the Bloch wave at the M-point. (f) Fundamental soliton originating from the Γ-point.[17]

Fig. 2
Fig. 2

(a) Single vortex on the Γ-TNBW, (b) elementary discrete vortex soliton, (c) M-TNBW with 24 vortices and total charge + 4 . Bottom panel shows the intensity profiles through the horizontal cut compared with nonlinear Bloch waves (dashed curves).

Fig. 3
Fig. 3

Dynamics of higher-order vortex solitons and evolution of their angular momenta: (a), (b) composed of four vortices with the total charge m = + 2 (solid line) and (c), (d) single vortex with m = + 1 (dashed line).

Fig. 4
Fig. 4

Two examples of M-TNBW vortex solitons. (a) Hexagonal, 24 vortices, zero charge. (b) Inverted triangle, 9 vortices, total charge m = 3 .

Equations (3)

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

i Ψ z + D ( 2 Ψ x 2 + 2 Ψ y 2 ) I 0 Ψ 1 + V ( x , y ) + Ψ 2 = 0 ,
V ( x , y ) = 2 V 0 [ 3 2 + cos ( k 12 r ) + cos ( k 13 r ) + cos ( k 23 r ) ] ,
j = 1 N c n j sin ( ϕ n ϕ j ) = 0 ,

Metrics