Abstract

We demonstrate the self-trapping of single- and double-charged optical vortices in waveguide lattices induced with a self-defocusing nonlinearity. Under appropriate conditions, a donut-shaped single-charged vortex evolves into a stable discrete gap vortex soliton, but a double-charged vortex turns into a self-trapped quadrupole-like structure. Spectrum measurement and numerical analysis suggest that the gap vortex soliton does not bifurcate from the edge of the Bloch band, quite different from previously observed gap spatial solitons. Our numerical findings are in good agreement with experimental observations.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  5. 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]
  6. 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 (2003).
    [CrossRef] [PubMed]
  7. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Królikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  8. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  9. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
    [CrossRef] [PubMed]
  10. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. A. Bezryadina, E. Eugenieva, and Z. Chen, "Self-trapping and flipping of double-charged vortices in optically induced photonic lattices," Opt. Lett. 31, 2456 (2006).
    [CrossRef] [PubMed]
  24. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
    [CrossRef] [PubMed]
  25. D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
    [CrossRef] [PubMed]
  26. R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
    [CrossRef] [PubMed]
  27. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
    [CrossRef] [PubMed]
  28. J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
    [CrossRef]
  29. M. �?ster and M. Johansson, "Stable stationary and quasiperiodic discrete vortex breathers with topological charge S=2," Phys. Rev. E 73, 066608 (2006).
    [CrossRef]
  30. E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
    [CrossRef]

2008

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

2007

T. Richter and F. Kaiser, "Anisotropic gap vortices in photorefractive media," Phys. Rev. A 76, 033818 (2007).
[CrossRef]

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

2006

P. G. Kevrekidis, H. Susanto, and Z. Chen, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity," Phys. Rev. E 74, 066606 (2006).
[CrossRef]

A. Bezryadina, E. Eugenieva, and Z. Chen, "Self-trapping and flipping of double-charged vortices in optically induced photonic lattices," Opt. Lett. 31, 2456 (2006).
[CrossRef] [PubMed]

M. �?ster and M. Johansson, "Stable stationary and quasiperiodic discrete vortex breathers with topological charge S=2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
[CrossRef]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

2005

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleicher, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," 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, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

2004

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

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

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

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

2003

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

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretetizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (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]

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 (2003).
[CrossRef] [PubMed]

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

2002

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

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

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1988

??ster, M.

M. �?ster and M. Johansson, "Stable stationary and quasiperiodic discrete vortex breathers with topological charge S=2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Alexander, T. J.

E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Bartal, G.

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

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[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] [PubMed]

Bezryadina, A.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[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, F.

Chen, X.

Chen, Z.

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

P. G. Kevrekidis, H. Susanto, and Z. Chen, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity," Phys. Rev. E 74, 066606 (2006).
[CrossRef]

A. Bezryadina, E. Eugenieva, and Z. Chen, "Self-trapping and flipping of double-charged vortices in optically induced photonic lattices," Opt. Lett. 31, 2456 (2006).
[CrossRef] [PubMed]

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

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, 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 soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," 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, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (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 (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, "Discretetizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (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]

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

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleicher, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," 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, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Denz, C.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

Efremidis, N. K.

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]

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 (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]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eugenieva, E.

Eugenieva, E. D.

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

Fischer, R.

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Fleicher, J. W.

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

Fleischer, J. W.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[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] [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 (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]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[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] [PubMed]

Johansson, M.

M. �?ster and M. Johansson, "Stable stationary and quasiperiodic discrete vortex breathers with topological charge S=2," Phys. Rev. E 73, 066608 (2006).
[CrossRef]

Joseph, R. I.

Kaiser, F.

T. Richter and F. Kaiser, "Anisotropic gap vortices in photorefractive media," Phys. Rev. A 76, 033818 (2007).
[CrossRef]

Kevrekidis, P. G.

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

P. G. Kevrekidis, H. Susanto, and Z. Chen, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity," Phys. Rev. E 74, 066606 (2006).
[CrossRef]

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

Kip, D.

Kivshar, Y.

Kivshar, Y. S.

E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
[CrossRef]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Krolikowski, W.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Królikowski, W.

Law, K.

Lederer, F.

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

Lou, C.

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

Makasyuk, I.

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

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

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

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

Manela, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleicher, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," 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, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[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] [PubMed]

Martin, H.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, 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 soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Musslimani, Z. H.

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

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

Neshev, D. N.

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

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

E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Richter, T.

T. Richter and F. Kaiser, "Anisotropic gap vortices in photorefractive media," Phys. Rev. A 76, 033818 (2007).
[CrossRef]

Runde, D.

Ruter, C. E.

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.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleicher, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," 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, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[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] [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]

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 (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]

Shandarov, V.

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Song, D.

Stepic, M.

Sukhorukov, A. A.

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Susanto, H.

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

P. G. Kevrekidis, H. Susanto, and Z. Chen, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity," Phys. Rev. E 74, 066606 (2006).
[CrossRef]

Tang, L.

Träger, D.

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch modes in two-dimensional photonic lattices," Opt. Express 14, 1913 (2006).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Wang, J.

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

Wang, X.

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Xu, J.

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

L. Tang, C. Lou, X. Wang, D. Song, X. Chen, J. Xu, Z. Chen, H. Susanto, K. Law, and P. G. Kevrekidis, "Observation of dipole-like gap solitons in self-defocusing waveguide lattices," Opt. Lett. 32, 3011 (2007).
[CrossRef] [PubMed]

Yang, J.

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

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

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

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. A

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

T. Richter and F. Kaiser, "Anisotropic gap vortices in photorefractive media," Phys. Rev. A 76, 033818 (2007).
[CrossRef]

E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, "Generation and detection of matter-wave gap vortices in optical lattices," Phys. Rev. A 74, 023605 (2006).
[CrossRef]

Phys. Rev. E

M. �?ster and M. Johansson, "Stable stationary and quasiperiodic discrete vortex breathers with topological charge S=2," Phys. Rev. E 73, 066608 (2006).
[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]

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

P. G. Kevrekidis, H. Susanto, and Z. Chen, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity," Phys. Rev. E 74, 066606 (2006).
[CrossRef]

Phys. Rev. Lett.

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, "Nonlinear spectum reshaping and gap-soliton-train trapping in optically inducd photonic structures," Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

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

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

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[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]

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

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, "Controlled generation and steering of spatial gap solitons," Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Y. S. Kivshar, "Reduced-symmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905 (2006).
[CrossRef] [PubMed]

Other

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Acedemic, San Diego, Calif. 2003).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental results of self-trapping of single-charged (top) and double-charged (bottom) vortices in a defocusing photonic lattice. (a) Interferograms showing the phase of the input vortex beams, (b) intensity patterns of self-trapped vortex beams at lattice output, (c, d) interferograms between (b) and a tilted plane wave (c) and an on-axis Gaussian beam (d), respectively, and (e) the k-space spectra of (b) where the dash squares mark the first Brillouin-zone of the square lattice. (a, c) are zoomed in with respect to (b, d) for better visualization.

Fig. 2.
Fig. 2.

Numerical results of self-trapping of single-charged (top) and double-charged (bottom) vortices in a defocusing photonic lattice corresponding to experimental results of Fig. 1. The propagation distance is 10 mm corresponding to the length of the crystal used in experiment.

Fig. 3.
Fig. 3.

Simulation results of single-charged (a) and double-charged (b) vortex beams propagating to a longer distance of 40 mm. Left panels show the output transverse (x-y) intensity pattern (left), its interferogram with a titled plane wave (middle), and its k-space spectrum (right) in both (a) and (b). Notice that the vortex singularity maintains in (a) but disappears in (b). Right panels show the propagation of a stable m=1vortex beam (c) and of an unstable quadrupole beam as arising from the breakup of m=2 vortex (d) long the longitudinal z-direction (from bottom to top) through the defocusing lattice.

Fig 4.
Fig 4.

Numerical solutions of self-trapped quadrupole [a.)] and single-charged vortices [b.) and c.)]. Shown are typical stationary patterns (first column), corresponding phase structure (second column), Fourier spectra (third column), and maximal instability growth rates (fourth column). Plots in fourth column are given as a function of the propagation constant µ, while the spectral bands are denoted by shaded areas. The first Bloch band is located to the right, where for the single-charged vortex family the stable node branch [solid line, b.)] collides with the unstable saddle branch [dashed line, c.)] before reaching the band edge. Zero growth rates indicate that the self-trapped structure is linearly stable.

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