Abstract

We present both experimental and theoretical results on discrete solitons in two-dimensional optically-induced photonic lattices in a variety of settings, including fundamental discrete solitons, vector-like discrete solitons, discrete dipole solitons, and discrete soliton trains. In each case, a clear transition from two-dimensional discrete diffraction to discrete trapping is demonstrated with a waveguide lattice induced by partially coherent light in a bulk photorefractive crystal. Our experimental results are in good agreement with the theoretical analysis of these effects.

© 2005 Optical Society of America

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  1. D.N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
    [CrossRef]
  3. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794 (1988).
    [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. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. 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]
  9. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  10. 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]
  11. Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef] [PubMed]
  12. B.A. Malomed and P.G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  13. J. Yang and Z.H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  14. D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically-induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  15. 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]
  16. M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef] [PubMed]
  17. Z. Chen and K. MaCarthy, “Spatial soliton pixles from partially coherent light,” Opt. Lett. 27, 2019 (2002).
    [CrossRef]
  18. Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (2004).
    [CrossRef] [PubMed]
  19. 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]
  20. J. Hudock, N. K. Efremidis, and D. N. Christodoulides, “Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays,” Opt. Lett. 29, 268 (2004).
    [CrossRef] [PubMed]
  21. D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  22. M.J. Ablowitz and Z.H. Musslimani, “Discrete vector spatial solitons in a nonlinear waveguide array,” Phys. Rev. E 65, 056618 (2002).
    [CrossRef]
  23. J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
    [CrossRef]
  24. J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef] [PubMed]
  25. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
    [CrossRef]
  26. P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
    [CrossRef]
  27. A.A. Sukhorukov and Y.S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
    [CrossRef]
  28. P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
    [CrossRef]
  29. S.R. Singh and D.N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
    [CrossRef]
  30. J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.
  31. A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
    [CrossRef] [PubMed]
  32. Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
    [CrossRef]

2004 (9)

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]

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

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

D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
[CrossRef]

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, “Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays,” Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (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 (7)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003).
[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]

D.N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (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]

2002 (5)

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]

M.J. Ablowitz and Z.H. Musslimani, “Discrete vector spatial solitons in a nonlinear waveguide array,” Phys. Rev. E 65, 056618 (2002).
[CrossRef]

A.A. Sukhorukov and Y.S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[CrossRef]

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

Z. Chen and K. MaCarthy, “Spatial soliton pixles from partially coherent light,” Opt. Lett. 27, 2019 (2002).
[CrossRef]

2001 (4)

P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
[CrossRef]

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

2000 (1)

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

1998 (1)

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]

1997 (1)

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

1995 (1)

S.R. Singh and D.N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[CrossRef]

1988 (1)

Ablowitz, M.J.

M.J. Ablowitz and Z.H. Musslimani, “Discrete vector spatial solitons in a nonlinear waveguide array,” Phys. Rev. E 65, 056618 (2002).
[CrossRef]

Aitchison, J. S.

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[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.

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

Bartal, G.

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.

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (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]

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Bishop, A. R.

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

Bishop, A.R.

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
[CrossRef]

P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
[CrossRef]

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]

Campbell, D.

D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
[CrossRef]

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, Z

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Chen, Z.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

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]

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]

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

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

Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (2004).
[CrossRef] [PubMed]

Z. Chen and K. MaCarthy, “Spatial soliton pixles from partially coherent light,” Opt. Lett. 27, 2019 (2002).
[CrossRef]

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Christodoulides, D. N.

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, “Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays,” Opt. Lett. 29, 268 (2004).
[CrossRef] [PubMed]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[CrossRef]

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794 (1988).
[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. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (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]

S.R. Singh and D.N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[CrossRef]

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Cohen, O.

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]

Coskun, T.

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Efremidis, N. K.

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.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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.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]

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Flach, S.

D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
[CrossRef]

Fleischer, J.W.

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]

Frantzeskakis, D.J.

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Hudock, J.

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, “Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays,” Opt. Lett. 29, 268 (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. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Joseph, R. I.

Kevrekidis, P. G.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[CrossRef]

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
[CrossRef]

Kevrekidis, P.G.

P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
[CrossRef]

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

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Kivshar, Y.

Kivshar, Y.S.

D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
[CrossRef]

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

A.A. Sukhorukov and Y.S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Krolikowski, W.

Lederer, F.

D.N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[CrossRef] [PubMed]

MaCarthy, K.

Makasyuk, I.

Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (2004).
[CrossRef] [PubMed]

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

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

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, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Malomed, B. A.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[CrossRef]

Malomed, B.A.

P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
[CrossRef]

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

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Manela, O.

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.

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

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

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Meier, J.

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Mitchell, M.

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Morandotti, R.

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[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.

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

M.J. Ablowitz and Z.H. Musslimani, “Discrete vector spatial solitons in a nonlinear waveguide array,” Phys. Rev. E 65, 056618 (2002).
[CrossRef]

Neshev, D.

Neshev, D.N.

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

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

Ostrovskaya, E.

Ostrovskaya, E.A.

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

Rasmussen, K.

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
[CrossRef]

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

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Segev, M.

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]

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Siberberg, Y.

D.N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[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]

Singh, S.R.

S.R. Singh and D.N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[CrossRef]

Smerzi, A.

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

Soljacic, M.

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Stegeman, G.

J. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Sukhorukov, A.A.

A.A. Sukhorukov and Y.S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Trombettoni, A.

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

Vishwanath, A.

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Xu, J.

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Yang, J.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Z. Chen, I. Makasyuk, A. Bezryadina, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett.,  29, 1656 (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]

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

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

J. Phys. A (1)

P.G. Kevrekidis, B.A. Malomed, and A.R. Bishop, “Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.” J. Phys. A 34, 9615 (2001).
[CrossRef]

Nature (2)

D.N. Christodoulides, F. Lederer, and Y. Siberberg, “Discretizing light behaviour 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. Commun. (1)

S.R. Singh and D.N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. E (6)

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

M.J. Ablowitz and Z.H. Musslimani, “Discrete vector spatial solitons in a nonlinear waveguide array,” Phys. Rev. E 65, 056618 (2002).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, “Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,” Phys. Rev. E 67, 056618 (2003).
[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]

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, “Twisted localized modes,” Phys. Rev. E 63, 036603 (2001).
[CrossRef]

A.A. Sukhorukov and Y.S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Phys. Rev. Lett. (11)

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. Meier, J. Hudock, D.N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays ”. Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

A. Smerzi, A. Trombettoni, P. G. Kevrekidis, and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,” Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

D. N. Christodoulides, T. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

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

M. Soljacic, M Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
[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]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and Defocusing in Waveguide Arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[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]

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Phys. Today (1)

D. Campbell, S. Flach, and Y.S. Kivshar, “Localizing energy through nonlinearity and discreteness,” Phys. Today,  57, 43 (2004).
[CrossRef]

Stud. Appl. Math. (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Other (2)

Z Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, “Experiments on Gaussian beams and vortices in optically-induced photonic lattices,” J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, “Necklace-like solitons in optically induced photonic lattices,” Phys. Rev. Lett, submitted.

Supplementary Material (3)

» Media 1: GIF (2129 KB)     
» Media 2: GIF (110 KB)     
» Media 3: GIF (116 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup. PBS: polarizing beam splitter; PZT: piezo-transducer; SBN: strantium barium niobate. The right insert shows a photonic lattice created by optical induction.

Fig. 2.
Fig. 2.

Experimental demonstration of a discrete soliton in a partially coherent lattice. (a) Input, (b) diffraction output without the lattice, (c) discrete diffraction at 900 V/cm, and (d) discrete soliton at 3000 V/cm. Top: 3D intensity plots; Bottom: 2D transverse patterns. Animation of the experimentally observed process can be viewed in the multimedia file. [Media 1]

Fig. 3.
Fig. 3.

Numerical results corresponding to Fig. 1(c–d). Inserts are 2D transverse patterns.

Fig. 4.
Fig. 4.

Output intensity patterns of a soliton-forming beam as a function of the intensity ratio at a fixed bias field (top) and as a function of the bias field at an intensity ratio (bottom).

Fig. 5.
Fig. 5.

Experimental and numerical results of a 2D discrete vector soliton. (a) input, (b) discrete diffraction at low bias field, (c, d) mutual trapping and decoupled output at high bias field, respectively. Row 1&2 show the two components of the vector soliton from experiment. Since the two components from simulations are the same, only one of the components from simulation is shown (Row 3).

Fig. 6.
Fig. 6.

Experimental results on dipole-like solitons in a 2D photonic lattice. Top panel: two beams are out-of-phase; Bottom panel: two beams are in-phase. (a) input; (b) output at a low bias field of 100V/mm; (c) and (d) output at a high bias field of 320V/mm with and without the lattice, respectively.

Fig. 7.
Fig. 7.

Numerical results corresponding to Fig. 6. For simplicity, numerical model does not include self-bending and anisotropic effects associated with the photorefractive nonlinearity.

Fig. 8.
Fig. 8.

Experimental demonstration of 2D discrete soliton trains. Shown are the transverse intensity patterns of a stripe beam taken from crystal input (a) and output (b-d) faces. (b) Normal diffraction, (c) discrete diffraction, and (d) discrete soliton trains. Arrows indicate initial location of the stripe. (e) and (f) are 3D intensity plots corresponding to (c) and (d), respectively.

Fig. 9.
Fig. 9.

Numerical results showing discrete diffraction (left) and discrete trapping (right) of a stripe beam in the lattice. Animations of the observed process as obtained from numerical simulations can be viewed in the media files. [Media 2] [Media 3]

Metrics