Abstract

Using numerical analysis we demonstrate the existence of vortex solitons at the edge and in the corners of two-dimensional triangular photonic lattice. We develop a concise picture of their behavior in both single-propagating and counterpropagating beam geometries. In the single-beam geometry, we observe stable surface vortex solitons for long propagation distances only in the form of discrete six-lobe solutions at the edge of the photonic lattice. Other observed solutions, in the form of ring vortex and discrete solitons with two or three lobes, oscillate during propagation in a way indicating the exchange of power between neighboring lobes. For higher beam powers we observe dynamical instabilities of surface vortex solitons and study orbital angular momentum transfer of such vortex states. In the two-beam counterpropagating geometry, all kinds of vortex solutions are stable for propagation distances of the order of typical experimental crystal lengths.

© 2011 OSA

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  1. Yu. S. Kivshar, “Nonlinear Tamm states and surface effects in periodic photonic structures,” Laser Phys. Lett. 5(10), 703–713 (2008).
    [CrossRef]
  2. S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
    [CrossRef]
  3. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache“Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
    [CrossRef] [PubMed]
  4. K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125–3127 (2006).
    [CrossRef] [PubMed]
  5. Y. V. Kartashov, V. A. Vysloukh, and L. Torner“Soliton emission in amplifying lattice surfaces,” Opt. Lett. 32, 2061–2063 (2007).
    [CrossRef] [PubMed]
  6. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  7. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  8. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173–3175 (2007).
    [CrossRef] [PubMed]
  9. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  10. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  11. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
    [CrossRef] [PubMed]
  12. M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
    [CrossRef]
  13. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner“Surface vortex solitons,” Opt. Express 14, 4049–4057 (2006).
    [CrossRef] [PubMed]
  14. D. Song, C. Lou, K. J. H. Law, L. Tang, Z. Ye, P. G. Kevrekidis, J. Xu, and Z. Chen“Self-trapping of optical vortices at the surface of an induced semi-infinite photonic lattice,” Opt. Express 18, 5873–5878 (2010).
    [CrossRef] [PubMed]
  15. M. Belić, M. Petrović, D. Jović, A. Strinić, D. Arsenović, K. Motzek, F. Kaiser, Ph. Jander, C. Denz, M. Tlidi, and P. Mandel, “Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals,” Opt. Express 12, 708–716 (2004).
    [CrossRef]
  16. M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
    [CrossRef]
  17. Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, “Experiments on Gaussian beams and vortices in optically induced photonic lattices,” J. Opt. Soc. Am. B 22, 1395–1405 (2005).
    [CrossRef]
  18. M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
    [CrossRef]
  19. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
    [CrossRef]
  20. M. S. Petrović“Counterpropagating mutually incoherent vortex-induced rotating structures in optical photonic lattices,” Opt. Express 14, 9415–9420 (2006).
    [CrossRef]
  21. D. M. Jović, S. Prvanović, R. D. Jovanović, and M. S. Petrović“Gaussian-induced rotation in periodic photonic lattices,” Opt. Lett. 32, 1857–1859 (2007).
    [CrossRef]
  22. V. I. Petviashvili“Equation of an extraordinary solution,” Plasma Phys. 2, 469 (1976).
  23. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
    [CrossRef]

2011

M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
[CrossRef]

2010

2009

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

2008

2007

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173–3175 (2007).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner“Soliton emission in amplifying lattice surfaces,” Opt. Lett. 32, 2061–2063 (2007).
[CrossRef] [PubMed]

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

D. M. Jović, S. Prvanović, R. D. Jovanović, and M. S. Petrović“Gaussian-induced rotation in periodic photonic lattices,” Opt. Lett. 32, 1857–1859 (2007).
[CrossRef]

2006

M. S. Petrović“Counterpropagating mutually incoherent vortex-induced rotating structures in optical photonic lattices,” Opt. Express 14, 9415–9420 (2006).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner“Surface vortex solitons,” Opt. Express 14, 4049–4057 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125–3127 (2006).
[CrossRef] [PubMed]

2005

2004

M. Belić, M. Petrović, D. Jović, A. Strinić, D. Arsenović, K. Motzek, F. Kaiser, Ph. Jander, C. Denz, M. Tlidi, and P. Mandel, “Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals,” Opt. Express 12, 708–716 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

1976

V. I. Petviashvili“Equation of an extraordinary solution,” Plasma Phys. 2, 469 (1976).

Aimez, V.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Ars, R.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Arsenovic, D.

Belic, M.

Belic, M. R.

M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
[CrossRef]

Belic, Milivoj R.

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

Bezryadina, A.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, “Experiments on Gaussian beams and vortices in optically induced photonic lattices,” J. Opt. Soc. Am. B 22, 1395–1405 (2005).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

Chen, Z.

D. Song, C. Lou, K. J. H. Law, L. Tang, Z. Ye, P. G. Kevrekidis, J. Xu, and Z. Chen“Self-trapping of optical vortices at the surface of an induced semi-infinite photonic lattice,” Opt. Express 18, 5873–5878 (2010).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, “Experiments on Gaussian beams and vortices in optically induced photonic lattices,” J. Opt. Soc. Am. B 22, 1395–1405 (2005).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

Christodoulides, D. N.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache“Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
[CrossRef] [PubMed]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, “Experiments on Gaussian beams and vortices in optically induced photonic lattices,” J. Opt. Soc. Am. B 22, 1395–1405 (2005).
[CrossRef]

Denz, C.

Desyatnikov, A. S.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Dreisow, F.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Egorov, A. A.

Hache, A.

Haché, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Heinrich, M.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

Iwanow, R.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Jander, Ph.

Jovanovic, R. D.

Jovic, D.

Jovic, D. M.

D. M. Jović, S. Prvanović, R. D. Jovanović, and M. S. Petrović“Gaussian-induced rotation in periodic photonic lattices,” Opt. Lett. 32, 1857–1859 (2007).
[CrossRef]

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

Kaiser, F.

Kartashov, Y. V.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner“Soliton emission in amplifying lattice surfaces,” Opt. Lett. 32, 2061–2063 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner“Surface vortex solitons,” Opt. Express 14, 4049–4057 (2006).
[CrossRef] [PubMed]

Keil, R.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

Kevrekidis, P. G.

Kivshar, Y. S.

M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar, “Nonlinear Tamm states and surface effects in periodic photonic structures,” Laser Phys. Lett. 5(10), 703–713 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173–3175 (2007).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125–3127 (2006).
[CrossRef] [PubMed]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Yu. S. Kivshar, and D. N. Christodoulides, “Experiments on Gaussian beams and vortices in optically induced photonic lattices,” J. Opt. Soc. Am. B 22, 1395–1405 (2005).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Law, K. J. H.

Lederer, F.

Lou, C.

Makasyuk, I.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache“Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
[CrossRef] [PubMed]

Mandel, P.

Martin, H.

Mazilu, D.

Mihalache, D.

Min, Y.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Motzek, K.

Neshev, D.

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Nolte, S.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Petrovic, M.

Petrovic, M. S.

M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
[CrossRef]

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

D. M. Jović, S. Prvanović, R. D. Jovanović, and M. S. Petrović“Gaussian-induced rotation in periodic photonic lattices,” Opt. Lett. 32, 1857–1859 (2007).
[CrossRef]

M. S. Petrović“Counterpropagating mutually incoherent vortex-induced rotating structures in optical photonic lattices,” Opt. Express 14, 9415–9420 (2006).
[CrossRef]

Petviashvili, V. I.

V. I. Petviashvili“Equation of an extraordinary solution,” Plasma Phys. 2, 469 (1976).

Prvanovic, S.

D. M. Jović, S. Prvanović, R. D. Jovanović, and M. S. Petrović“Gaussian-induced rotation in periodic photonic lattices,” Opt. Lett. 32, 1857–1859 (2007).
[CrossRef]

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

Ramirez, L. P. R.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Salamo, G.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Schiek, R.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Siviloglou, G. A.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Sohler, W.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Song, D.

Sorel, M.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache“Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
[CrossRef] [PubMed]

Strinic, A.

Sukhorukov, A. A.

Suntsov, S.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache“Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
[CrossRef] [PubMed]

Szameit, A.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Tang, L.

Tlidi, M.

Torner, L.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner“Soliton emission in amplifying lattice surfaces,” Opt. Lett. 32, 2061–2063 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner“Surface vortex solitons,” Opt. Express 14, 4049–4057 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Tünnermann, A.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, V. A. Vysloukh, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner“Observation of two-dimensional lattice interface solitons,” Opt. Lett. 33, 663–665 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Volatier, M.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

Vysloukh, V. A.

Wang, X.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Xu, J.

Yang, H.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[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 an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

Ye, Z.

J. Nonlinear Opt. Phys. Mater.

S. Suntsov, K. G. Makris, G. A. Siviloglou, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, M. Volatier, V. Aimez, R. Ars, M. Sorel, Y. Min, W. Sohler, X. Wang, A. Bezryadina, and Z. Chen“Observation of one- and two-dimensional discrete surface spatial solitons,” J. Nonlinear Opt. Phys. Mater. 16(4), 401–426 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys. Lett.

Yu. S. Kivshar, “Nonlinear Tamm states and surface effects in periodic photonic structures,” Laser Phys. Lett. 5(10), 703–713 (2008).
[CrossRef]

Laser. Photon. Rev.

M. S. Petrović, M. R. Belić, C. Denz, and Y. S. Kivshar“Counterpropagating optical beams and solitons,” Laser. Photon. Rev. 5, 214–233 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner“Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009).
[CrossRef]

M. S. Petrović, D. M. Jović, Milivoj R. Belić, and S. Prvanović, “Angular momentum transfer in optically induced photonic lattices,” Phys. Rev. A 76, 023820 (2007).
[CrossRef]

Phys. Rev. Lett.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman“Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Plasma Phys.

V. I. Petviashvili“Equation of an extraordinary solution,” Plasma Phys. 2, 469 (1976).

Prog. Opt.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Studies Appl. Math.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen“Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory an experiment,” Studies Appl. Math. 113, 389–412 (2004).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (1624 KB)     
» Media 2: MOV (2101 KB)     
» Media 3: MOV (2148 KB)     
» Media 4: MOV (1296 KB)     

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Figures (5)

Fig. 1
Fig. 1

Narrow surface ring vortex solitons. Input vortex beams are shown at the edge (a) and in the corner (b) of the lattice, with the layout of the lattice beams indicated by open circles. (c) Power diagram for the existence of narrow surface vortex solitons. Insets depict the corresponding intensity distributions for the corner and the edge vortex solitons. The lines in the insets depict the lattice outlines. Parameters: Γ = 11, the maximum lattice intensity I0 = 1.

Fig. 2
Fig. 2

Six-lobe discrete surface vortex solitons. Top row: The edge surface modes. Bottom row: The corner surface modes. The layout of the lattice beams is only shown in the first column. (a), (e) The input vortex beams. Different kinds of edge (b), (c), and corner vortex solitons (f), (g), are shown with the corresponding power diagrams (d), (h). The phase distributions are presented as insets. The parameters are as in Fig. 1.

Fig. 3
Fig. 3

Three-lobe discrete surface vortex solitons. The figure layout is as in Fig. 2. The parameters are as in Fig. 1.

Fig. 4
Fig. 4

Dynamical behavior of surface ring vortex solitons. Movies of the intensity distribution are shown along the propagation direction: (a) ( Media 1). The inset depicts the corresponding solitonic solutions. (b) The normalized z component of the angular momentum.

Fig. 5
Fig. 5

Oscillating behavior of the edge surface vortex solitons. Top row: The edge vortex solitons. Movies of the intensity distributions are shown along the propagation direction: (a) ( Media 2), (b) ( Media 3), (c) ( Media 4). Insets depict the corresponding solitonic solutions. Bottom row: The normalized z component of the angular momentum for the corresponding vortex solitons.

Equations (3)

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

i z F + Δ F + Γ I + I g 1 + I + I g F = 0 ,
i z B + Δ B + Γ I + I g 1 + I + I g B = 0 ,
μ u + Δ u + Γ u | u | 2 + I g 1 + | u | 2 + I g = 0.

Metrics