Abstract

We investigate the existence of spatial optical solitons supported by an interface between two nonlinear lattices with different saturation parameters. Dipole, quadrupole, and vortex solitons are found in the nonlinear surface lattices. The slight different saturation degree between two sides of the interface leads to a remarkable asymmetry of solitons with higher power. We reveal that multipole and vortex solitons are stable when their power exceeds a threshold value, and stable localized surface nonlinear modes with very high peaks are possible.

© 2010 Optical Society of America

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  1. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  2. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  3. F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
    [CrossRef]
  4. 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]
  5. 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]
  6. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (2006).
    [CrossRef] [PubMed]
  7. 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]
  8. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  9. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Surface vortex solitons,” Opt. Express 14, 4049–4057 (2006).
    [CrossRef] [PubMed]
  10. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
    [CrossRef] [PubMed]
  11. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1949 (2008).
    [CrossRef] [PubMed]
  12. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef] [PubMed]
  13. F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
    [CrossRef] [PubMed]
  14. L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
    [CrossRef] [PubMed]
  15. H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  16. T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
    [CrossRef]
  17. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Vector solitons in nonlinear lattices,” Opt. Lett. 34, 3625–3627 (2009).
    [CrossRef] [PubMed]
  18. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Two-dimensional solitons in nonlinear lattices,” Opt. Lett. 34, 770–772 (2009).
    [CrossRef] [PubMed]
  19. P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, “Observation of two-dimensional nonlocal gap solitons,” Opt. Lett. 34, 295–297 (2009).
    [CrossRef] [PubMed]
  20. J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
    [CrossRef]

2009 (5)

2008 (5)

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1949 (2008).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[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]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
[CrossRef]

2007 (2)

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]

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

2006 (5)

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

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

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

2005 (2)

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]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005).
[CrossRef]

2003 (1)

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
[CrossRef]

Bang, O.

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Bennet, F. H.

Bezryadina, A.

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]

Chen, Z.

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]

Christodoulides, D. N.

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. Hache, 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]

Dong, G.

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
[CrossRef]

Dreisow, F.

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, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Egorov, A. A.

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (2006).
[CrossRef] [PubMed]

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, 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]

Heinrich, M.

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, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Hu, B.

Hukriede, J.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Vector solitons in nonlinear lattices,” Opt. Lett. 34, 3625–3627 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Two-dimensional solitons in nonlinear lattices,” Opt. Lett. 34, 770–772 (2009).
[CrossRef] [PubMed]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1949 (2008).
[CrossRef] [PubMed]

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]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[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]

Kip, D.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
[CrossRef]

Kivshar, Y. S.

P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, “Observation of two-dimensional nonlocal gap solitons,” Opt. Lett. 34, 295–297 (2009).
[CrossRef] [PubMed]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

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

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (2006).
[CrossRef] [PubMed]

Krolikowski, W.

P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, “Observation of two-dimensional nonlocal gap solitons,” Opt. Lett. 34, 295–297 (2009).
[CrossRef] [PubMed]

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

Lederer, F.

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, D. N. Christodoulides, G. I. Stegeman, A. Hache, 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]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Two-dimensional solitons in nonlinear lattices,” Opt. Lett. 34, 770–772 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Vector solitons in nonlinear lattices,” Opt. Lett. 34, 3625–3627 (2009).
[CrossRef] [PubMed]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Mayteevarunyoo, T.

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
[CrossRef]

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. 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 Y. 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, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Neshev, D. N.

P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, “Observation of two-dimensional nonlocal gap solitons,” Opt. Lett. 34, 295–297 (2009).
[CrossRef] [PubMed]

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

Nolte, S.

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, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Pérez-García, V. M.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

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, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Rasmussen, P. D.

Rosberg, C. R.

P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, “Observation of two-dimensional nonlocal gap solitons,” Opt. Lett. 34, 295–297 (2009).
[CrossRef] [PubMed]

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

Runde, D.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
[CrossRef]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Salamo, G.

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

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, 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, D. N. Christodoulides, G. I. Stegeman, A. Hache, 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]

Sukhorukov, A. A.

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, 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.

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, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Torner, L.

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
[CrossRef] [PubMed]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Two-dimensional solitons in nonlinear lattices,” Opt. Lett. 34, 770–772 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Vector solitons in nonlinear lattices,” Opt. Lett. 34, 3625–3627 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33, 1747–1949 (2008).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[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]

Torres, P. J.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Tunnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

Tünnermann, A.

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vicencio, R. A.

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

Vysloukh, V. A.

Wang, X.

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]

Yang, H.

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

Ye, F.

J. Phys. D (1)

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. A (2)

F. Ye, Y. V. Kartashov, and L. Torner, “Nonlocal surface dipoles and vortices,” Phys. Rev. A 77, 033829 (2008).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).
[CrossRef]

Phys. Rev. E (1)

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

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

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

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and Y. S. Kivshar, “Observation of defect-free surface modes in optical waveguide arrays,” Phys. Rev. Lett. 101, 203902 (2008).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Field modulus for surface (a),(b) dipoles residing on the nearest lattice sites; (c),(d) dipoles residing on the diagonal lattice sites; (e) on-site quadrupole; and (f) off-site quadrupole. b = 0.2 in (a) and (c), and 7.0 in (b) and (d)–(f). Here and in the following, S r = 0.08 for dipoles and 0.09 for quadrupoles and vortices; S l = 0.1 , w R = 3 unless stated otherwise.

Fig. 2
Fig. 2

Properties of surface multipole solitons. (a),(b) Power of dipole and quadrupole solitons versus b. Dashed lines correspond to the solitons shown in Figs. 1a, 1f. Inset: power versus b near points of inflection. Perturbation growth rates of (c) dipole solitons, (d) off-site quadrupoles, and (e) on-site quadrupoles. (f) The differences of peak value versus b for dipoles residing on the nearest lattice sites and off-site quadrupoles (dashed line).

Fig. 3
Fig. 3

(a),(b),(e) Stable and (c),(d) unstable propagation of multipole solitons at b = 6.84 in (a), (b), and (e), and b = 1.2 in (c) and (d). z = 512 in (a), (b), and (e); 0 in (c); and 90 in (d). Other parameters are the same as in Fig. 1.

Fig. 4
Fig. 4

Field modulus for surface vortices at b = ( a ) 0.1 and (b) 7.0. (c) Power versus b for vortex solitons, where dashed part corresponds to the unstable solutions. (d),(e) Noncanonical phase structures corresponding to (a) and (b). (f) Stable propagation of surface vortex soliton at b = 7.4 and z = 512 .

Fig. 5
Fig. 5

Field modulus for corner surface quadrupoles at (a) b = 7.0 , w s = 3 and (b) b = 5.7 , w s = 2.5 . (c) Power and instability growth rate of corner surface solitons versus propagation constant. (d) Differences of peak values between strong and weak soliton components at w s = 2.5 and 3.

Equations (4)

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

i q z + 1 2 ( 2 x 2 + 2 y 2 ) q + σ ( x , y ) | q | 2 1 + S | q | 2 q = 0 ,
1 2 ( 2 x 2 + 2 y 2 ) w r , i b w r , i + σ ( w r 2 + w i 2 ) 1 + S ( w r 2 + w i 2 ) w r , i = 0.
λ u r = 1 2 ( 2 x 2 + 2 y 2 ) u i b u i + σ [ 3 w i 2 + w r 2 + S ( w r 2 + w i 2 ) 2 ] [ 1 + S ( w r 2 + w i 2 ) ] 2 u i + 2 σ w r w i [ 1 + S ( w r 2 + w i 2 ) ] 2 u r ,
λ u i = 1 2 ( 2 x 2 + 2 y 2 ) u r b u r + σ [ 3 w r 2 + w i 2 + S ( w r 2 + w i 2 ) 2 ] [ 1 + S ( w r 2 + w i 2 ) ] 2 u r + 2 σ w r w i [ 1 + S ( w r 2 + w i 2 ) ] 2 u i ,

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