We demonstrate self-trapping of singly-charged vortices at the surface of an optically induced two-dimensional photonic lattice. Under appropriate conditions of self-focusing nonlinearity, a singly-charged vortex beam can self-trap into a stable semi-infinite gap surface vortex soliton through a four-site excitation. However, a single-site excitation leads to a quasi-localized state in the first photonic gap, and our theoretical analysis illustrates that such a bandgap surface vortex soliton is always unstable. Our experimental results of stable and unstable topological surface solitons are corroborated by direct numerical simulations and linear stability analysis.

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1. 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. Arès, 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(04), 401 (2007). [CrossRef]
2. Yu. S. Kivshar, “Nonlinear Tamm states and surface effects in periodic photonic structures,” Laser Phys. Lett. 5(10), 703–713 (2008). [CrossRef]
3. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30(18), 2466–2468 (2005). [CrossRef] [PubMed]
4. 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(6), 063901 (2006). [CrossRef] [PubMed]
5. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96(7), 073901 (2006). [CrossRef] [PubMed]
6. 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(8), 083901 (2006). [CrossRef] [PubMed]
7. G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14(12), 5508–5516 (2006). [CrossRef] [PubMed]
8. K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, “Surface lattice solitons,” Opt. Lett. 31(18), 2774–2776 (2006). [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(12), 123903 (2007). [CrossRef] [PubMed]
10. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “S. Nolte A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98(17), 173903 (2007). [CrossRef]
11. Y. V. Kartashov and L. Torner, “Multipole-mode surface solitons,” Opt. Lett. 31(14), 2172–2174 (2006). [CrossRef] [PubMed]
12. A. Szameit, Y. V. Kartashov, V. A. Vysloukh, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner, “Angular surface solitons in sectorial hexagonal arrays,” Opt. Lett. 33, 2466 (2005).
13. 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(6), 063832 (2009). [CrossRef]
14. X. Wang, A. Samodurov, and Z. Chen, “Demonstration of surface soliton arrays at the edge of a two-dimensional photonic lattice,” Opt. Lett. 33(11), 1240–1242 (2008). [CrossRef] [PubMed]
15. H. Susanto, P. G. Kevrekidis, B. A. Malmed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66, 046602 (2002).
16. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Surface vortex solitons,” Opt. Express 14(9), 4049–4057 (2006). [CrossRef] [PubMed]
17. B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001). [CrossRef] [PubMed]
18. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003). [CrossRef] [PubMed]
19. J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008). [CrossRef]
20. M. S. Petrović, S. Prvanovic, and D. M. Jovic, “Soliton with different topological charges,” Phys. Rev. A 79(2), 021803 (2009). [CrossRef]
21. 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(12), 123903 (2004). [CrossRef] [PubMed]
22. 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(12), 123904 (2004). [CrossRef] [PubMed]
23. G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005). [CrossRef] [PubMed]
24. D. Song, C. Lou, L. Tang, X. Wang, W. Li, X. Chen, K. J. Law, H. Susanto, P. G. Kevrekidis, J. Xu, and Z. Chen, “Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity,” Opt. Express 16(14), 10110–10116 (2008). [CrossRef] [PubMed]

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. Arès, 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(04), 401 (2007). [CrossRef]

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]

Opt. Express

• G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express 14(12), 5508–5516 (2006). [CrossRef] [PubMed]
• Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Surface vortex solitons,” Opt. Express 14(9), 4049–4057 (2006). [CrossRef] [PubMed]
• D. Song, C. Lou, L. Tang, X. Wang, W. Li, X. Chen, K. J. Law, H. Susanto, P. G. Kevrekidis, J. Xu, and Z. Chen, “Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity,” Opt. Express 16(14), 10110–10116 (2008). [CrossRef] [PubMed]

Opt. Lett.

• K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, “Surface lattice solitons,” Opt. Lett. 31(18), 2774–2776 (2006). [CrossRef] [PubMed]
• K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30(18), 2466–2468 (2005). [CrossRef] [PubMed]
• Y. V. Kartashov and L. Torner, “Multipole-mode surface solitons,” Opt. Lett. 31(14), 2172–2174 (2006). [CrossRef] [PubMed]
• A. Szameit, Y. V. Kartashov, V. A. Vysloukh, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, and L. Torner, “Angular surface solitons in sectorial hexagonal arrays,” Opt. Lett. 33, 2466 (2005).
• X. Wang, A. Samodurov, and Z. Chen, “Demonstration of surface soliton arrays at the edge of a two-dimensional photonic lattice,” Opt. Lett. 33(11), 1240–1242 (2008). [CrossRef] [PubMed]
• J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28(21), 2094–2096 (2003). [CrossRef] [PubMed]

Phys. Rev. A

• J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008). [CrossRef]
• M. S. Petrović, S. Prvanovic, and D. M. Jovic, “Soliton with different topological charges,” Phys. Rev. A 79(2), 021803 (2009). [CrossRef]
• 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(6), 063832 (2009). [CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

• H. Susanto, P. G. Kevrekidis, B. A. Malmed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66, 046602 (2002).
• B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(2), 026601 (2001). [CrossRef] [PubMed]

Phys. Rev. Lett.

• 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(12), 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(12), 123904 (2004). [CrossRef] [PubMed]
• G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005). [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(6), 063901 (2006). [CrossRef] [PubMed]
• Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96(7), 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(8), 083901 (2006). [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(12), 123903 (2007). [CrossRef] [PubMed]
• A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, “S. Nolte A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98(17), 173903 (2007). [CrossRef]

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