Abstract

We find the existence of two kinds of solitons at the interface of optical superlattices with both spatially modulated nonlinearity and linear refraction index. The first kind of solitons can either drift across the lattice, or deflect to the uniform nonlinear medium. The dynamics of such solitons mainly depends on their powers. The other kind of solitons can stably propagate along the surface, and can be controlled by additional Gaussian beams. In addition, we demonstrate the input-angle-dependent reflection, trapping, and refraction with nearly no losses by launching sech-shaped solitons.

©2011 Optical Society of America

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  1. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30(18), 2466–2468 (2005).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  13. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15(2), 589–595 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  18. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  23. Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
    [Crossref] [PubMed]
  24. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
    [Crossref] [PubMed]
  25. G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
    [Crossref] [PubMed]
  26. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” arXiv:1010.2254 (to appear in Rev. Mod. Phys.).
  27. H. Sakaguchi and B. A. Malomed, “Gap solitons in quasiperiodic optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026601 (2006).
    [Crossref] [PubMed]
  28. H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
    [Crossref]
  29. M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, “Controllable soliton emission from a Bose-Einstein condensate,” Phys. Rev. Lett. 95(15), 153903 (2005).
    [Crossref] [PubMed]
  30. A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
    [Crossref] [PubMed]
  31. Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102(13), 133903 (2009).
    [Crossref] [PubMed]
  32. A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003).
    [Crossref]
  33. Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
    [Crossref]
  34. M. Shokooh-Saremi, V. G. Ta'eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B 23(7), 1323–1331 (2006).
    [Crossref]

2010 (2)

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[Crossref]

2009 (1)

Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102(13), 133903 (2009).
[Crossref] [PubMed]

2008 (4)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
[Crossref] [PubMed]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, A. Tünnermann, T. Pertsch, and L. Torner, “Surface solitons at interfaces of arrays with spatially modulated nonlinearity,” Opt. Lett. 33(10), 1120–1122 (2008).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

2007 (5)

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattice gap solitons,” Opt. Lett. 32(11), 1390–1392 (2007).
[Crossref] [PubMed]

M. I. Molina and Y. S. Kivshar, “Interface localized modes and hybrid lattice solitons in waveguide arrays,” Phys. Lett. A 362(4), 280–282 (2007).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15(2), 589–595 (2007).
[Crossref] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (2007).
[Crossref] [PubMed]

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

2006 (15)

M. Shokooh-Saremi, V. G. Ta'eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B 23(7), 1323–1331 (2006).
[Crossref]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
[Crossref] [PubMed]

D. Blömer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, “Nonlinear refractive index of fs-laser-written waveguides in fused silica,” Opt. Express 14(6), 2151–2157 (2006).
[Crossref] [PubMed]

H. Sakaguchi and B. A. Malomed, “Gap solitons in quasiperiodic optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026601 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31(17), 2595–2597 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice kink solitons,” Opt. Express 14(25), 12365–12372 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96(7), 073901 (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(6), 063901 (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]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31(11), 1693–1695 (2006).
[Crossref] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31(15), 2332–2334 (2006).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, Y. S. Kivshar, and M. Molina, “Surface multi-gap vector solitons,” Opt. Express 14(11), 4780–4785 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14(11), 4808–4814 (2006).
[Crossref] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31(21), 3125–3127 (2006).
[Crossref] [PubMed]

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]

2005 (5)

2003 (1)

A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003).
[Crossref]

Assanto, G.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Baker, N. J.

Barak, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Blömer, D.

Brocas, A.

Canioni, L.

Chen, F.

Chen, G.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Chen, W. H.

Christodoulides, D. N.

Cisneros, L. A.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

Dreisow, F.

Eggleton, B. J.

Elliott, S. R.

A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003).
[Crossref]

Fibich, G.

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
[Crossref] [PubMed]

Garanovich, I. L.

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(6), 063901 (2006).
[Crossref] [PubMed]

He, Y. J.

Heinrich, M.

Hizanidis, K.

Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102(13), 133903 (2009).
[Crossref] [PubMed]

Hudock, J.

Iwanow, R.

Kartashov, Y. V.

Kip, D.

Kivshar, Y. S.

Kominis, Y.

Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102(13), 133903 (2009).
[Crossref] [PubMed]

Krolikowski, W.

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]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15(2), 589–595 (2007).
[Crossref] [PubMed]

Littler, I. C. M.

Liu, L.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Liu, W.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Luther-Davies, B.

Makris, K. G.

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[Crossref]

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattice gap solitons,” Opt. Lett. 32(11), 1390–1392 (2007).
[Crossref] [PubMed]

H. Sakaguchi and B. A. Malomed, “Gap solitons in quasiperiodic optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026601 (2006).
[Crossref] [PubMed]

Manela, O.

Mazilu, D.

Michinel, H.

M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, “Controllable soliton emission from a Bose-Einstein condensate,” Phys. Rev. Lett. 95(15), 153903 (2005).
[Crossref] [PubMed]

Mihalache, D.

Min, Y.

Minzoni, A. A.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

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(8), 083901 (2006).
[Crossref] [PubMed]

Molina, M.

Molina, M. I.

M. I. Molina and Y. S. Kivshar, “Interface localized modes and hybrid lattice solitons in waveguide arrays,” Phys. Lett. A 362(4), 280–282 (2007).
[Crossref]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31(15), 2332–2334 (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]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31(11), 1693–1695 (2006).
[Crossref] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (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(6), 063901 (2006).
[Crossref] [PubMed]

Moss, D. J.

Motzek, K.

Neshev, D. N.

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]

Nolte, S.

Peleg, O.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Pérez-García, V. M.

M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, “Controllable soliton emission from a Bose-Einstein condensate,” Phys. Rev. Lett. 95(15), 153903 (2005).
[Crossref] [PubMed]

Pertsch, T.

Richardson, M.

Rodas-Verde, M. I.

M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, “Controllable soliton emission from a Bose-Einstein condensate,” Phys. Rev. Lett. 95(15), 153903 (2005).
[Crossref] [PubMed]

Rosberg, C. R.

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]

Ruan, Y.

Runde, D.

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[Crossref]

H. Sakaguchi and B. A. Malomed, “Gap solitons in quasiperiodic optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026601 (2006).
[Crossref] [PubMed]

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (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(6), 063901 (2006).
[Crossref] [PubMed]

Sarger, L.

Schiek, R.

Schreiber, T.

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

Shandarov, V.

Shokooh-Saremi, M.

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Sivan, Y.

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
[Crossref] [PubMed]

Siviloglou, G. A.

Skuse, B. D.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

Smyth, N. F.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

Soffer, A.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Sohler, W.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (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(6), 063901 (2006).
[Crossref] [PubMed]

Stegeman, G. I.

Stepic, M.

Stucchio, C.

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Sukhorukov, A. A.

Suntsov, S.

Szameit, A.

Ta'eed, V. G.

Torner, L.

Tünnermann, A.

Vicencio, R. A.

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31(11), 1693–1695 (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]

Vysloukh, V. A.

Wang, H. Z.

Weinstein, M. I.

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
[Crossref] [PubMed]

Worthy, A. L.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

Xu, L.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Xu, Y.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (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(6), 063901 (2006).
[Crossref] [PubMed]

Ye, F.

Zakery, A.

A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003).
[Crossref]

Zhang, Q.

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

Zoubir, A.

Appl. Phys. Lett. (1)

Q. Zhang, W. Liu, L. Liu, L. Xu, Y. Xu, and G. Chen, “Large and opposite changes of the third-order optical nonlinearities of chalcogenide glasses by femtosecond and continuous-wave laser irradiation,” Appl. Phys. Lett. 91(18), 181917 (2007).
[Crossref]

J. Non-Cryst. Solids (1)

A. Zakery and S. R. Elliott, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Express (8)

D. Blömer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, “Nonlinear refractive index of fs-laser-written waveguides in fused silica,” Opt. Express 14(6), 2151–2157 (2006).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice kink solitons,” Opt. Express 14(25), 12365–12372 (2006).
[Crossref] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, “Vector discrete nonlinear surface waves,” Opt. Express 13(20), 7720–7725 (2005).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, Y. S. Kivshar, and M. Molina, “Surface multi-gap vector solitons,” Opt. Express 14(11), 4780–4785 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14(11), 4808–4814 (2006).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15(2), 589–595 (2007).
[Crossref] [PubMed]

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]

Opt. Lett. (9)

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31(11), 1693–1695 (2006).
[Crossref] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32(21), 3098–3100 (2007).
[Crossref] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Lattice-supported surface solitons in nonlocal nonlinear media,” Opt. Lett. 31(17), 2595–2597 (2006).
[Crossref] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31(15), 2332–2334 (2006).
[Crossref] [PubMed]

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattice gap solitons,” Opt. Lett. 32(11), 1390–1392 (2007).
[Crossref] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31(21), 3125–3127 (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, V. A. Vysloukh, and L. Torner, “Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity,” Opt. Lett. 33(15), 1747–1749 (2008).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, A. Tünnermann, T. Pertsch, and L. Torner, “Surface solitons at interfaces of arrays with spatially modulated nonlinearity,” Opt. Lett. 33(10), 1120–1122 (2008).
[Crossref] [PubMed]

Phys. Lett. A (1)

M. I. Molina and Y. S. Kivshar, “Interface localized modes and hybrid lattice solitons in waveguide arrays,” Phys. Lett. A 362(4), 280–282 (2007).
[Crossref]

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Phys. Rev. A (1)

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81(1), 013624 (2010).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

H. Sakaguchi and B. A. Malomed, “Gap solitons in quasiperiodic optical lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026601 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (8)

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L. Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett. 104(5), 053903 (2010).
[Crossref] [PubMed]

Y. Sivan, G. Fibich, and M. I. Weinstein, “Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates,” Phys. Rev. Lett. 97(19), 193902 (2006).
[Crossref] [PubMed]

M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, “Controllable soliton emission from a Bose-Einstein condensate,” Phys. Rev. Lett. 95(15), 153903 (2005).
[Crossref] [PubMed]

A. Barak, O. Peleg, C. Stucchio, A. Soffer, and M. Segev, “Observation of soliton tunneling phenomena and soliton ejection,” Phys. Rev. Lett. 100(15), 153901 (2008).
[Crossref] [PubMed]

Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102(13), 133903 (2009).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96(7), 073901 (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(6), 063901 (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]

Other (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” arXiv:1010.2254 (to appear in Rev. Mod. Phys.).

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Figures (4)
Fig. 1
Fig. 1 The lateral movable solitons: (a) Solitons power U versus propagation constant b with p = 2. The white area is the semi-infinite gap. The red dots correspond to the threshold value bd in (b). (b), (c) Low-cutoff bc , Uc , trap threshold bt , Ut , and deflection threshold bd , Ud , depend on σ at p = 2, the dash line in (b) indicates the lower edge of the semi-infinite gap. Insert: the modulation profile R(x) with ε = 0.3, d1 = 2, and d2 = 1. Profiles of solitons for (d) b = 5.5, (e) b = 6.4, (f) b = 9.2 and (j) b = 14 for σ = 0.35, p = 2; (k) b = 4.1 for σ = 0.8; (l) b = 8.9 for σ = 1.1. Panels below them are solitons propagation: (g) drifting across lattice; (h) trapping at the inside lattice; (i) trapping near the surface; (m), (n) deflection from the surface; (o) splitting.

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Fig. 2
Fig. 2 The stable surface solitons: (a) Solitons power U versus propagation constant b for p = 2, σ = 0.8, the white area is the semi-infinite gap. (b) Real part of perturbation growth rate δ vs b for (a). (c, d) Stable soliton for b = 4.1, p = 2 and σ = 0.8. (e) Low cut-off bc and stable threshold bs depend on σ at p = 2. Domain above bs is for stable propagation. The dash line indicates the lower edge of the semi-infinite gap. (f) Excitation of surface soliton by inputting a Gaussian beam with A = 2.86, w = 0.6, x0 = −0.07.

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Fig. 3
Fig. 3 (a) Turning the stable soliton corresponding to Fig. 2(c) to deflect by additional Gaussian beam with A = 1.1, x0 = 0.3 and w = 0.3. (b) Deflection angle θ controlled by the parameters of Gaussian beams: amplitude A and center x0 , with the width w = 0.3. (c) The same with (a) except for A = 0.3.

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Fig. 4
Fig. 4 (a) Superimposed results: solitons drifting, trapping and deflection by inputting Gaussian beams (x0 = 0.4, w = 0.55) with A = 3.1, A = 3.4, and A = 3.5. (b) Deflection angle θ versus A, the white region is the solitons deflection case. (c) Soliton refraction by launching a sech-shaped soliton from x0 = −1.4 with A = 4.2, v = 0.2, for σ = 0.2 and p = 2, (d) refractive angle versus incident angle. (e) Soliton reflection by launching a sech-shaped soliton with A = 4, v = 0.2 for σ = 0.4 and p = 2; (f), (g) Soliton trapping with v = 0.55 and v = 0.64; (h) the output channel positions x versus v, the grey region is for solitons reflection.

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Equations (3)

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2 i β 0 ∂ A ∂ Z = − ∂ 2 A ∂ X 2 − 2 β 0 k 0 n 2 [ 1 − σ R ( X ) ] | A | 2 A − k 0 2 Δ χ R ( X ) A ,
i ∂ q ∂ z = − 1 2 ∂ 2 q ∂ x 2 − [ 1 − σ R ( x ) ] | q | 2 q − p R ( x ) q ,
P = ∫ − ∞ ∞ ∫ − ∞ ∞ 1 2 c ε 0 n 0 2 | E | 2 d X d Y = 1 2 c ε 0 n 0 2 W Y ∫ − ∞ ∞ | A | 2 d X = c ε 0 n 0 w y 2 k 0 2 n 2 ∫ − ∞ ∞ | u | 2 d x = c ε 0 n 0 w y 2 k 0 2 n 2 U ,

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