Abstract

We study the surface line defect gap solitons (SLDGSs) in an interface between a line defect of two-dimensional (2D) square optical lattice and the uniform media with focusing saturable nonlinearity. Some unique properties are revealed that the surface line defect of square optical lattice can profoundly affect the shape and stability of soliton. Stable soltion for the case of negative defect can exist in both of the semi-infinite gap and the first gap; unlike in the square lattice without defect, soliton can only exist in the semi-infinite gap. For the case of the positive defect, the solitons exist in the semi-inifite gap and stably exist in the low power region.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, “Discrete surface solitons,” Opt. Lett. 30, 2466–2468 (2005).
    [CrossRef] [PubMed]
  4. M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-inifinite binary waveguide arrays,” Opt. Lett. 31, 2332–2334 (2006).
    [CrossRef] [PubMed]
  5. Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
    [CrossRef] [PubMed]
  6. E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
    [CrossRef]
  7. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, Y. S. Kivshar, and A. Hache, “Observation of surface gap solitons in semi-infinite wave guide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
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  10. 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]
  11. J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006).
    [CrossRef]
  12. W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
    [CrossRef] [PubMed]
  13. J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
    [CrossRef]
  14. W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
    [CrossRef] [PubMed]
  15. M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
    [CrossRef]
  16. Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
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  18. X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
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  19. A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
    [CrossRef] [PubMed]
  20. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  21. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
    [CrossRef] [PubMed]
  22. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
    [CrossRef]
  23. J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary wave in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
    [CrossRef]
  24. J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277(14), 6862–6876 (2008).
    [CrossRef]
  25. D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
    [CrossRef] [PubMed]

2010 (3)

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
[CrossRef]

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
[CrossRef] [PubMed]

2009 (2)

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

2008 (1)

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277(14), 6862–6876 (2008).
[CrossRef]

2007 (4)

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary wave in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
[CrossRef] [PubMed]

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

2006 (8)

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006).
[CrossRef]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef] [PubMed]

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

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

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

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

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

2005 (1)

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

2004 (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

2003 (2)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

1995 (2)

M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20, 2075–2077 (1995).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

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]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

Buryak, A. V.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
[CrossRef] [PubMed]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, W. H.

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

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

W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
[CrossRef] [PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef] [PubMed]

Chen, Y.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

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]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

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]

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Cronin-Golomb, M.

M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20, 2075–2077 (1995).
[CrossRef] [PubMed]

Dreisow, F.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Garanovich, I. L.

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

Hache, A.

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

He, Y.

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
[CrossRef]

He, Y. J.

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

W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
[CrossRef] [PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef] [PubMed]

Heinrich, M.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Ilan, B.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[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, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

Kip, D.

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

Kivshar, Y. S.

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

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

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
[CrossRef] [PubMed]

Krolikowski, W.

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

Lakoba, T. I.

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary wave in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

Lederer, F.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Li, R. H.

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

Li, Y.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Makasyuk, I.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 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]

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

Malomed, B. A.

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

Mihalache, D.

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

Mitchell, A.

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

Molina, M. I.

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

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

Neshev, D. N.

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

Nolte, S.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Pang, W.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
[CrossRef] [PubMed]

Pertsch, T.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Piestun, R.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

Rosberg, C. R.

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

Rüter, C. E.

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

Schonbrun, E.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Shandarov, V.

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

Smironov, E.

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

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]

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

Stepic, M.

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

Sukhorukov, A. A.

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

Suntsov, S.

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

Szameit, A.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Torner, L.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[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, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

Tünnermann, A.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

Vicencio, R. A.

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

Vysloukh, V. A.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[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, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

Wang, H.

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
[CrossRef]

X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
[CrossRef] [PubMed]

Wang, H. Z.

W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
[CrossRef] [PubMed]

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

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef] [PubMed]

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]

Wu, T. W.

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

Xie, J.

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
[CrossRef]

Yang, J.

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277(14), 6862–6876 (2008).
[CrossRef]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary wave in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

Yu, Z.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zhang, H.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zheng, L. X.

X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
[CrossRef] [PubMed]

Zhou, J.

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Zhu, X.

X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
[CrossRef] [PubMed]

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

J. Comput. Phys. (1)

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 277(14), 6862–6876 (2008).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Xie, Y. He, and H. Wang, “Surface defect gap solitons in one-dimensional chirped optical lattices,” J. Opt. Soc. Am. B 27(3), 484–487 (2010).
[CrossRef]

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in opticallly indued nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

W. H. Chen, Y. J. He, and H. Z. Wang, “Defect superlattice solitons,” Opt. Express 15(22), 14498–14503 (2007).
[CrossRef] [PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271–11276 (2006).
[CrossRef] [PubMed]

W. H. Chen, X. Zhu, T. W. Wu, and R. H. Li, “Defect solitons in two-dimensional optical lattices,” Opt. Express 18(11), 10956–10962 (2010).
[CrossRef] [PubMed]

X. Zhu, H. Wang, and L. X. Zheng, “Defect solitons in kagome optical lattices,” Opt. Express 18(20), 20786–20792 (2010).
[CrossRef] [PubMed]

Opt. Lett. (7)

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, F. Lederer, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional defect surface solitons,” Opt. Lett. 34(6), 797–799 (2009).
[CrossRef] [PubMed]

M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20, 2075–2077 (1995).
[CrossRef] [PubMed]

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

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

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329–2331 (2006).
[CrossRef] [PubMed]

E. Smironov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338–2340 (2006).
[CrossRef]

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

Phys. Rev. A (1)

Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80, 043824 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 035601 (2006).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 026609 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (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, 123903 (2007).
[CrossRef] [PubMed]

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically indued real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Insability of solitons governed by quadratic nonlinearity,” Phys. Rev. Lett. 75, 591–595 (1995).
[CrossRef] [PubMed]

Stud. Appl. Math. (2)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

J. Yang and T. I. Lakoba, “Universally-convergent squared-operator iteration methods for solitary wave in general nonlinear wave equations,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

Other (1)

Y. J. He, and B. A. Malomed, “Surface waves and boundary effects in DNLS equations,” in The Discrete Nonlinear Schrodinger Equation: Mathematical Analysis, Numerical Computations, and Physcal Perspectives, P. G. Kevrekidis, ed., (Springer, 2009), pp. 259–276.
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Band structure of square optical lattices (blank region corresponding to Bloch band);Semi-infinite gap (SI gap) and the first gap (1st gap) have been noted. (b) The square optical lattices with a positive line defect(ɛ = 0.5). (c) The square optical lattices with a negative line defect(ɛ = −0.5). In (b) and (c), a line defect exists at the surface between the uniform media (the left side) and square lattice (the right side).

Fig. 2
Fig. 2

(Color online)(ɛ = 0). (a) Power diagram of surface gap solitons (blue regions corresponding to Bloch bands. (b) Re(δ) versus constant μ for surface gap solitons. Profile (|u|) of surface gap soliton for μ = 1.55 (point A) at (c) z=0, (d) z=100, and (e) z=200. Profile (|u|) of surface gap soliton for μ = 2.6 (point B) at (f) z=0, (g) z=100, and (h) z=200.

Fig. 3
Fig. 3

(Color online)(ɛ = 0). Profile (|u|) of surface gap soliton for μ = 3.52 (point C) at (a) z=0, (b) z=100, and (c) z=200.

Fig. 4
Fig. 4

(Color online)(ɛ = −0.5). (a) Power diagram of SLDGSs (blue regions corresponding to Bloch bands. (b) Re(δ) versus constant μfor SLDGSs Profile (|u|) of SLDGS for μ = 1.85 (point A) at (c) z=0, (d) z=100, and (e) z=200. Profile (|u|) of SLDGS for μ = 2.95 (point B) at (f) z=0, (g) z=100, and (h) z=200.

Fig. 5
Fig. 5

(Color online)(ɛ = −0.5). Profile (|u|) of SLDGSs for μ = 3.54 (point C) at (c) z=0, (d) z=100, and (e) z=200. Profile (|u|) of SLDGS for μ = 4.45 (point D) at (f) z=0, (g) z=100, and (h) z=200.

Fig. 6
Fig. 6

(Color online)(ɛ = 0.5). (a) Power diagram of SLDGSs (blue regions corresponding to Bloch bands. (b) Re(δ) versus propagate constant μ for SLDGSs. Profile (|u|) of SLDGS for μ = 2.35 (point A) at (c) z=0, (d) z=100, and (e) z=200. Profile (|u|) of SLDGS for μ = 1.5 (point B) at (f) z=0, (g) z=100, and (h) z=200.

Equations (5)

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

i q z + q x x + q y y E 0 q 1 + I L + | q | 2 = 0 .
I L = I 0 cos 2 ( x ) cos 2 ( y ) × { 1 + ɛ exp [ ( x 2 ) 4 / 128 ] } , ( x π 2 ) ,
u x x + u y y + E 0 u 1 + I L + | u | 2 + μ u = 0 .
q = exp ( i μ z ) { u ( x , y ) + [ v ( x , y ) w ( x , y ) ] exp ( δ z ) + [ v ( x , y ) + w ( x , y ) ] * exp ( δ * z ) } ,
{ δ v = i [ ( w x x + w y y ) + μ w E 0 w / ( 1 + I L + u 2 ) ] , δ w = i [ ( v x x + v y y ) + μ v E 0 v ( 1 + I L + u 2 ) / ( 1 + I L + u 2 ) 2 ] .

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