Abstract

We propose a simple model for the realization of symmetrically and antisymmetrically shape-preserving nonlinear waves with nonvanishing intensities at infinity. A finite lattice embedded into a defocusing saturable medium can support various families of novel solitons, including out-of-phase and in-phase solitons with symmetric and antisymmetric profiles. Although the lattice is finite, the existence and stability of solitons depend strongly on the band-gap structure of the corresponding infinite lattice. Saturable nonlinearity enhances the pedestal height and renormalized energy flow of solitons evidently. In particular, increasing the lattice site number or saturation degree of nonlinearity can considerably suppresses the instability of solitons. In addition, we find two branches of in-phase solitons in finite lattices and one branch of them can be dynamically stable. Our findings may provide a helpful hint for linking the solitons supported by infinite and finite lattices.

© 2011 OSA

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  1. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, 1982).
  2. G. Maugin, Nonlinear Waves in Elastic Crystals (Oxford University Press, 2000).
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    [CrossRef]
  4. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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, 2332–2334 (2006).
    [CrossRef] [PubMed]
  8. E. Smirnov, 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] [PubMed]
  9. Y. Kominis, A. Papadopoulos, and K. Hizanidis, “Surface solitons in waveguide arrays: analytical solutions,” Opt. Express 15, 10041–10051 (2007).
    [CrossRef] [PubMed]
  10. Y. Kominis and K. Hizanidis, “Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces,” Phys. Rev. Lett. 102, 133903 (2009).
    [CrossRef] [PubMed]
  11. Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
    [CrossRef] [PubMed]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  13. 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]
  14. Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
    [CrossRef]
  15. V. V. Konotop and S. Takeno, “Stationary dark localized modes: discrete nonlinear Schrödinger equations,” Phys. Rev. E 60, 1001–1008 (1999).
    [CrossRef]
  16. P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
    [CrossRef]
  17. Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31, 2888–2890 (2006).
    [CrossRef] [PubMed]
  18. J. Belmonte-Beitia and J. Cuevas, “Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics,” J. Math. Phys. 52, 032702 (2011).
    [CrossRef]
  19. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [CrossRef]
  20. Y. S. Kivshar and B. A. Malomed, “Raman-induced optical shocks in nonlinear fibers,” Opt. Lett. 18, 485–487 (1993).
    [CrossRef] [PubMed]
  21. S. Wabnitz, “Chiral polarization solitons in elliptically birefringent spun optical fibers,” Opt. Lett. 34, 908–910 (2009).
    [CrossRef] [PubMed]
  22. G. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).
  23. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Izdatel Nauka, 1988).
  24. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice kink solitons,” Opt. Express 14, 12365–12372 (2006).
    [CrossRef] [PubMed]
  25. C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
    [CrossRef]
  26. F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures,” Opt. Lett. 33, 1288–1290 (2008).
    [CrossRef] [PubMed]
  27. J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
    [CrossRef]

2011 (2)

J. Belmonte-Beitia and J. Cuevas, “Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics,” J. Math. Phys. 52, 032702 (2011).
[CrossRef]

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

2010 (1)

2009 (3)

S. Wabnitz, “Chiral polarization solitons in elliptically birefringent spun optical fibers,” Opt. Lett. 34, 908–910 (2009).
[CrossRef] [PubMed]

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
[CrossRef]

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

2008 (2)

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

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures,” Opt. Lett. 33, 1288–1290 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (8)

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780–4785 (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, 2332–2334 (2006).
[CrossRef] [PubMed]

E. Smirnov, 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] [PubMed]

Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31, 2888–2890 (2006).
[CrossRef] [PubMed]

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

2005 (1)

2004 (1)

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
[CrossRef]

1999 (1)

V. V. Konotop and S. Takeno, “Stationary dark localized modes: discrete nonlinear Schrödinger equations,” Phys. Rev. E 60, 1001–1008 (1999).
[CrossRef]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

1996 (1)

L. Stenflo, “Theory of nonlinear plasma surface waves,” Phys. Scr. T63, 59–62 (1996).
[CrossRef]

1993 (1)

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Izdatel Nauka, 1988).

Alexander, T. J.

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
[CrossRef]

Assanto, G.

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

Belmonte-Beitia, J.

J. Belmonte-Beitia and J. Cuevas, “Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics,” J. Math. Phys. 52, 032702 (2011).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Izdatel Nauka, 1988).

Christodoulides, D. N.

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

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]

Cuevas, J.

J. Belmonte-Beitia and J. Cuevas, “Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics,” J. Math. Phys. 52, 032702 (2011).
[CrossRef]

Dodd, R. K.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, 1982).

Dong, L.

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

Eilbeck, J. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, 1982).

Garanovich, I. L.

Gibbon, J. D.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, 1982).

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]

He, Y.

Hizanidis, K.

Hu, B.

Huang, C.

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

Kartashov, Y. V.

Kip, D.

Kivshar, Y. S.

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
[CrossRef]

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]

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, 2332–2334 (2006).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
[CrossRef]

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Raman-induced optical shocks in nonlinear fibers,” Opt. Lett. 18, 485–487 (1993).
[CrossRef] [PubMed]

Kominis, Y.

Konotop, V. V.

V. V. Konotop and S. Takeno, “Stationary dark localized modes: discrete nonlinear Schrödinger equations,” Phys. Rev. E 60, 1001–1008 (1999).
[CrossRef]

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, 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, 1–126 (2008).
[CrossRef]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
[CrossRef]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

Makris, K. 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]

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.

Maugin, G.

G. Maugin, Nonlinear Waves in Elastic Crystals (Oxford University Press, 2000).

Mihalache, D.

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]

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, 2332–2334 (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]

Morris, H. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic Press, 1982).

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, 083901 (2006).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
[CrossRef]

Papadopoulos, A.

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, 083901 (2006).
[CrossRef] [PubMed]

Rüter, C. E.

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]

Segev, M.

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

Shandarov, V.

Silberberg, Y.

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

Smirnov, E.

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.

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

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]

Stenflo, L.

L. Stenflo, “Theory of nonlinear plasma surface waves,” Phys. Scr. T63, 59–62 (1996).
[CrossRef]

Stepic, M.

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]

Takeno, S.

V. V. Konotop and S. Takeno, “Stationary dark localized modes: discrete nonlinear Schrödinger equations,” Phys. Rev. E 60, 1001–1008 (1999).
[CrossRef]

Torner, L.

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.

Wabnitz, S.

Wang, J.

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
[CrossRef]

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]

Yang, J.

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009).
[CrossRef]

Ye, F.

Zheng, J.

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

Zhong, S.

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

J. Math. Phys. (1)

J. Belmonte-Beitia and J. Cuevas, “Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics,” J. Math. Phys. 52, 032702 (2011).
[CrossRef]

J. Opt. B (1)

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices,” J. Opt. B 6, S309–S317 (2004).
[CrossRef]

Opt. Commun. (1)

C. Huang, J. Zheng, S. Zhong, and L. Dong, “Interface kink solitons in defocusing saturable nonlinear media,” Opt. Commun. 284, 4225–4228 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

F. Ye, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures,” Opt. Lett. 33, 1288–1290 (2008).
[CrossRef] [PubMed]

S. Wabnitz, “Chiral polarization solitons in elliptically birefringent spun optical fibers,” Opt. Lett. 34, 908–910 (2009).
[CrossRef] [PubMed]

Y. He, D. Mihalache, and B. Hu, “Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities,” Opt. Lett. 35, 1716–1718 (2010).
[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, 2332–2334 (2006).
[CrossRef] [PubMed]

E. Smirnov, 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).
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Figures (6)

Fig. 1
Fig. 1

Profiles of symmetric solitons. s = 0.5 for out-of-phase (a–c and f) and 0.2 for in-phase (d, e) solitons. The shaded stripes represent the regions R ≥ 0.5. b = −0.3 in (c, d) and −1.5 in (e), p = 16 in (f) and 4 in other panels. In all cases Ω = 2 and n = 13.

Fig. 2
Fig. 2

(a) Band-gap structure of infinite lattice R(x) = cos2x). Bands are shown gray and gaps are shown white. Existence domains of out-of-phase solitons at s = 0.5 (b) and in-phase solitons at s = 0.2 (c). (d) Renormalized energy flow versus propagation constant for out-of-phase solitons in lattices with different site number n. Inset: Ur versus b for different saturation parameter s. p = 4 in (d) and Ω = 2,n = 13 in all panels.

Fig. 3
Fig. 3

Areas of stability and instability (shaded) on the (b,s) plane (a) and (b,n) plane (b) for out-of-phase solitons. Dotted line denotes the upper edge of the second band. Renor-malized energy flow versus propagation constant for two types of in-phase solitons (c) and in-phase I solitons at different s (d). Inset: Ur of in-phase I solitons near bupp at s = 0.2. n = 13 in (a, b, d), s = 0.2 in (b, c) and p = 4 in all panels.

Fig. 4
Fig. 4

Perturbation growth rate versus propagation constant for out-of-phase solitons at s = 0.5 (a) and two types of in-phase solitons at s = 0.2 (b). (c) Spectrum of the linearization operator for out-of-phase soliton at b = −1.0. (d, e) Stable propagations of out-of-phase soliton at b = −0.45 and in-phase I soliton at b = −0.25. (f) Unstable propagation of out-of-phase soliton at b = −1.0. White noises with σ noise 2 = 0.01 were added into the initial inputs. p = 4 in (a–f) and n = 13 in (b–f).

Fig. 5
Fig. 5

(a) Band-gap structure of periodic lattice R(x) = 1 – cos(Ωx). (b) Renormalized energy flow versus propagation constant for out-of-phase solitons. Inset: Ur versus b for two types of in-phase solitons. (c) Examples of out-of-phase solitons. (d) Profiles of two types of in-phase solitons at b = −0.3. The shaded stripes represent the regions R ≥ 1. s = 0.5 for out-of-phase solitons and 0.2 for in-phase solitons. p = 2,n = 12 in (b–d) and Ω = 4 in all cases.

Fig. 6
Fig. 6

Perturbation growth rate versus propagation constant for out-of-phase solitons (a) and in-phase solitons (b). Stable propagation examples of out-of-phase soliton at b = −0.5 (c) and in-phase I soliton at b = −0.55 (d). s = 0.5 for out-of-phase solitons and 0.2 for in-phase solitons. In all the cases p = 2,n = 12,Ω = 4.

Equations (3)

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i q z = 1 2 2 q x 2 + q | q | 2 1 + s | q | 2 p R ( x ) q
δ u = 1 2 2 v x 2 + b v p R v + w 2 + s w 4 ( 1 + s w 2 ) 2 v , δ v = 1 2 2 u x 2 b u + p R u 3 w 2 + s w 4 ( 1 + s w 2 ) 2 u .
U r = [ w ( x ) | b 1 + b s | 1 / 2 H ( x ) ] 2 d x

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