Abstract

We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of the surface solitons shrink with an increase in the amplitude of the imaginary part of complex potential.

© 2012 Optical Society of America

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  1. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
    [CrossRef]
  2. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
    [CrossRef]
  3. K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  4. S. V. Dmitriev, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 35, 2976 (2010).
    [CrossRef]
  5. F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805 (2011).
    [CrossRef]
  6. A. E. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
    [CrossRef]
  7. Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
    [CrossRef]
  8. C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
    [CrossRef]
  9. F. K. Abdullaev, V. V. Konotop, M. Salerno, and A. Yulin, Phys. Rev. E 82, 056606 (2010).
    [CrossRef]
  10. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
    [CrossRef]
  11. Y. V. Bludov, and V. V. Konotop, Phys. Rev. A 81, 013625 (2010).
    [CrossRef]
  12. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Euro. Phys. Lett. 91, 34003 (2010).
    [CrossRef]
  13. D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
    [CrossRef]
  14. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  15. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
    [CrossRef]
  16. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef]
  17. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef]
  18. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef]
  19. E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [CrossRef]
  20. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef]
  21. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  22. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
    [CrossRef]
  23. M. Ablowitz and Z. Musslimani, Opt. Lett. 30, 2140 (2005).
    [CrossRef]

2012 (1)

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
[CrossRef]

2011 (2)

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805 (2011).
[CrossRef]

A. E. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

2010 (6)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

F. K. Abdullaev, V. V. Konotop, M. Salerno, and A. Yulin, Phys. Rev. E 82, 056606 (2010).
[CrossRef]

Y. V. Bludov, and V. V. Konotop, Phys. Rev. A 81, 013625 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Euro. Phys. Lett. 91, 34003 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef]

S. V. Dmitriev, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 35, 2976 (2010).
[CrossRef]

2009 (1)

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

2008 (4)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

2007 (2)

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

2006 (4)

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef]

2005 (2)

1989 (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805 (2011).
[CrossRef]

F. K. Abdullaev, V. V. Konotop, M. Salerno, and A. Yulin, Phys. Rev. E 82, 056606 (2010).
[CrossRef]

Ablowitz, M.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
[CrossRef]

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

Bludov, Y. V.

Y. V. Bludov, and V. V. Konotop, Phys. Rev. A 81, 013625 (2010).
[CrossRef]

Chen, Z.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

Chow, K. W.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Christodoulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef]

Dmitriev, S. V.

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

El Ganainy, R.

K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

Hache, A.

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef]

He, Y.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Kartashov, Y. V.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805 (2011).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Euro. Phys. Lett. 91, 34003 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

S. V. Dmitriev, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 35, 2976 (2010).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

Konotop, V. V.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805 (2011).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Euro. Phys. Lett. 91, 34003 (2010).
[CrossRef]

Y. V. Bludov, and V. V. Konotop, Phys. Rev. A 81, 013625 (2010).
[CrossRef]

F. K. Abdullaev, V. V. Konotop, M. Salerno, and A. Yulin, Phys. Rev. E 82, 056606 (2010).
[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

Lam, C.-K.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Liu, J.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
[CrossRef]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef]

Malomed, B. A.

A. E. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
[CrossRef]

Mihalache, D.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, Phys. Rev. A 85, 013831 (2012).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Phys. Rev. A 77, 043828 (2008).
[CrossRef]

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, 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, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

Morandotti, R.

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

Musslimani, Z.

Musslimani, Z. H.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef]

K. G. Makris, R. El Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

Nolte, S.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef]

Salamo, G.

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

Salerno, M.

F. K. Abdullaev, V. V. Konotop, M. Salerno, and A. Yulin, Phys. Rev. E 82, 056606 (2010).
[CrossRef]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Shandarov, V.

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef]

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef]

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef]

Tünnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Field modulus distribution (blue curves) for surface solitons in defocusing medium at (a) γ=0.6224 and pi=1 and (b) γ=0.9590 at pi=1.5. (c) Field modulus distribution for surface solitons in focusing medium at γ=0.6671 and pi=1. Real prRr (curve 1) and imaginary piRi+γ (curve 2) parts of potential were downscaled for illustrative purposes.

Fig. 2.
Fig. 2.

(a) Energy flow and (b) propagation constant of surface solitons versus γ in focusing (curves labeled with Uf, bf) and defocusing (curves labeled Ud, bd) media at pi=1. Circles correspond to solitons in Figs. 1(a) and 1(c). (c) Lower border of existence domain for surface solitons in focusing medium as a function of pi.

Fig. 3.
Fig. 3.

Domains of stability for surface solitons in (a) focusing and (b) defocusing medium on the plane (pi,γ). In focusing medium solitons are stable in the area between curves γcruγlow and γcrlγlow, while in defocusing medium solitons are stable in the area below curve γuppγlow. (c) Real part of perturbation growth rate versus γ for solitons in focusing medium at pi=1.

Fig. 4.
Fig. 4.

(a) Stable propagation of surface solitons in defocusing medium at γ=0.3249, pi=0.6, and (b) growth of peak amplitude of unstable solitons in focusing medium at γ=1.2030, pi=2.0.

Equations (2)

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iqξ=122qη2+σq|q|2{prRr(η)i[piRi(η)+γ]}H(η)q,
δu=12d2vdη2prHRrv+H(piRi+γ)u+bv+2σuwiwr+σv(3wi2+wr2),δv=+12d2udη2+prHRru+H(piRi+γ)vbuσu(3wr2+wi2)2σvwiwr,

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