Abstract

We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear refractive index attains its maxima, we found that nonlinear surface waves exist and can be made stable only within a limited band of input energy flows and for lattice depths exceeding a lower threshold.

© 2008 Optical Society of America

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References

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  1. H. E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North Holland, 1991).
  2. D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
  3. A. A. Maradudin, in Optical and Acoustic Waves in Solids--Modern Topics, M.Borissov ed. (World Scientific, 1983), p. 72.
  4. C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).
  5. F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
    [CrossRef]
  6. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  7. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  9. M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  10. E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
    [CrossRef]
  17. H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
    [CrossRef]
  18. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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2007 (4)

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

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

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

2006 (11)

2005 (3)

1993 (1)

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

1991 (1)

H. E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North Holland, 1991).

1989 (1)

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

1985 (1)

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

1983 (1)

A. A. Maradudin, in Optical and Acoustic Waves in Solids--Modern Topics, M.Borissov ed. (World Scientific, 1983), p. 72.

Bertolotti, M.

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

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] [PubMed]

Blömer, D.

Boardman, A.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Brocas, A.

Burghoff, J.

Canioni, L.

Carretero-Gonzalez, R.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Chen, Z.

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

Christodoulides, D. N.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

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

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]

D. Blömer, A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express 14, 2151 (2006).
[CrossRef] [PubMed]

Egorov, A. A.

Flach, S.

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Frantzeskakis, D. J.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Haché, A.

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

Hudock, J.

Kartashov, Y. V.

Kevrekidis, P. G.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Kip, D.

Kivshar, Y. S.

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[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] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Lederer, F.

Leine, L.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Mai, X.

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

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

Malomed, B. A.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Manela, O.

Maradudin, A. A.

A. A. Maradudin, in Optical and Acoustic Waves in Solids--Modern Topics, M.Borissov ed. (World Scientific, 1983), p. 72.

Mihalache, D.

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, Opt. Lett. 31, 2329 (2006).
[CrossRef] [PubMed]

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

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] [PubMed]

Molina, M. I.

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[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] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

Morandotti, R.

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

Muschall, R.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[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] [PubMed]

Nolte, S.

Pertsch, T.

Peschel, T.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Ponath, H. E.

H. E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North Holland, 1991).

Richardson, M.

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] [PubMed]

Rüter, C. E.

Salamo, G.

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

Sarger, L.

Schmidt-Hattenberger, C.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Schreiber, T.

Seaton, C. T.

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

Segev, M.

Shandarov, V.

Sibilia, C.

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

Smirnov, E.

Sorel, M.

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

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

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

H. E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North Holland, 1991).

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

Stepic, M.

Suntsov, S.

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

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

Susanto, H.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Szameit, A.

Torner, L.

Trutschel, U.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Tünnermann, A.

Vicencio, R. A.

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[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] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wächter, C.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Wang, X.

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

Winful, H. G.

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

Yang, H.

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

Zoubir, A.

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

Opt. Commun. (1)

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, U. Trutschel, A. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[CrossRef]

Opt. Eng. (1)

C. T. Seaton, X. Mai, G. I. Stegeman, and H. G. Winful, Opt. Eng. 24, 593 (1985).

Opt. Express (4)

Opt. Lett. (6)

Phys. Lett. A (1)

R. A. Vicencio, S. Flach, M. I. Molina, and Y. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Phys. Rev. E (1)

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-Gonzalez, and D. J. Frantzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

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

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

Prog. Opt. (1)

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

Other (2)

A. A. Maradudin, in Optical and Acoustic Waves in Solids--Modern Topics, M.Borissov ed. (World Scientific, 1983), p. 72.

H. E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North Holland, 1991).

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Figures (3)

Fig. 1
Fig. 1

Profiles of surface solitons with b=(a) 0.8, (b) 1.7, and (c) 3.2 at p = 3 , σ = 0.6 . The gray (red online) indicates the interface position. The black (blue online) in (c) indicates the soliton center shift relative to the interface.

Fig. 2
Fig. 2

Energy flow versus propagation constant and (b) Hamiltonian versus energy flow at p = 3 , σ = 0.6 . The points marked by circles in (a) correspond to profiles as shown in Fig. 1. Black curves show stable branches, while gray (red online) curves correspond to unstable branches. Stability domains (c) on the plane ( σ , U ) at p = 3 and (d) on the plane ( p , U ) at σ = 0.7 . (e) The cutoff versus lattice depth at σ = 0.7 . (f) The real part of the perturbation growth rate versus propagation constant at p = 3 , σ = 0.6 .

Fig. 3
Fig. 3

(a) Position of the integral soliton center along the η axis versus energy flow. Gray (red online) curves show the unstable branches, black curves show the stable branches, the arrow shows the direction in which the propagation constant increases. (b) The output energy flow concentrated within a ring of radius w s 2 at ξ = 16 versus input energy flow upon surface wave excitation by a Gaussian beam A exp ( η 2 ζ 2 ) . Gray (red online) circles indicate minimal and maximal input energy flows at which effective surface wave excitation occurs. In all cases p = 3 and σ = 0.6 .

Equations (5)

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

i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) [ 1 σ R ( η , ζ ) ] q 2 q p R ( η , ζ ) q .
U = q 2 d η d ζ ,
H = 1 2 [ q η 2 + q ζ 2 2 p R q 2 ( 1 σ R ) q 4 ] d η d ζ .
δ u = 1 2 ( 2 v η 2 + 2 v ζ 2 ) + b v ( 1 σ R ) v w 2 p R v ,
δ v = 1 2 ( 2 u η 2 + 2 u ζ 2 ) b u + 3 ( 1 σ R ) u w 2 + p R u ,

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