Abstract

We discover that, at the edge of an optical lattice imprinted in a saturable nonlinear medium, one-dimensional surface solitons exist only within a band of light intensities and that they cease to exist when the lattice depth exceeds an upper threshold. We also reveal the generation of arrays of two-dimensional surface solitons mediated by the transverse modulational instability of one-dimensional solitons, a process that is found to exhibit specific features associated to properties of the optical lattice.

© 2006 Optical Society of America

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  1. H.E.Ponath and G.I.Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).
  2. A. A. Maradudin, in Optical and Acoustic Waves in Solids--Modern Topics, M.Borissov, ed. (World Scientific, 1983), p. 72.
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    [CrossRef] [PubMed]
  5. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  6. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  7. J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Express 13, 7720 (2005).
    [CrossRef] [PubMed]
  8. 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] [PubMed]
  9. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (2)

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] [PubMed]

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

2005 (2)

2004 (1)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

2003 (3)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

1995 (1)

1990 (1)

1989 (1)

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

1988 (1)

N. N. Akhmediev and N. V. Ostrovskaya, Sov. Phys. Tech. Phys. 33, 1333 (1988).

1987 (1)

J. V. Moloney, Phys. Rev. A 36, 4563 (1987).
[CrossRef] [PubMed]

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev and N. V. Ostrovskaya, Sov. Phys. Tech. Phys. 33, 1333 (1988).

Bertolotti, M.

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

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, Z.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Christodoulides, D. N.

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] [PubMed]

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

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Express 13, 7720 (2005).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Cronin-Golomb, M.

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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] [PubMed]

Hudock, J.

Kartashov, Y. V.

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

Kivshar, Y.

Kivshar, Y. S.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

Krolikowski, W.

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

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, 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]

Maradudin, A. A.

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

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Mihalache, D.

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, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

Moloney, J. V.

J. V. Moloney, Phys. Rev. A 36, 4563 (1987).
[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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Neshev, D.

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

Ostrovskaya, E.

Ostrovskaya, N. V.

N. N. Akhmediev and N. V. Ostrovskaya, Sov. Phys. Tech. Phys. 33, 1333 (1988).

Rosanov, N. N.

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

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] [PubMed]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Sibilia, C.

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

Smirnov, V. A.

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] [PubMed]

Stegeman, G. I.

Suntsov, S.

Torner, L.

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

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

Vysloukh, V. A.

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

Vyssotina, N. V.

Yang, H.

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] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

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

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

J. V. Moloney, Phys. Rev. A 36, 4563 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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] [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).

Sov. Phys. Tech. Phys. (1)

N. N. Akhmediev and N. V. Ostrovskaya, Sov. Phys. Tech. Phys. 33, 1333 (1988).

Other (3)

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, arXiv.org e-print archive, March 24, 2006, http://arxiv.org/abs/physics/0603202.

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

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

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Figures (4)

Fig. 1
Fig. 1

Profiles of [(a) and (c)] odd and [(b) and (d)] even surface solitons. In (a) and (b) b = 5.2 . In (c) and (d) b = 7 . Gray regions, R ( η ) > 1 2 ; white regions, R ( η ) 1 2 . In all cases E = 10 and p = 2 .

Fig. 2
Fig. 2

(a) Energy flow versus propagation constant for odd (black curve) and even (red curve) surface solitons. Domains of existence of surface solitons on (b) ( p , b ) plane at E = 10 and on (c) ( E , b ) plane at p = 2 . (d) Perturbation growth rate versus propagation constant for odd (black curve) and even (red curve) solitons at Ω = 0 , E = 10 , and p = 2 . Circles, points where odd and even soliton profiles and perturbation growth rates coincide.

Fig. 3
Fig. 3

Perturbation growth rate for (a) odd and (b) even surface solitons versus propagation constant b and modulation frequency Ω at E = 10 and p = 2 .

Fig. 4
Fig. 4

Development of TMI of quasi-1D surface wave at (a) Ω = 0.6 , (b) 1.3, and (c) 1.7. Field modulus distributions are shown at different distances. White dashed lines, interface position. Quasi-1D surface wave corresponds to b = 5.5 , E = 10 , and p = 2 .

Equations (4)

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

i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) E q q 2 + p R ( η ) 1 + q 2 + p R ( η ) at η 0 ,
i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) at η < 0 .
δ u = 1 2 ( d 2 v d η 2 Ω 2 v ) + b v E v w 2 + p R 1 + w 2 + p R ,
δ v = 1 2 ( d 2 u d η 2 Ω 2 u ) b u + E u [ 3 w 2 + p R 1 + w 2 + p R 2 w 4 + 2 p R w 2 ( 1 + w 2 + p R ) 2 ] ,

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