Abstract

It is theoretically shown that discrete nonlinear surface waves are possible in waveguide lattices. These self-trapped states are located at the edge of the array and can exist only above a certain power threshold. The excitation characteristics and stability properties of these surface waves are systematically investigated.

© 2005 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  2. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  3. D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
    [CrossRef]
  4. A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
    [CrossRef]
  5. M. Miyagi and S. Nishida, Sci. Rep. Res. Inst. Tohoku Univ. Ser. B 24, 53 (1972).
  6. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef] [PubMed]
  7. N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).
  8. U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
    [CrossRef]
  9. C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).
  10. G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
    [CrossRef] [PubMed]
  11. M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
    [CrossRef] [PubMed]
  12. H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, Opt. Lett. 9, 238 (1984).
    [CrossRef] [PubMed]
  13. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  14. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  15. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  16. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
    [CrossRef]
  17. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
    [CrossRef]
  18. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  19. S. G. Davison and M. Steslicka, Basic Theory of Surface States (Oxford, 1992).
  20. M. I. Molina, Phys. Rev. B 71, 035404 (2005).
    [CrossRef]

2005 (2)

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

M. I. Molina, Phys. Rev. B 71, 035404 (2005).
[CrossRef]

2004 (2)

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

2003 (3)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1995 (2)

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
[CrossRef] [PubMed]

1988 (1)

1985 (2)

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

1984 (1)

1983 (1)

U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
[CrossRef]

1980 (1)

1978 (1)

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

1972 (1)

M. Miyagi and S. Nishida, Sci. Rep. Res. Inst. Tohoku Univ. Ser. B 24, 53 (1972).

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

Artigas, D.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Boardman, A. D.

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

Chilwell, J. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

Cho, A. Y.

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

Christodoulides, D. N.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

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

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Cronin-Golomb, M.

Davison, S. G.

S. G. Davison and M. Steslicka, Basic Theory of Surface States (Oxford, 1992).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Efremidis, N. K.

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

Egan, P.

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Fleischer, J. W.

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

Garcia Quirino, G. S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Iwanow, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Joseph, R. I.

Khoo, I. C.

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

Kuz’menko, Y. V.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

Langbein, U.

U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
[CrossRef]

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

Lederer, F.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
[CrossRef]

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

Meier, J.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

Mihalache, D.

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

Min, Y.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Miyagi, M.

M. Miyagi and S. Nishida, Sci. Rep. Res. Inst. Tohoku Univ. Ser. B 24, 53 (1972).

Molina, M. I.

M. I. Molina, Phys. Rev. B 71, 035404 (2005).
[CrossRef]

Morandotti, R.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Nishida, S.

M. Miyagi and S. Nishida, Sci. Rep. Res. Inst. Tohoku Univ. Ser. B 24, 53 (1972).

Pertsch, T.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Ponath, H. E.

U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
[CrossRef]

Salamo, G.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

Sanchez-Mondragon, J. J.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Schiek, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Seaton, C. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, Opt. Lett. 9, 238 (1984).
[CrossRef] [PubMed]

Segev, M.

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

Shoemaker, R. L.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Smith, S. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

Sohler, W.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Sorel, M.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

Stegeman, G. I.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, Opt. Lett. 9, 238 (1984).
[CrossRef] [PubMed]

Stepanov, S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Steslicka, M.

S. G. Davison and M. Steslicka, Basic Theory of Surface States (Oxford, 1992).

Tomlinson, W. J.

Torner, L.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

Vach, H.

Valera, J. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

Yang, H.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

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]

IEEE J. Quantum Electron. (1)

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, IEEE J. Quantum Electron. QE-21, 782 (1985).

Nature (3)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

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

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

U. Langbein, F. Lederer, and H. E. Ponath, Opt. Commun. 46, 167 (1983).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (1)

M. I. Molina, Phys. Rev. B 71, 035404 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef]

Sci. Rep. Res. Inst. Tohoku Univ. Ser. B (1)

M. Miyagi and S. Nishida, Sci. Rep. Res. Inst. Tohoku Univ. Ser. B 24, 53 (1972).

Sov. Phys. JETP (1)

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

Other (2)

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, H. E. Ponath and G. I. Stegeman, eds. (North-Holland, 1991), p. 73.
[CrossRef]

S. G. Davison and M. Steslicka, Basic Theory of Surface States (Oxford, 1992).

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Figures (5)

Fig. 1
Fig. 1

Diffraction pattern in a semi-infinite array when only the first waveguide is excited. The inset depicts a semi-infinite waveguide array.

Fig. 2
Fig. 2

Normalized power versus eigenvalue μ for an in-phase surface soliton.

Fig. 3
Fig. 3

Normalized intensity profiles associated with discrete nonlinear surface waves for (a) μ = 3.2 and (b) μ = 2.92 . The corresponding insets are their stability diagrams (ω represents the perturbation eigenvalue).

Fig. 4
Fig. 4

(a) Stable and (b) unstable evolution of the nonlinear surface waves shown in Figs. 3(a), 3(b), respectively.

Fig. 5
Fig. 5

Propagation dynamics when only the first waveguide site is excited with input power (a) 390 W and (b) 732 W .

Equations (3)

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

i d a 0 d Z + a 1 + a 0 2 a 0 = 0 ,
i d a n d Z + ( a n + 1 + a n 1 ) + a n 2 a n = 0 ,
a n ( Z ) = A 0 [ i n m J n m ( 2 Z ) + i n + m J n + m + 2 ( 2 Z ) ] .

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