Abstract

We provide what we believe to be the first experimental demonstration of linear Shockley-like surface states in an optically induced semi-infinite photonic superlattice. Such surface states appear only when the induced superlattice consisting of alternating strong and weak bonds is terminated properly at the surface. Our experimental results are in good agreement with our theoretical analysis.

© 2009 Optical Society of America

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  1. I. E. Tamm, Phys. Z. Sowjetunion 1, 733 (1933).
  2. W. Shockley, Phys. Rev. 56, 317 (1939).
    [CrossRef]
  3. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [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), Vol. 29, p. 73.
  5. F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, T. Trutschel, A. D. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
    [CrossRef]
  6. 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]
  7. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. Molina, and Y. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  9. E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [CrossRef] [PubMed]
  10. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  11. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  12. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  13. Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
    [CrossRef]
  14. R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 29, 2890 (2004).
    [CrossRef]
  15. M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
    [CrossRef] [PubMed]
  16. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
    [CrossRef] [PubMed]
  17. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
    [CrossRef] [PubMed]
  18. N. Malkova and C. Ning, Phys. Rev. B 73, 113113 (2006).
    [CrossRef]

2008 (1)

2007 (3)

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
[CrossRef] [PubMed]

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. Tunnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

2006 (6)

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]

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

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

N. Malkova and C. Ning, Phys. Rev. B 73, 113113 (2006).
[CrossRef]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
[CrossRef] [PubMed]

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

2004 (1)

2003 (1)

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

2002 (1)

1993 (1)

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

1978 (1)

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

1939 (1)

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

1933 (1)

I. E. Tamm, Phys. Z. Sowjetunion 1, 733 (1933).

Aimez, V.

Aitchison, J. S.

Ares, R.

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]

Boardman, A. D.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, T. Trutschel, A. D. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[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), Vol. 29, p. 73.

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]

Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
[CrossRef]

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, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
[CrossRef] [PubMed]

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. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

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

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

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

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), Vol. 29, p. 73.

Fleischer, J. W.

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

Garanovich, I. L.

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]

Heinrich, M.

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, 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] [PubMed]

Kip, D.

Kivshar, Y.

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

Kivshar, Y. S.

Krolikowski, W.

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

Langbein, U.

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), Vol. 29, p. 73.

Lederer, F.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, T. Trutschel, A. D. Boardman, and C. Wächter, Opt. Commun. 99, 95 (1993).
[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), Vol. 29, p. 73.

Leine, L.

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

Makris, K. G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
[CrossRef] [PubMed]

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. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Malkova, N.

N. Malkova and C. Ning, Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Mandelik, D.

McCarthy, K.

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), Vol. 29, p. 73.

Mitchell, A.

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

Molina, M.

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

Molina, M. I.

Morandotti, R.

Muschall, R.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, T. Trutschel, A. D. 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. Molina, and Y. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Ning, C.

N. Malkova and C. Ning, Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Nolte, S.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

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

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

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

Peschel, T.

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

Rosberg, C. R.

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

Ruter, C.

Ruter, 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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Schmidt-Hattenberger, C.

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

Segev, M.

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

Shandarov, V.

Shockley, W.

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

Silberberg, Y.

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] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 29, 2890 (2004).
[CrossRef]

Stegeman, G. I.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
[CrossRef] [PubMed]

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. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stepic, M.

Sukhorukov, A. A.

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volantier, V. Aimez, R. Ares, C. Ruter, and D. Kip, Opt. Express 15, 4663 (2007).
[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]

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

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

Tamm, I. E.

I. E. Tamm, Phys. Z. Sowjetunion 1, 733 (1933).

Torner, L.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, 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] [PubMed]

Trutschel, T.

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

Tunnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1132 (2008).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, 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. Molina, and Y. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Volantier, M.

Vysloukh, V. A.

Wächter, C.

F. Lederer, L. Leine, R. Muschall, T. Peschel, C. Schmidt-Hattenberger, T. Trutschel, A. D. 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]

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]

Nature (1)

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

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. (1)

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

Phys. Rev. B (1)

N. Malkova and C. Ning, Phys. Rev. B 73, 113113 (2006).
[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. Tunnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (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] [PubMed]

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

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

Phys. Z. Sowjetunion (1)

I. E. Tamm, Phys. Z. Sowjetunion 1, 733 (1933).

Other (1)

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), Vol. 29, p. 73.

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Figures (4)

Fig. 1
Fig. 1

(a) Intensity profiles used to create superlattice structures (solid curve) by superimposing two periodic patterns (dashed black and gray curves). (b) Simplified structure used in our theoretical model, where surface termination bond is located in the right end; Δ n denotes surface index perturbation, and d is the lattice period. (c) Transverse patterns of induced lattices with an interface between homogeneous medium (right black region) and an SL with either an SB (top) or a WB (middle) termination, or a simple lattice (bottom). (d) Schematic illustration of a probe beam aiming at the interface.

Fig. 2
Fig. 2

Experimental results. (a)–(c) Zoom-in images of three induced lattice structures of Fig. 1c with transverse intensity profiles superimposed as gray curves. Arrows indicate the location of surface waveguide excited by the probe beam. (d)–(f) Linear outputs of the probe beam exiting the lattices of (a)–(c), respectively. (g)–(i) Interferograms of the output probe beam with a titled plane wave. The dotted line added in (g) is for better visualization of the phase structure in the output of the Shockley-like surface state.

Fig. 3
Fig. 3

Numerical results. (a)–(c) First row shows three lattice structures used in simulation corresponding to Figs. 2a, 2b, 2c, the second row shows the output transverse intensity patterns of the signal beam after 1 cm of propagation corresponding to Figs. 2d, 2e, 2f, and the third and fourth rows show the output patterns and interferograms (with a tilted plane wave) of the signal beam after 4 cm of propagation. Right panels, A–C show surface beam propagation up to 4 cm along z direction in lattices corresponding to (a)–(c), respectively.

Fig. 4
Fig. 4

Theoretical results for linear surface modes in the SL. Top left, variation of spectrum versus index difference n 1 n 2 [as illustrated in Fig. 1b] showing formation of the surface states [middle black (red online) line] for n 1 > n 2 . Top middle, evolution of the spectrum of the SL of nine waveguides at n 1 n 2 = 1.5 × 10 5 as a function of the surface index perturbation Δ n defined in Fig. 1b. Top right, Shockley-like surface mode corresponding to observation in Fig. 2a. Bottom panels (a)–(d), surface modes as Δ n is varied, corresponding to the modes marked as (a)–(d) in the top middle panel.

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