Abstract

The observation of nonlinear staggered surface states at the interface between a substrate and a one-dimensional self-defocusing nonlinear waveguide array is reported. Launching of staggered input beams of different power in the first channel of the array results in formation of localized structures in different channels. Our experimental results are confirmed numerically.

© 2006 Optical Society of America

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References

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  1. I. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).
  2. H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
    [CrossRef] [PubMed]
  3. D. Middleton and R. H. Mellen, J. Acoust. Soc. Am. 90, 741 (1991).
    [CrossRef]
  4. A. Kavokin, I. Shelykh, and G. Malpuech, Appl. Phys. Lett. 87, 261105 (2005).
    [CrossRef]
  5. K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
    [CrossRef]
  6. D. Kossel, J. Opt. Soc. Am. 56, 1434 (1966).
  7. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
    [CrossRef]
  8. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef] [PubMed]
  9. I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
    [CrossRef]
  10. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  11. 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]
  12. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  13. Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
    [CrossRef] [PubMed]
  14. H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  15. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  16. M. Stepic, D. Kip, Lj. Hadzievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
    [CrossRef]
  17. F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
    [CrossRef] [PubMed]
  18. M. I. Molina, R. A. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  19. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  20. K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
    [CrossRef]
  21. Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

2006

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]

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

2005

2004

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

M. Stepic, D. Kip, Lj. Hadzievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

2003

K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
[CrossRef]

2002

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2000

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

1998

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

1993

1991

D. Middleton and R. H. Mellen, J. Acoust. Soc. Am. 90, 741 (1991).
[CrossRef]

1990

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

1988

1980

1977

1966

D. Kossel, J. Opt. Soc. Am. 56, 1434 (1966).

1932

I. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).

Agulló-Rueda, F.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Aitchison, J. S.

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

Boardmann, A. D.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Boyd, A. R.

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

Brum, J. A.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Buse, K.

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Chang, L. L.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Chen, F.

Christodoulides, D. N.

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, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

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

Efremidis, N. K.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Egan, P.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Eisenberg, H.

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

Esaki, L.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Fleischer, J. W.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[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]

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

Hadzievski, Lj.

M. Stepic, D. Kip, Lj. Hadzievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Hong, C.-S.

Hong, J. M.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Hukriede, J.

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Joseph, R. I.

Kartashov, Y. V.

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

Kavokin, A.

A. Kavokin, I. Shelykh, and G. Malpuech, Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Khorasani, S.

K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
[CrossRef]

Kip, D.

Kivshar, Yu. S.

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

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
[CrossRef] [PubMed]

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Kossel, D.

D. Kossel, J. Opt. Soc. Am. 56, 1434 (1966).

Krätzig, E.

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Krolikowski, W.

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Makris, K. 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]

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

Malpuech, G.

A. Kavokin, I. Shelykh, and G. Malpuech, Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Maluckov, A.

M. Stepic, D. Kip, Lj. Hadzievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Manela, O.

Mehrany, K.

K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
[CrossRef]

Mellen, R. H.

D. Middleton and R. H. Mellen, J. Acoust. Soc. Am. 90, 741 (1991).
[CrossRef]

Mendez, E. E.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Middleton, D.

D. Middleton and R. H. Mellen, J. Acoust. Soc. Am. 90, 741 (1991).
[CrossRef]

Mitchell, A.

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Molina, M. I.

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

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

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]

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

Neshev, D. N.

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Ohno, H.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

Peithmann, K.

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Rashidian, B.

K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
[CrossRef]

Rosberg, C. R.

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Runde, D.

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]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Shandarov, V.

Shelykh, I.

A. Kavokin, I. Shelykh, and G. Malpuech, Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

Silberberg, Y.

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

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.

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, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Stepic, M.

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

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, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Tamm, I.

I. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).

Tomlinson, W. J.

Torner, L.

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

Vicencio, R. A.

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

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

Vysloukh, V. A.

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

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]

Yariv, A.

Yeh, P.

Zharov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Appl. Phys. Lett.

A. Kavokin, I. Shelykh, and G. Malpuech, Appl. Phys. Lett. 87, 261105 (2005).
[CrossRef]

J. Acoust. Soc. Am.

D. Middleton and R. H. Mellen, J. Acoust. Soc. Am. 90, 741 (1991).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Phys. Rev. B

K. Peithmann, J. Hukriede, K. Buse, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Phys. Rev. E

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

M. Stepic, D. Kip, Lj. Hadzievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardmann, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Phys. Rev. Lett.

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]

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

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, Phys. Rev. Lett. 64, 2555 (1990).
[CrossRef] [PubMed]

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

Phys. Z. Sowjetunion

I. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).

Semicond. Sci. Technol.

K. Mehrany, S. Khorasani, and B. Rashidian, Semicond. Sci. Technol. 18, 582 (2003).
[CrossRef]

Other

Shortly after submission of this Letter we became aware of the following preprint describing similar experimental results: C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, 'Observation of surface gap solitons in semi-infinite waveguide arrays,' arXiv: physics/0603202.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: M, mirror; BS, beam splitter; CL, cylindrical lens; ML, microscope lens; WA, waveguide array; CCD, CCD camera. Inset: (a) observed (nonlinear) output from the array, and (b) corresponding interference picture.

Fig. 2
Fig. 2

Output patterns for staggered input excitation of three channels (intensity ratio 1:0.5:0.1) at four different input powers. Left column: experimental results for (a) discrete diffraction (low-power regime), (b) P = 9 μ W , (c) P = 22.5 μ W , and (d) P = 225 μ W . Right column: simulation results for (e) linear discrete diffraction, (f) P = 10 μ W , (g) P = 22 μ W , and (h) P = 230 μ W .

Fig. 3
Fig. 3

Output patterns for single-channel excitation and four different input powers. Left column: experimental results for (a) discrete diffraction, (b) P = 32.5 μ W , (c) P = 270 μ W , and (d) P = 450 μ W . Right column: simulation results for (e) discrete diffraction, (f) P = 32 μ W , (g) P = 275 μ W , and (h) P = 450 μ W .

Fig. 4
Fig. 4

Comparison of (a), (c) experimental and (b), (d) numerical results for single-channel excitation: (a), (b) Discrete diffraction and (c), (d) localization at P = 490 μ W .

Equations (1)

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i E y + 1 2 k 2 E z 2 + k n ( z ) + Δ n nl n s E = 0 .

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