Abstract

We have studied theoretically and experimentally the properties of optical surface modes at the hetero-interface between two meta-materials. These meta-materials consisted of two 1D AlGaAs waveguide arrays with different band structures.

© 2007 Optical Society of America

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  1. I. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).
  2. W. Shockley, "On the Surface States Associated with a Periodic Potential," Phys. Rev. 56, 317-23 (1939).
    [CrossRef]
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  4. V.M. Agranovich and D. L. Mills, Surface Polaritons (North Holland, Amsterdam, 1984).
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  7. S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
    [CrossRef]
  8. P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
    [CrossRef]
  9. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
    [CrossRef] [PubMed]
  10. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
    [CrossRef] [PubMed]
  11. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
    [CrossRef]
  12. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
    [CrossRef] [PubMed]
  13. U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
    [CrossRef]
  14. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
    [CrossRef] [PubMed]
  15. Henrike Trompeter, Ulf Peschel, Thomas Pertsch, Falk Lederer, Ulrich Streppel, Dirk Michaelis, and Andreas Bräuer, "Tailoring guided modes in waveguide arrays," Opt. Express 11, 3404-11 (2003).
    [CrossRef] [PubMed]
  16. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and Alain Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-68 (2005).
    [CrossRef] [PubMed]
  17. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H.  Yang, G. Salamo and M. Sorel, "Observation of surface discrete solitons," Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  18. G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, Y.-H. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508-16 (2006).
    [CrossRef] [PubMed]
  19. E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338-2340 (2006).
    [CrossRef] [PubMed]
  20. 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," Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  21. A. A. Maradudin, "Nonlinear surface electromagnetic waves," in Optical and Acoustic Waves in Solids-Modern Topics, (World Scientific, Singapore, 1983), pp. 72-142.
  22. U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
    [CrossRef]
  23. N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).
  24. K.G. Makris, J. Hudock, D.N. Christodoulides, G.I. Stegeman, O. Manela, and M. Segev, "Surface lattice solitons," Opt. Lett. 31, 2774-6 (2006).
    [CrossRef] [PubMed]
  25. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).
  26. J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

2006 (5)

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, Y.-H. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508-16 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338-2340 (2006).
[CrossRef] [PubMed]

K.G. Makris, J. Hudock, D.N. Christodoulides, G.I. Stegeman, O. Manela, and M. Segev, "Surface lattice solitons," Opt. Lett. 31, 2774-6 (2006).
[CrossRef] [PubMed]

2005 (3)

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and Alain Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-68 (2005).
[CrossRef] [PubMed]

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

2003 (4)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

Henrike Trompeter, Ulf Peschel, Thomas Pertsch, Falk Lederer, Ulrich Streppel, Dirk Michaelis, and Andreas Bräuer, "Tailoring guided modes in waveguide arrays," Opt. Express 11, 3404-11 (2003).
[CrossRef] [PubMed]

D.N. Christodoulides, F. Lederer and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

1999 (2)

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

1985 (1)

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).

1983 (1)

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
[CrossRef]

1978 (1)

P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
[CrossRef]

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

1965 (1)

1939 (1)

W. Shockley, "On the Surface States Associated with a Periodic Potential," Phys. Rev. 56, 317-23 (1939).
[CrossRef]

1932 (1)

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

Aitchison, J. S.

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).

Cho, A. Y.

P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
[CrossRef]

Christodoulides, D.

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

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, "Observation of surface discrete solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, Y.-H. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508-16 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and Alain Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-68 (2005).
[CrossRef] [PubMed]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Christodoulides, D.N.

K.G. Makris, J. Hudock, D.N. Christodoulides, G.I. Stegeman, O. Manela, and M. Segev, "Surface lattice solitons," Opt. Lett. 31, 2774-6 (2006).
[CrossRef] [PubMed]

D.N. Christodoulides, F. Lederer and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

Garmire, E.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Garvin, H.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Hache, A.

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

Hache, Alain

Hudock, J.

Hunsperger, R.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Iwanow, R.

Jones, A.L.

Kip, D.

Kivshar, Yu. S.

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).

Krolikowski, W.

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Kuz’menko, Y. V.

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).

Langbein, U.

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
[CrossRef]

Lederer, F.

D.N. Christodoulides, F. Lederer and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
[CrossRef]

Makris, K. G.

Makris, K.G.

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

Manela, O.

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Meier, J.

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

Min, Y.-H.

Min, Y-H

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Mitchell, A.

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Modotto, D.

Molina, M. I.

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," Phys. Rev. Lett. 97, 083901 (2006).
[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, "Observation of surface discrete solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

Neshev, D. N.

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Peschel, U.

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

Ponath, H. E.

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
[CrossRef]

Rosberg, C. R.

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

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

Schiek, R.

Segev, M.

Shandarov, V.

Shockley, W.

W. Shockley, "On the Surface States Associated with a Periodic Potential," Phys. Rev. 56, 317-23 (1939).
[CrossRef]

Silberberg, Y.

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

D.N. Christodoulides, F. Lederer and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

Siviloglou, G. A.

Smirnov, E.

Sohler, W.

Somekh, S.

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Sorel, M.

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

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, "Interactions of discrete solitons with structural defects," Opt. Lett. 28, 834-836 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

Stanley, C. R.

Stegeman, G. I.

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides and G. I. Stegeman, Y.-H. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508-16 (2006).
[CrossRef] [PubMed]

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

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and Alain Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-68 (2005).
[CrossRef] [PubMed]

Stegeman, G.I.

Stepic, M.

Suntsov, S.

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and Alain Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-68 (2005).
[CrossRef] [PubMed]

Tamm, I.

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

Vicencio, R. A.

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," Phys. Rev. Lett. 97, 083901 (2006).
[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, "Observation of surface discrete solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

Yariv, A.

P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
[CrossRef]

Appl. Phys. Lett. (3)

S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-48 (1973).
[CrossRef]

P. Yeh, A. Yariv and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32(2), 104-105 (1978).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Nonlinearly induced escape from a defect state in waveguide arrays," Appl. Phys. Lett. 75, 1348-50 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

Journal of Optoelectronics Review (1)

J. Meier, D. Christodoulides, G. I. Stegeman, H.  Yang, G. Salamo, R. Morandotti, J. S. Aitchison and Y. Silberberg, "Wide Beam Stabilities and Instabilities in One Dimensional Arrays of Kerr-Nonlinear Channel Waveguides," Journal of Optoelectronics Review 13, 75-84 (2005).

Nature (1)

D.N. Christodoulides, F. Lederer and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

U. Langbein, F. Lederer, and H. E. Ponath, "A new type of nonlinear slab-guided waves," Opt. Commun. 46, 167-169 (1983).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. (1)

W. Shockley, "On the Surface States Associated with a Periodic Potential," Phys. Rev. 56, 317-23 (1939).
[CrossRef]

Phys. Rev. Lett. (6)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-Focusing and Defocusing in Waveguide Arrays," Phys. Rev. Lett. 86, 3296-9 (2001).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison," Band-gap structure of waveguide arrays and excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-9 (1999).
[CrossRef]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y-H Min and W. Sohler, "Discrete Talbot Effect," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

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

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," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Phys. Z. Sowjetunion (1)

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

Sov. Phys. JETP (1)

N. N. Akhmediev, V. I. Korneev, and Y. V. Kuz’menko, "Excitation of nonlinear surface waves by Gaussian light beams," Sov. Phys. JETP 61, 62-67 (1985).

Other (4)

A. A. Maradudin, "Nonlinear surface electromagnetic waves," in Optical and Acoustic Waves in Solids-Modern Topics, (World Scientific, Singapore, 1983), pp. 72-142.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

A. A. Maradudin and G. I. Stegeman, "Surface Acoustic Waves," in Surface Phonons, W. Kress and F. W. De Wette, eds. (Springer-Verlag, Berlin, 1991), pp. 5-35.

V.M. Agranovich and D. L. Mills, Surface Polaritons (North Holland, Amsterdam, 1984).

Supplementary Material (1)

» Media 1: AVI (2468 KB)     

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Figures (9)

Fig. 1
Fig. 1

(a) AlGaAs hetero-interface waveguide array composition. (b) Details of the dimensions of the two arrays where d is the separation between the two dissimilar arrays.

Fig. 2.
Fig. 2.

BPM simulations for d = 4 μm when a single boundary channel of the left (a) and right (b) arrays was excited, respectively. The position of the interface is shown by a dashed line; Z is the propagation distance.

Fig. 3.
Fig. 3.

Simulated discrete diffraction intensity patterns when the distance between arrays is decreased. (a), (b) d = 3 μm; (c), (d) d = 2 μm. Boundary channel of the left-side (a), (c) and right-side (b), (d) arrays was excited.

Fig. 4.
Fig. 4.

Intensity patterns observed at the output facet of AlGaAs samples for different separations between two arrays for (a) d = 4 μm, (b) d = 3 μm, and (c) d = 2 μm. Intensity distributions when the first channel of the left (blue curves) and of the right (red curves) array is excited are shown. The position of the interface is shown by a dotted line.

Fig. 5.
Fig. 5.

(a) Band structure of the composite array showing the first order bands of the right-side array (red, top) and of the left-side array (blue, middle), and part of the second order band (red, bottom) of the right-side array. (b) Electric field distribution associated with the interface mode.

Fig. 6.
Fig. 6.

(a) Intensity distribution associated with the interface mode. (b),(d) Numerically obtained BPM results: (b) output intensity and (d) propagation of the beam as would be seen from the top. (c) Intensity pattern of an interface mode observed experimentally at the output of AlGaAs sample.

Fig. 7.
Fig. 7.

(a) The derivative of the first band measured in the middle of the right-side array. (b) The structure of the derivatives of the first bands of the left-side array and of the right-side array with an input beam overlapping the interface. This array showed no interface mode, in agreement with theory. (c) Same as (b) but in an array showing an interface mode identified by the yellow ellipses.

Fig. 8.
Fig. 8.

Movie showing the dependence of the output intensity distribution from a composite array when the relative phase between adjacent channels was varied. Here d = 2 μm. [Media 1]

Fig. 9.
Fig. 9.

The regions of existence for interface modes with unstaggered-unstaggered, staggered-staggered and unstaggered-staggered field distributions for coupled arrays such as AlGaAs hetero-structure at 1550 nm. The position of the experimentally investigated interface mode is shown by a red dot.

Equations (1)

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i U z + 1 2 k 2 U x 2 + k 0 V ( x ) U = 0 ,

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