Abstract

In homogeneous arrays of coupled waveguides, Floquet–Bloch waves are known to travel freely across the waveguides. We introduce a systematic discussion of the built-in patterning of the coupling constant between neighboring waveguides. Key patterns provide functions such as redirecting, guiding, and focusing these waves, up to nonlinear all-optical routing. This opens the way to light control in a functionalized discrete space, i.e., discrete photonics.

© 2009 Optical Society of America

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2009 (1)

2008 (3)

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arès, E. H. Yang, and G. Salamo, Opt. Express 16, 10480 (2008).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (1)

2003 (3)

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

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

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

2001 (2)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1995 (1)

1987 (1)

R. A. Syms, IEEE J. Quantum Electron. 23, 525 (1987).
[CrossRef]

Aimez, V.

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, Opt. Lett. 30, 3174 (2005).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Angelis, C. D.

Arès, R.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Belabas, N.

Bouchoule, S.

Bräuer, A.

Christodoulides, D. N.

Conforti, M.

Dreisow, F.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

Hasegawa, A.

Heinrich, M.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Katayama, S.

Kivshar, Y. S.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

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

Levenson, J. A.

Locatelli, A.

Makris, K. G.

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

Matsumoto, M.

Meier, J.

Michaelis, D.

Minot, C.

Modotto, D.

Moison, J.-M.

Molina, M. I.

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, M. Volatier, V. Aimez, R. Arès, E. H. Yang, and G. Salamo, Opt. Express 16, 10480 (2008).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, Opt. Lett. 30, 3174 (2005).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Nolte, S.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Pertsch, T.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

Peschel, U.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

Sagnes, I.

Salamo, G.

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, Opt. Lett. 30, 3174 (2005).
[CrossRef] [PubMed]

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

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Sorel, M.

Stegeman, G. I.

Streppel, U.

Suntsov, S.

Syms, R. A.

R. A. Syms, IEEE J. Quantum Electron. 23, 525 (1987).
[CrossRef]

Szameit, A.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Trompeter, H.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

Tünnermann, A.

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Vicencio, R. A.

Volatier, M.

Yang, E. H.

Yang, H.

IEEE J. Quantum Electron. (1)

R. A. Syms, IEEE J. Quantum Electron. 23, 525 (1987).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

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

New J. Phys. (1)

A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, and A. Tünnermann, New J. Phys. 10, 103020 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

D. N. Christodoulides and E. D. Eugenieva, Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Discrete diffractive optics, examples for c high c low = 2 . (a) Oblique planar boundary, graphic determination of ray directions for k x , i n = 0 , q z q x = 2 ; (b) numerical solution; (c) elliptical boundary; (d) double elliptical boundary; (lens), focusing geometry; (e) imaging geometry. C-patterns are superimposed.

Fig. 2
Fig. 2

Confinement and metamaterial: (a) channel and (d) periodic stack C-patterns. Dots (resp. blue squares, diamonds) refer to C-pattern (resp. channel and barrier material); c high c low = 2 . (b) k z ( k x ) band diagram for the channel with 4 high-C couplings surrounded by low-C barriers. (e) Folded band diagram for the stack of 4 high- C 4 low-C couplings. (c), (f) DOMs: discrete k z levels (crosses), convolution with a Gaussian of arbitrary width 0.03 (solid curve), and in (f) transmission T ( k z ) (triangles).

Fig. 3
Fig. 3

Double tunnel barrier C-pattern. (a) Symbol code is the same as in Fig. 2, probe and pump beams are shown as transverse and axial arrows. (b) Probe transmission T for a channel of 6 ( c = 1 ) interguide couplings with tunnel barriers with 1 ( c = 0.5 ) coupling, with indication of confined k z levels (diamonds). (c) Evolution of T with pump power for various probe k z indicated in (b) by markers, with model predictions shown as light gray curves.

Equations (2)

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

a m z = i ( c m + 1 , m a m + 1 + c m , m 1 a m 1 ) .
| q z + 2 q x sin k x , r q z + 2 q x sin k x , i | ( t 1 ) 2 + | q z + 2 q x c out c in sin k x , t q z + 2 q x sin k x , i | t 2 = 1 .

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