Abstract

The possibility of controlling discrete diffraction and refraction in a multiband waveguide array by periodic waveguide bending is theoretically demonstrated. Resonance effects, leading to the enhancement or inhibition of discrete diffraction, are found and related to the quantum analog of field-induced n-photon resonances in semiconductor superlattices. A very distinct behavior for light refraction is found for odd or even resonances. In particular, for even resonances, the two-band behavior of the straight binary array is quenched, resulting in the inhibition of double refraction.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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2005 (2)

2004 (3)

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[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]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

2003 (2)

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, 054902 (2003).

2002 (3)

2001 (1)

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

2000 (2)

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

P. H. Rivera and P. A. Schulz, Phys. Rev. B 61, R7865 (2000).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Aitchison, J. S.

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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

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

Augustin, M.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Christodoulides, D. N.

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Conforti, M.

De Angelis, C.

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

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

Etrich, C.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Fuchs, H.-J.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Iliew, R.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kivshar, Y. S.

Kley, E.-B.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Krolikowski, W.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Lederer, F.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

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

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Locatelli, A.

Longhi, S.

S. Longhi, Opt. Lett. 30, 2137 (2005).
[CrossRef] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Mandelik, D.

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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Modotto, D.

Morandotti, R.

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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

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

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Neshev, D.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Nolte, S.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

Rivera, P. H.

P. H. Rivera and P. A. Schulz, Phys. Rev. B 61, R7865 (2000).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Schelle, D.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Schulz, P. A.

P. H. Rivera and P. A. Schulz, Phys. Rev. B 61, R7865 (2000).
[CrossRef]

Silberberg, Y.

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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

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. 85, 1863 (2000).
[CrossRef] [PubMed]

Sorel, M.

Sukhorukov, A. A.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tünnermann, A.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

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

Opt. Lett. (4)

Phys. Rev. B (1)

P. H. Rivera and P. A. Schulz, Phys. Rev. B 61, R7865 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 90, 054902 (2003).

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

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

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Other (1)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, arXiv.org: http://arxiv.org/abs/quant-ph/0511132.

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Figures (3)

Fig. 1
Fig. 1

(a) Refractive index profile of a binary array. (b) Schematic of a binary array with a periodically curved axis. (c) Numerically computed band diagram (first two minibands) of a straight array for a = 22 μ m , w 1 = 3.5 μ m , w 2 = 2.6 μ m , Δ n = 0.005 , λ = 1.44 μ m , n s = 2.138 . The bandgap separating the two minibands is E g 2.4344 mm 1 . (d) Bloch-wave excitation coefficients versus incidence angle, normalized to the Bragg angle, for the first three bands of the array.

Fig. 2
Fig. 2

Impulse response (modulus of ϕ) of an L = 2 cm long binary array versus normalized modulation depth κ for a few values of spatial modulation period: (a) Λ = 4000 μ m ( E g Ω 1.55 ) , (b) Λ = 5162 μ m ( E g Ω = 2 ) , and (c) Λ = 7743 μ m ( E g Ω = 3 ) . The wide waveguide is initially excited. Parameter values are as in Fig. 1.

Fig. 3
Fig. 3

Light propagation in an L = 8 cm long binary array illuminated by a tilted Gaussian beam (spot size w 0 = 25 μ m , incidence angle θ i θ B = 0.6 ): (a) Straight array; (b) sinusoidally curved array with A = 26 μ m ( κ = 3.248 ) and Λ = 5162 μ m ( s = 2 resonance); (c) sinusoidally curved array with A = 48 μ m ( κ = 4 ) and Λ = 7743 μ m ( s = 3 resonance). Parameter values of the array are the same as in Fig. 1. The lower plots are the results predicted by coupled-mode equation (2).

Equations (4)

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

i ϕ z = 2 2 n s 2 ϕ x 2 + [ n s n ( x ) ] ϕ + n s x ̈ 0 ( z ) x ϕ ,
i E ̇ l + Δ ( E l + 1 + E l 1 ) + [ ( 1 ) l E g 2 + κ Ω l sin ( Ω z ) ] E l = 0 ,
i E ¯ ̇ l + Δ e ( E ¯ l + 1 + E ¯ l 1 ) = 0
i E ¯ ̇ l + Δ e ( 1 ) l ( E ¯ l + 1 E ¯ l 1 ) = 0

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