Abstract

We study subwavelength light propagation in arrays of coupled metal–dielectric waveguides with a periodically curved axis and show analytically and numerically that subwavelength diffraction management, including self-imaging effects, can be achieved by a suitable engineering of the bending geometry.

© 2010 Optical Society of America

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  1. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (6)

M. Y.-C. Xu and J. S. Aitchison, Opt. Lett. 34, 350 (2009).
[CrossRef] [PubMed]

G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B 79, 201103(R) (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

W. M. Saj, Opt. Express 17, 13615 (2009).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

2008 (5)

2007 (3)

2006 (5)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 74, 066609 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
[CrossRef] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

2005 (1)

1986 (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Aitchison, J. S.

Bartal, G.

G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B 79, 201103(R) (2009).
[CrossRef]

Bozhevolnyi, S. I.

T. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

S. I. Bozhevolnyi and J. Jung, Opt. Express 16, 2676 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Conforti, M.

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

De Angelis, C.

de Sterke, C. M.

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Dignam, M. M.

Doering, S.

Dreisow, F.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

Dunlap, D. H.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Ebbesen, T.

T. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

Fahr, S.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
[CrossRef] [PubMed]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Genet, C.

T. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Guasoni, M.

Heinrich, M.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

Iyer, R.

Jung, J.

Kang, Z.

Kenkre, V. M.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Kivshar, Yu. S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Lederer, F.

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Lerosey, G.

G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B 79, 201103(R) (2009).
[CrossRef]

Lin, W.

W. Lin and G. P. Wang, Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

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

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Nolte, S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Saj, W. M.

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Sukhorukov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Szameit, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

Tünnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef] [PubMed]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Wan, J.

Wang, G. P.

Z. Kang and G. P. Wang, J. Opt. Soc. Am. B 25, 1984 (2008).
[CrossRef]

W. Lin and G. P. Wang, Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, Opt. Lett. 31, 1322 (2006).
[CrossRef] [PubMed]

Xu, M. Y.-C.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Zhang, X.

G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B 79, 201103(R) (2009).
[CrossRef]

Appl. Phys. Lett. (2)

W. Lin and G. P. Wang, Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

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

Nat. Phys. (1)

A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Nat. Phys. 5, 271 (2009).
[CrossRef]

Nature (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. B (2)

G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B 79, 201103(R) (2009).
[CrossRef]

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Phys. Rev. E (1)

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. E 74, 066609 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

Phys. Today (1)

T. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Science (1)

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of a curved MIM plasmonic waveguide array. (b) Transverse profile of the relative dielectric permittivity. (c) Bending profile realizing nonparaxial self-imaging condition for a typical MIM array [with parameters as in Fig. 2b]; a sinusoidal bending profile is also shown for comparison.

Fig. 2
Fig. 2

Time-average intensity flowing in the x direction (normalized to the maximum) (a) in a straight silver–air–silver array; (b) in a curved array with the bending profile γ , which realizes the self-imaging condition ( Γ = Γ 0 ) ; and (c) in a curved array where the self-imaging condition is not fulfilled ( Γ = Γ 0 2 ) .

Fig. 3
Fig. 3

Normalized intensity at the output of the MIM array of Fig. 2b for different input wavelengths. The inset shows the percentage of the output power trapped in the central waveguide as a function of the relative wavelength detuning Δ λ λ 0 ( λ 0 = 630 nm ) , representing the deviation from the self-imaging condition.

Equations (4)

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

2 H z σ 2 + ε η ( 1 ε H z η ) + ( 2 π λ ) 2 ε H z = G ,
G = ( 1 1 h 2 ) 2 H z σ 2 + 1 h 3 h σ H z σ + 1 R h H z η .
i d c n d σ = Δ ( c n + 1 + c n 1 ) n 2 π a n e λ R ( σ ) c n .
Λ R 0 = 2.405 λ n e a .

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