Abstract

A theoretical study is presented on the optical transmission through square hole arrays drilled in optically thin films, where transmission may occur through both the holes and the metal layer. It is shown that, as the thickness of the metal film decreases, the coupling of light with short-range surface plasmons redshifts the extraordinary optical transmission peak to longer wavelengths. At the same time, the maximum-to-minimum transmittance ratio is kept high even for metal thicknesses as small as one skin depth.

© 2008 Optical Society of America

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  1. T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
    [CrossRef] [PubMed]
  4. I. R. Hooper and J. R. Sambles, Phys. Rev. B 70, 045421 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
    [CrossRef]

2007 (2)

See C. Genet and T. W. Ebbesen, Nature 445, 39 (2007) and references therein.
[CrossRef] [PubMed]

A. V. Kats, M. L. Nesterov, and A. Y. Nikitin, Phys. Rev. B 76, 045413 (2007).
[CrossRef]

2005 (3)

2004 (2)

2003 (1)

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

2002 (1)

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

2001 (3)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Agrawal, A.

Azad, A. K.

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Cao, Q.

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Darmanyan, S. A.

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

de Fornel, F.

D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats, Opt. Express 12, 3652 (2004).
[CrossRef] [PubMed]

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

Ebbesen, T. W.

See C. Genet and T. W. Ebbesen, Nature 445, 39 (2007) and references therein.
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Economou, E. N.

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Genet, C.

See C. Genet and T. W. Ebbesen, Nature 445, 39 (2007) and references therein.
[CrossRef] [PubMed]

Gérard, D.

Ghaemi, H. F.

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Grillot, F. D.

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

Hooper, I. R.

I. R. Hooper and J. R. Sambles, Phys. Rev. B 70, 045421 (2004).
[CrossRef]

Kats, A. V.

A. V. Kats, M. L. Nesterov, and A. Y. Nikitin, Phys. Rev. B 76, 045413 (2007).
[CrossRef]

Kim, T. J.

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Krishnan, A.

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Lalanne, P.

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Lezec, H. L.

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Nahata, A.

Nesterov, M. L.

A. V. Kats, M. L. Nesterov, and A. Y. Nikitin, Phys. Rev. B 76, 045413 (2007).
[CrossRef]

Nikitin, A. Y.

A. V. Kats, M. L. Nesterov, and A. Y. Nikitin, Phys. Rev. B 76, 045413 (2007).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Salomon, L.

D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats, Opt. Express 12, 3652 (2004).
[CrossRef] [PubMed]

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

Sambles, J. R.

I. R. Hooper and J. R. Sambles, Phys. Rev. B 70, 045421 (2004).
[CrossRef]

Shou, X.

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wolff, P. A.

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Zayats, A. V.

D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats, Opt. Express 12, 3652 (2004).
[CrossRef] [PubMed]

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Zhang, W.

Nature (2)

T. W. Ebbesen, H. L. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

See C. Genet and T. W. Ebbesen, Nature 445, 39 (2007) and references therein.
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Krishnan, T. Thio, T. J. Kim, H. L. Lezec, T. W. Ebbesen, P. A. Wolff, J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (3)

I. R. Hooper and J. R. Sambles, Phys. Rev. B 70, 045421 (2004).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).
[CrossRef]

A. V. Kats, M. L. Nesterov, and A. Y. Nikitin, Phys. Rev. B 76, 045413 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

L. Salomon, F. D. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110 (2001).
[CrossRef] [PubMed]

Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

Zero-order transmittance through 2DHAs in gold, as a function of the film thickness ( P = 400 and a = 160 nm ) (a) ε I = ε II = 1.0 ; ε III = 2.25 and (b) ε I = ε II = ε III = 2.25 . The spectral position as a function of w for both the EOT maximum (triangular symbols) and the EOT minimum (circular symbols) are shown in panel (c). Dashed curves summarize data obtained from panel (a) while solid curves are used for data taken from panel (b). The horizontal dashed line renders λ SPP ( ± 1 , 0 ) .

Fig. 2
Fig. 2

For a holey thin film with w = 20 nm ( P = 400 nm and ε I = ε II = ε III = 2.25 ), panel (a) shows transmittance versus wavelength for different hole sizes. Vertical dashed curves display several values of λ LR ( n , m ) and λ SR ( n , m ) (see text) at k in = 0 . (b) 2DHA dispersion relations along the x direction for a = 60 nm (circular symbols). Solid curves represent the folded dispersion relations of LR and SR modes for the unperforated film. The inset in panel (b) shows an E field map in the x z plane ( y = P 2 ) at the EOT wavelength. (c) EOT maxima (square symbols), minima (circular symbols), and λ ̃ SR (triangular symbols) as a function of the hole size.

Fig. 3
Fig. 3

Transmission spectra for two different film widths obtained with the approximate analytical method w = 10 and w = 8 nm ( a = 160 nm ) . Inset, zoom close to the LR wavelengths (corresponding λ LR ( ± 1 , 0 ) wavelengths are represented by vertical dashed curves).

Equations (1)

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( k x in + 2 π n P ) 2 + ( k y in + 2 π m P ) 2 = q mode 2 ( λ ) .

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