Abstract

Surface plasmon polaritons (SPPs) and diffraction effects such as Rayleigh anomalies (RAs) play key roles in the transmission of light through periodic subwavelength hole arrays in metal films. Using a combination of theory and experiment we show how refractive index (RI) sensitive transmission features arise from hole arrays in thin gold films. We show that large transmission amplitude changes occur over a narrow range of RI values due to coupling between RAs and SPPs on opposite sides of the metal film. Furthermore, we show how to predict, on the basis of a relatively simple analysis, the periodicity and other system parameters that should be used to achieve this “RA-SPP” effect for any desired RI range.

© 2007 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
    [CrossRef]
  2. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  9. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Edition (Artech House, Mass., 2005).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
    [CrossRef]
  13. A. Hessel and A. A. Oliner, "A New Theory of Wood’s Anomalies on Optical Gratings," Appl. Opt. 4, 1275-1297 (1965).
    [CrossRef]
  14. S. Darmanyan, M. Neviere, and A. Zayats, "Analytical theory of optical transmission through periodically structured metallic films via tunnel-coupled surface polariton modes," Phys. Rev. B  70, 075103 (9 pages) (2004).
    [CrossRef]
  15. J. Steele, C. Moran, C. Aguirre, A. Lee, N. Halas, "Metallodielectric gratings with subwavelength slots: Optical properties," Phys. Rev. B  68, 205103 (7 pages) (2003).
    [CrossRef]
  16. P. R. H. Stark, A. E. Halleck, D. N. Larson, "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology," Methods 37, 37-47 (2005).
    [CrossRef] [PubMed]

2007

Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
[CrossRef]

2006

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

2005

2003

C. Genet, M. P. van Exter, J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

1965

Benabbas, A.

Bigot, J.-Y.

Chang, S.-H.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

Genet, C.

C. Genet, M. P. van Exter, J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
[CrossRef]

Ghaemi, H. F.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

Gray, S. K.

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

Halleck, A. E.

P. R. H. Stark, A. E. Halleck, D. N. Larson, "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology," Methods 37, 37-47 (2005).
[CrossRef] [PubMed]

Halte, V.

Henzie, J.

Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
[CrossRef]

Hessel, A.

Larson, D. N.

P. R. H. Stark, A. E. Halleck, D. N. Larson, "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology," Methods 37, 37-47 (2005).
[CrossRef] [PubMed]

Lee, M. H.

Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
[CrossRef]

Lee, T. W.

Lee, T.-W.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

Mack, N. H.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Malyarchuk, V.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Nuzzo, R. G.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Odom, T. W.

Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
[CrossRef]

Oliner, A. A.

Rogers, J. A.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Schatz, G. C.

Soares, J. A. N. T.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Stark, P. R. H.

P. R. H. Stark, A. E. Halleck, D. N. Larson, "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology," Methods 37, 37-47 (2005).
[CrossRef] [PubMed]

Stewart, M. E.

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Thio, T.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

van Exter, M. P.

C. Genet, M. P. van Exter, J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
[CrossRef]

Woerdman, J. P.

C. Genet, M. P. van Exter, J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

Appl. Opt.

Methods

P. R. H. Stark, A. E. Halleck, D. N. Larson, "Short order nanohole arrays in metals for highly sensitive probing of local indices of refraction as the basis for a highly multiplexed biosensor technology," Methods 37, 37-47 (2005).
[CrossRef] [PubMed]

Nature (London)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 - 669 (1998).
[CrossRef]

Nature Nanotech.

Q1. J. Henzie, M. H. Lee, T. W. Odom, "Multiscale Patterning of Plasmonic Metamaterials," Nature Nanotech. 2, 549-554 (2007).
[CrossRef]

Opt. Commun.

C. Genet, M. P. van Exter, J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
[CrossRef]

Opt. Express

Phys. Rev. B

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

Proc. Nat. Acad. Sci. (USA)

M. E. Stewart, N. H. Mack, V. Malyarchuk, J. A. N. T. Soares, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, "Quantitative multispectral biosensing and 1D imaging using quasi-3D plasmonic crystals," Proc. Nat. Acad. Sci. (USA) 103, 17143 - 17148 (2006).
[CrossRef]

Other

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Edition (Artech House, Mass., 2005).

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B  66, 195105 (11 pages) (2002).
[CrossRef]

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (8 pages) (2003).
[CrossRef]

Z. Ruan and M. Qiu, "Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances," Phys. Rev. Lett.  96, 233901 (4 pages) (2006).
[CrossRef] [PubMed]

S. Darmanyan, M. Neviere, and A. Zayats, "Analytical theory of optical transmission through periodically structured metallic films via tunnel-coupled surface polariton modes," Phys. Rev. B  70, 075103 (9 pages) (2004).
[CrossRef]

J. Steele, C. Moran, C. Aguirre, A. Lee, N. Halas, "Metallodielectric gratings with subwavelength slots: Optical properties," Phys. Rev. B  68, 205103 (7 pages) (2003).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Hole array system under study showing (a) schematic representation and (b) SEM image. Light is incident from region I towards a thin gold film (region II), perforated with a square array of nanoholes, and the transmission spectrum is obtained in region III.

Fig. 2.
Fig. 2.

Zero-order positions of (1, 0) SPP-BWs and RAs [Eqs. (1) and (2)] as a function n III for n I=1.52 and P=400 nm. The n I SPP-BWs and RAs are denoted AS and AR, and the n III SPP-BWs and RAs as BS and BR.

Fig. 3.
Fig. 3.

FDTD and experimental zero-order transmission spectra for n III<n I. The letters are assignments based on Fig. 2.

Fig. 4.
Fig. 4.

FDTD and experimental zero-order transmission spectra for n IIIn I. The letters are assignments based on Fig. 2.

Fig. 5.
Fig. 5.

(a) FDTD calculated zero-order transmission spectra showing a rapid increase in amplitude as n III is varied through the region of the RA-SPP. (b) Experimental results consistent with (a).

Fig.6.
Fig.6.

RCWA calculations of the (a) zero and (b) first-order transmission as n III is varied through the region of the RA-SPP.

Fig. 7.
Fig. 7.

FDTD calculated frequency resolved |Ez |2 at λ=679 nm with n III=1.70: (a) region near the hole and (b) 200 nm above the gold film. The hole is centered at the origin and the film boundaries are outlined in white.

Equations (4)

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λ SPP = P ( s 1 2 + s 2 2 ) 1 2 Re ( ε Au ( λ SPP ) ε X ε Au ( λ SPP ) + ε X ) 1 2 ,
λ RA = P ( w 1 2 + w 2 2 ) 1 2 n X ,
n III = Re ( ε Au ( λ RA SPP ) ε I ε Au ( λ RA SPP ) + ε I ) 1 2 ,
P = λ RA SPP n III .

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