Abstract

We have analyzed the transmission process through single subwavelength apertures surrounded by a set of periodic grooves in optically thick Ag films. On one hand, we found that the intensity of both single- and double-corrugated structures follows just one exponential regime as a function of the hole depth. On the other hand, it is shown that the transmission process can be separated into three independent steps: coupling in, transmission through the aperture and coupling out. This is in contrast with the transmission through hole arrays reported by previous studies where two transmission regimes were found. These findings are of relevance not only for further understanding the enhanced transmission but also for any applications based on this phenomenon.

© 2004 Optical Society of America

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References

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    [CrossRef]
  2. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, ???Extraordinary optical transmission through sub-wavelength hole arrays,??? Nature 391, 667-669 (1998).
    [CrossRef]
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    [CrossRef]
  4. A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, ???Effects of hole depth on enhanced light transmission through subwavelength apertures,??? Appl. Phys. Lett. 81, 4327-4329 (2002).
    [CrossRef]
  5. E. Altewischer, M.P. van Exter, and J.P. Woerdman, ???Non reciprocal reflection of a subwavelength hole array,??? Opt. Lett. 28, 1906-1908 (2003).
    [CrossRef] [PubMed]
  6. W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, and T.W. Ebbesen, ???Surface Plasmon Polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,??? Phys. Rev. Lett. 92, 107401 (2004).
    [CrossRef] [PubMed]
  7. J.A. Porto, F.J. García-Vidal, and J.B. Pendry, ???Transmission resonances on metallic gratings with very narrow slits,??? Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  8. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, ???Theory of light transmission through subwavelength periodic hole arrays,??? Phys. Rev. B 62, 16100 (2000).
    [CrossRef]
  9. L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, K.M. Pellerin, T. Thio, J.B. Pendry, and T.W. Ebbesen, ???Theory of extraordinary optical transmission through subwavelength hole arrays,??? Phys. Rev. Lett. 86, 1114-1117 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. J.-M. Vigoureux, ???Analysis of the Ebbesen experiment in the light of evanescent short range diffraction,??? Opt. Comun. 198, 257-263 (2001).
    [CrossRef]
  12. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, ???Strong discontinuities in the complex photonic band structure of transmission metallic gratings,??? Phys. Rev. B 63, 33107 (2001).
    [CrossRef]
  13. F.J. García-Vidal, H.J. Lezec, T.W. Ebbesen, and L. Martín-Moreno, ???Multiple paths to enhance optical transmission through a single subwavelength slit,??? Phys. Rev. Lett. 90, 213901 (2003).
    [CrossRef] [PubMed]
  14. 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 (2003).
    [CrossRef]
  15. C. Genet, M.P. van Exter, and J.P. Woerdman, ???Fano-type interpretation of red shifts and red tails in hole array transmission spectra,??? Opt. Commun. 225, 331-336 (2003).
    [CrossRef]
  16. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, ???Enhanced light transmission through a single subwavelength aperture,??? Opt. Lett. 26, 1972-1974 (2001).
    [CrossRef]
  17. T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, ???Giant optical transmission of sub-wavelength apertures: physics and applications,??? Nanotechnology 13, 429-432 (2002).
    [CrossRef]
  18. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martín-Moreno, F.J. García-Vidal, and T.W. Ebbesen, ???Beaming light from a subwavelength aperture,??? Science 297, 820-822 (2002).
    [CrossRef] [PubMed]
  19. L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, A. Degiron, and T.W. Ebbesen, ???Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,??? Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  20. F.J. García-Vidal, L. Martín-Moreno, H.J. Lezec, and T.W. Ebbesen, ???Focusing light with a subwavelength aperture flanked by surface corrugations,??? Appl. Phys. Lett. 83, 4500-4502 (2003).
    [CrossRef]
  21. W.L. Barnes, A. Dereux, and T.W. Ebbesen, ???Surface plasmon subwavelength optics,??? Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  22. A. P. Hibbins and J. R. Sambles, ???Grating enhanced microwave transmission through a subwavelength aperture in a thick metal plate,??? Appl. Phys. Lett. 81, 4661-4663 (2002).
    [CrossRef]
  23. M. J. Lockyear, A. P. Hibbins, and J.R. Sambles, ???Surface-topogaphy-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture,??? Appl. Phys. Lett. 84, 2040-2042 (2004).
    [CrossRef]
  24. E. Moreno, F.J. García-Vidal, and L. Martín-Moreno, ???Enhanced transmission and beaming of light via photonic crystal surface modes,??? Phys. Rev. B 69, 121402 (2004).
    [CrossRef]
  25. P. Kramper, M. Agio, C.M. Soukoulis, A. Birner, F. Müller, R.B. Wehrpohn, U. Gösele, and V. Sandoghdar, ???Highly directional emission from photonic crystal waveguides of subwavelength width,??? Phys. Rev. Lett. 92, 113903 (2004).
    [CrossRef] [PubMed]
  26. A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, ???Optical transmission properties of a single subwavelength aperture in a real metal,??? Opt. Commun. (to be published).

Appl. Phys. Lett. (4)

A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, ???Effects of hole depth on enhanced light transmission through subwavelength apertures,??? Appl. Phys. Lett. 81, 4327-4329 (2002).
[CrossRef]

F.J. García-Vidal, L. Martín-Moreno, H.J. Lezec, and T.W. Ebbesen, ???Focusing light with a subwavelength aperture flanked by surface corrugations,??? Appl. Phys. Lett. 83, 4500-4502 (2003).
[CrossRef]

A. P. Hibbins and J. R. Sambles, ???Grating enhanced microwave transmission through a subwavelength aperture in a thick metal plate,??? Appl. Phys. Lett. 81, 4661-4663 (2002).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J.R. Sambles, ???Surface-topogaphy-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture,??? Appl. Phys. Lett. 84, 2040-2042 (2004).
[CrossRef]

Nanotechnology (1)

T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, ???Giant optical transmission of sub-wavelength apertures: physics and applications,??? Nanotechnology 13, 429-432 (2002).
[CrossRef]

Nature (2)

W.L. Barnes, A. Dereux, and T.W. Ebbesen, ???Surface plasmon subwavelength optics,??? Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

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

Opt. Commun. (3)

A. Krishnan, T. Thio, T.J. Kim, H.J. Lezec, T.W. Ebbesen, P.A. Wolff, J. Pendry, L. Martín-Moreno, and F.J. García-Vidal, ???Evanescently coupled resonance in surface plasmon enhanced transmission,??? Opt. Commun. 200, 1-7 (2001).
[CrossRef]

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

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, ???Optical transmission properties of a single subwavelength aperture in a real metal,??? Opt. Commun. (to be published).

Opt. Comun. (1)

J.-M. Vigoureux, ???Analysis of the Ebbesen experiment in the light of evanescent short range diffraction,??? Opt. Comun. 198, 257-263 (2001).
[CrossRef]

Opt. Lett. (2)

Phys, Rev. (1)

H.A. Bethe, ???Theory of diffraction by small holes,??? Phys, Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. B (5)

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 (2003).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, ???Strong discontinuities in the complex photonic band structure of transmission metallic gratings,??? Phys. Rev. B 63, 33107 (2001).
[CrossRef]

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

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, ???Theory of light transmission through subwavelength periodic hole arrays,??? Phys. Rev. B 62, 16100 (2000).
[CrossRef]

E. Moreno, F.J. García-Vidal, and L. Martín-Moreno, ???Enhanced transmission and beaming of light via photonic crystal surface modes,??? Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Phys. Rev. Lett. (6)

P. Kramper, M. Agio, C.M. Soukoulis, A. Birner, F. Müller, R.B. Wehrpohn, U. Gösele, and V. Sandoghdar, ???Highly directional emission from photonic crystal waveguides of subwavelength width,??? Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, A. Degiron, and T.W. Ebbesen, ???Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,??? Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, K.M. Pellerin, T. Thio, J.B. Pendry, and T.W. Ebbesen, ???Theory of extraordinary optical transmission through subwavelength hole arrays,??? Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, and T.W. Ebbesen, ???Surface Plasmon Polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,??? Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

J.A. Porto, F.J. García-Vidal, and J.B. Pendry, ???Transmission resonances on metallic gratings with very narrow slits,??? Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

F.J. García-Vidal, H.J. Lezec, T.W. Ebbesen, and L. Martín-Moreno, ???Multiple paths to enhance optical transmission through a single subwavelength slit,??? Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Science (1)

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martín-Moreno, F.J. García-Vidal, and T.W. Ebbesen, ???Beaming light from a subwavelength aperture,??? Science 297, 820-822 (2002).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Transmission spectra of cylindrical apertures surrounded by 5 concentric grooves on the input side, for a range of hole depths h. The geometric parameters are detailed in the text.

Fig. 2.
Fig. 2.

Intensity as a function of h for bull’s eye structures with corrugations on the input side (diamonds), and on both sides (squares). The data are derived from Figs. 1 and 3 at three different wavelengths: λ=650 nm (black), λ=700 nm (red), λ=750 nm (blue).

Fig. 3.
Fig. 3.

Transmission spectra of cylindrical apertures surrounded by 5 concentric grooves on both sides, for a range of hole depths h.

Fig. 4.
Fig. 4.

Ratio between the transmission spectra of Fig. 1 and those of isolated apertures without corrugations of same dimensions.

Fig. 5.
Fig. 5.

Ratio between the transmission spectra of Fig. 3 and those of holes of same dimensions surrounded by a bull’s eye structure on the exit side only.

Equations (6)

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

I ci ( λ , h ) = f ci ( λ ) . T ( λ , h ) . f e ( λ ) ,
I ( λ , h ) = f i ( λ ) . T ( λ , h ) . f e ( λ ) ,
I ci ( λ , h ) I ( λ , h ) = f ci ( λ ) f i ( λ ) .
I ce ( λ , h ) = f i ( λ ) . T ( λ , h ) . f ce ( λ ) ,
I cie ( λ , h ) = f ci ( λ ) . T ( λ , h ) . f ce ( λ ) .
I cie ( λ , h ) I ce ( λ , h ) = f ci ( λ ) f i ( λ ) .

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