Abstract

In this paper we extend our theoretical treatment of the extraordinary optical transmission through hole arrays to the case of circular holes and beyond the subwavelength limit. Universal curves for the optical transmission in different regimes of the geometrical parameters defining the array are presented. Finally, we further develop the statement by showing that extraordinary transmission phenomena should be expected for any system where transmission is through two localized modes, weakly coupled between them and coupled to a continuum.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. H. A. Bethe, ???Theory of diffraction by small holes,??? Phys. Rev. 66, 163 (1944).
    [CrossRef]
  2. A. Roberts, ???Electromagnetic Theory of diffraction by a circular aperture in a thick, perfectly conducting screen,??? J. Opt. Soc. Am. A 4, 1970 (1987).
  3. 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]
  4. L. Martin-Moreno, F.J. Garcia-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]
  5. F.J. Garcia-Vidal and L. Martin-Moreno, ???Transmission and focusing of light in one-dimensional periodically nanostructured metals,??? Phys. Rev. B 66, 155412 (2002).
    [CrossRef]
  6. E. Popov, M. Nevire, S. Enoch, and R. Reinisch, ???Theory of light transmission through subwavelength periodic hole arrays,??? Phys. Rev. B 62, 16100 (2000).
    [CrossRef]
  7. J.B. Pendry and A. MacKinnon, ???Calculation of photon dispersion relations,??? Phys. Rev. Lett. 69, 2772 (1992); P.M. Bell et al., Comp. Phys. Commun. 85, 306 (1995).
    [CrossRef] [PubMed]
  8. In the Fourier expansion formalism we are not aware of any published data on how convergency as a function of wavenumber cutoff is reached.
  9. L.D.Landau, E.M. Lifshitz and L.P. Pitaievskii: Electrodynamics of Continuous Media, (Pergamon Press, Oxford, 1984).
  10. P.M. Morse and H. Feshbach:Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).
  11. We take the dielectric constant for silver from: Handbook of Optical Constants of Solids , edited by E.D. Palik (Academic, Orlando, 1985).
  12. J. Gomez-Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, ???Enhanced transmission of Thz radiation through subwavelength holes,??? Phys. Rev. B 68, 201306 (2003).
    [CrossRef]
  13. F. Miyamaru and M. Hangyo, ???Finite size effects of trannsmission property for metal hole arrays in subterahertz region,??? Appl. Phys. Lett. 84, 2742 (2004).
    [CrossRef]
  14. H. Cao and A. Nahata, ???Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,??? Opt. Express 12, 1004-1010 (2004).
    [CrossRef] [PubMed]
  15. M. Beruete, M, Sorrola, I. Campillo, J.S. Dolado, L. Martin-Moreno, J. Bravo-Abad, and F.J. Garcia-Vidal, ???Enhanced millimeter wave transmission through subwavelength hole arrays,??? (Opt. Lett., in press).
  16. Q. Cao and P. Lalanne, ???Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,??? Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef] [PubMed]
  17. 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]
  18. J.B. Pendry, L. Martin-Moreno and F.J. Garcia-Vidal, ???Mimicking surface plasmons with structured surfaces,??? Science Express, 10.1126, 8 July 2004.

Appl. Phys. Lett. (1)

F. Miyamaru and M. Hangyo, ???Finite size effects of trannsmission property for metal hole arrays in subterahertz region,??? Appl. Phys. Lett. 84, 2742 (2004).
[CrossRef]

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

Nature (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 391, 667-669 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

M. Beruete, M, Sorrola, I. Campillo, J.S. Dolado, L. Martin-Moreno, J. Bravo-Abad, and F.J. Garcia-Vidal, ???Enhanced millimeter wave transmission through subwavelength hole arrays,??? (Opt. Lett., in press).

Phys. Rev. (1)

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

Phys. Rev. B (3)

J. Gomez-Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, ???Enhanced transmission of Thz radiation through subwavelength holes,??? Phys. Rev. B 68, 201306 (2003).
[CrossRef]

F.J. Garcia-Vidal and L. Martin-Moreno, ???Transmission and focusing of light in one-dimensional periodically nanostructured metals,??? Phys. Rev. B 66, 155412 (2002).
[CrossRef]

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

Phys. Rev. Lett. (4)

J.B. Pendry and A. MacKinnon, ???Calculation of photon dispersion relations,??? Phys. Rev. Lett. 69, 2772 (1992); P.M. Bell et al., Comp. Phys. Commun. 85, 306 (1995).
[CrossRef] [PubMed]

L. Martin-Moreno, F.J. Garcia-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]

Q. Cao and P. Lalanne, ???Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,??? Phys. Rev. Lett. 88, 057403 (2002).
[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]

Science Express (1)

J.B. Pendry, L. Martin-Moreno and F.J. Garcia-Vidal, ???Mimicking surface plasmons with structured surfaces,??? Science Express, 10.1126, 8 July 2004.

Other (4)

In the Fourier expansion formalism we are not aware of any published data on how convergency as a function of wavenumber cutoff is reached.

L.D.Landau, E.M. Lifshitz and L.P. Pitaievskii: Electrodynamics of Continuous Media, (Pergamon Press, Oxford, 1984).

P.M. Morse and H. Feshbach:Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).

We take the dielectric constant for silver from: Handbook of Optical Constants of Solids , edited by E.D. Palik (Academic, Orlando, 1985).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Total transmittance spectra for a square array of circular holes of diameter 2r=280nm perforated in a silver film of thickness h=320nm. The period of the array is d=750nm. Black curve shows our result imposing SIBC and considering an effective hole diameter (see text). Blue curve renders T(λ) for the case in which silver is replaced by a perfect conductor and the red curve is an intermediate case in which perfect metal boundary conditions are assumed in the flat metallic interfaces but an effective hole diameter is considered.

Fig. 2.
Fig. 2.

Comparison between the transmission spectra of a square array of circular holes of diameter 2r=280nm (black curve) with the corresponding ones of square array of square holes with two different sides: a=280nm (red curve) and a=248nm (blue curve).

Fig. 3.
Fig. 3.

Total transmittance spectra for different square arrays of circular holes perforated in perfect conductors. Panel (a) shows the case r/d=0.1 for different values of the thickness h/d (note that the transmittance in this panel is shown in logarithmic scale). Panels (b), (c) and (d) analyze the cases r/d=0.2, r/d=0.3 and r/d=0.4, respectively. In all cases the wavelength is expressed in units of the period of the array, d

Fig. 4.
Fig. 4.

Imaginary (full lines) and Real (dashed lines) parts of ρ (see text) for three different values of the hole radius: r=120nm (black curves), r=140nm (red curves) and r=160nm (blue curves). In the three cases, the period of the array d is 750nm. In the inset we compare the results for Im(ρ) for the case r=140nm with different approximations to the dielectric constant of silver: real silver (red line), lossless silver (green line) and perfect conductor (purple line).

Fig. 5.
Fig. 5.

Transmission versus energy spectra for the 1D QM analog depicted in the upper panel: a three-barrier potential of strengthsV=30 with geometrical parameters L 1=L 2=5 andW 1=W 3=1. Three cases with different intermediate barrier lengthsW 2 are considered: W 2=1.5 (black curve), W 2=2.5 (red curve) andW 2=3.5 (blue curve).

Equations (1)

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

t 0 = τ 12 ϕ P τ 23 1 ρ L ρ R ϕ P 2

Metrics