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Optical transmission through circular hole arrays in optically thick metal films

L. Martín-Moreno and F. J. García-Vidal

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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

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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.

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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).

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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

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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).

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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).

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Equations (1)

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t 0 = τ 12 ϕ P τ 23 1 − ρ L ρ R ϕ P 2
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