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Efficiency and finite size effects in enhanced transmission through subwavelength apertures

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We investigate transmission efficiency and finite size effects for the subwavelength hole arrays. Experiments and simulations show how the finite size effects depend strongly on the hole diameter. The transmission efficiency reaches an asymptotic upper value when the array is larger than the surface plasmon propagation length on the corrugated surface. By comparing the transmission of arrays with that of the corresponding single holes, the relative enhancement is found to increase as the hole diameter decreases. In the conditions of the experiments the enhancement is one to two orders of magnitude but there is no fundamental upper limit to this value.

©2008 Optical Society of America

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Figures (6)

Fig. 1.
Fig. 1. (Color online) (a) Experimental transmission spectra for finite size arrays made of 5×5, 11×11, 21×21 and 31×31 holes. The arrays were milled in thick 275nm suspended Ag film with a period P=600nm and a hole diameter d=268nm. Transmissions are normalized to the hole area. The ticks indicate the position of main resonances labelled according the index (i, j) presented in Eq. (1). (b) Transmission spectra, normalized also to the area occupied by the holes, obtained from the numerical simulations using the modal expansion (ME) formalism. The geometrical parameters are the same as in the experiments. Inset: Comparison of ME and finite difference time domain (FDTD) calculations for the infinite array.
Fig. 2.
Fig. 2. (a) Experimental normalized maximum transmitted intensities as a function of the number of holes (N) for increasing hole diameters (d=216, 268 and 294nm). (b) Experimental full width at half maximum (FWHM) corresponding to the data presented in panel (a). (c) and (d) Results of the numerical simulations using the same geometrical parameters as in the experiments presented in panel (a) and (b). Errors bars are determined from the data dispersions obtained from several measurements on separate structures on a test sample.
Fig. 3.
Fig. 3. (a) and (b) Scanning electron microscopy images of an array of 40×40 holes (P=430nm and d=300nm) milled through a 295nm thick Au film. (c) Corresponding single hole. Images presented in panels (b) and (c) have the same scale. As it can be seen in panels (b) and (c), geometrical parameters of the holes are as identical as possible at the level of the array or at the single hole level.
Fig. 4.
Fig. 4. (Color online) Transmission spectra of a d=300nm single hole milled in a 295nm thick Au film obtained by increasing the numerical aperture of the collecting objective. Each curve is an average of the spectra of 3 isolated holes of the same dimensions. Inset: Measured transmission as a function of the solid angle of collection evaluated at 600nm and 800nm.
Fig. 5.
Fig. 5. (Color online) (a) and (b) Respectively experimental transmission spectra of an array of 40×40 holes (P=430nm), and a single hole made in the same 295nm Au film with increasing diameter (d=150, 200, 250 and 300nm). The film was deposited on a glass substrate and covered with an index matching fluid (n=1.53). The increase of transmission and of the noise in the long wavelength limit mainly visible for the d=150nm hole correspond to the noise level of our experimental setup which typically increase with the wavelength. For all the structures, the transmitted light as been collected using the same objective (Nikon Plan Fluor 100×) with numerical aperture fixed to 1.3. Each single hole curve is an average of the spectra of 3 isolated holes of the same dimensions. (c) and (d) Corresponding theoretical results. All the data are presented in logarithmic scale.
Fig. 6.
Fig. 6. (Color online) (a) Ratio of the transmission of the array to the transmission of the corresponding single hole for d=150, 200, 250 and 300nm. (b) Corresponding theoretical results. All the data are presented in logarithmic scale.

Equations (1)

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λ ( i , j ) = P i 2 + j 2 ε m ε d ε m + ε d
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