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Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays

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Abstract

Transmission enhancements of order 1000 have been reported for subwavelength hole arrays in metal films and attributed to surface plasmon (SP) resonance. We show that the properly normalized enhancement factor is consistently less than 7, and that similar enhancements occur in nonmetallic systems that do not support SPs. We present a new model in which the transmission is modulated not by coupling to SPs but by interference of diffracted evanescent waves generated by subwavelength features at the surface, leading to transmission suppression as well as enhancement. This mechanism accounts for the salient optical properties of subwavelength apertures surrounded by periodic surface corrugations.

©2004 Optical Society of America

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Figures (9)

Fig. 1.
Fig. 1. Optical characterization of an N×N array (P=410 nm) of cylindrical holes (d=150 nm) in a silver film (t=175 nm) on glass, overcoated with index-matching fluid. (a,b,c) SEM micrographs of structures for N=1, 4, and 9, respectively (horizontal field of view FOV=5µm, observation angle with respect to normal a=45°); (d) as-collected transmission spectra for selected N; (e) corresponding per-hole transmission coefficient TR,N (λ) for selected N.
Fig. 2.
Fig. 2. Optical characterization of a 9×9 array of cylindrical holes in a suspended Ag film as a function of array period P and hole diameter d. (a) Per-hole transmission coefficient TR ,9(λ) for selected P (at constant d) and transmission coefficient TR ,1(λ) of an equivalent isolated hole; (b) resulting array enhancement factor G 9(λ)=TR ,9=TR ,1 for selected P; (c) per-hole transmission coefficients TR ,9(λ) (thick lines) and TR ,1(λ) (thin lines) for selected d (at constant P); (d) resulting array enhancement factor G 9(λ) for selected d.
Fig. 3.
Fig. 3. (a) As-collected transmission spectra of 15×15 hole arrays in suspended films of: tungsten (W, t=400 nm, d=300 nm, P=600 nm); amorphous silicon (a-Si, t=200 nm, d=250 nm, P=550 nm); and silver (Ag, t=300 nm, d=250 nm, P=750 nm); (b) zero-order transmission (Ag, T[0]) and first-order reflectivity (Ag, R[1]) of a 25×25 array (P=820 nm) of holes (d=250 nm) in suspended Ag (t=300 nm), compared to first-order reflectivity (Si, R[1]) of a 25×25 array (P=820 nm) of cylindrical dimples (d=300 nm, depth h≃1 µm) in undoped Si.
Fig. 4.
Fig. 4. Geometry of optical scattering by a hole in a screen in (a) real space and (b) k-space.
Fig. 5.
Fig. 5. Characterization of CDEW amplitude and phase by in-plane interferometry. (a) Device geometry: double row of cylindrical holes (d=250 nm, P=500 nm) in a suspended Ag film (t=300 nm) with row-row spacing L varied in integer multiples of P; (b and c) SEM micrographs of devices with L=1.5 and 3 µm, respectively (FOV=7.6 µm, a=52°); (d) wavelength positions of interference maxima λm,K (where m is interference order), plotted as a function of L: experimental data (symbols), CDEW model (dashed lines), and SP model (dotted line, shown only for case m=K); (e) CDEW amplitude C as function of traveled distance L: experimental data (symbols) and 1/L fit (dashed line).
Fig. 6.
Fig. 6. Characterization of distance-dependence of CDEW amplitude by interferometry in a circular configuration. (a) Device geometry: single hole (d=300 nm) in a silver film (t=250 nm) on glass surrounded by a single circular groove (width w=150 nm, depth h=100 nm) with radius R varied in integer multiples of P=600 nm; (b and c) SEM micrographs of devices with R=3 and 4.2 µm, respectively (FOV=12.5 µm, a=52°); (d) enhancement factor G(λ) plotted for increasing normalized radius K=R/P; (e) CDEW amplitude C as a function of normalized traveled radial distance K=R/P: experimental data (symbols) and 1/R fit (solid line).
Fig. 7.
Fig. 7. Spectral effect of increasing the number of surface-wave sources: experimental results compared to simple analytical predictions for single slit surrounded by ±N periodic grooves. (a) SEM micrograph (FOV=12.7 µm, a=45°) of experimental device consisting of a single slit (width w=100 nm, length l=10 µm) in a silver film (t=340 nm) on glass, surrounded by ±5 grooves (P=650 nm, w=100 nm, h≃50 nm); (b) experimental transmission spectra, N varied from 1 to 5 with other parameters constant as in (a); (c) intensity modulation at slit entrance predicted by SP model; (d) intensity modulation at slit entrance predicted by CDEW model.
Fig. 8.
Fig. 8. Cascaded two-surface modulation function [A(λ)]2 for a 9×9 hole array facing identical dielectric media on both sides: function derived from experimental data of Fig. 1 compared to prediction of CDEW model.
Fig. 9.
Fig. 9. Surface-wave detector consisting of a single hole (d=300 nm) surrounded by 16 ring grooves (w=150 nm, h=100 nm) in a silver film (t=250 nm) on glass. Grooves form a concentric grating with period P=600 nm, starting at radius 4P. (a) SEM micrograph of device (FOV=30.4 µm, a=52°); (b) effect on gain spectrum G(λ) of increasing holegrating radial distance by increments of P/10.

Equations (4)

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E ( x , z = 0 ) = E 0 π [ Si ( k 0 ( x + d 2 ) ) Si ( k 0 ( x d 2 ) ) ] ,
E ( x ) = E 0 π d x cos ( k 0 x + π 2 ) .
T C ( λ ) = A 1 ( λ ; n 1 , P 1 , d 1 ) T H ( λ ; n H , d , t ) A 2 ( λ ; n 2 , P 2 , d 2 ) f C ( λ ; NA , P 2 , d 2 ) ,
A 1 ( λ ) = ( 1 + 2 j = 1 N α d jP cos ( 2 π λ n eff jP + π 2 ) ) 2 ,
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