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Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films

Shih-Hui Chang, Stephen K. Gray, and George C. Schatz

Open Access Open Access

Abstract

Extensive 3-D finite-difference time-domain simulations are carried out to elucidate the nature of surface plasmon polaritons (SPPs) and localized surface plasmon polaritons (LSPs) generated by nanoscale holes in thin metallic films interacting with light. Both isolated nanoholes and square arrays of nanoholes in gold films are considered. For isolated nanoholes, we expand on an earlier discussion of Yin et al. [Appl. Phys. Lett. 85, 467–469 (2004)] on the origins of fringe patterns in the film and the role of near-field scanning optical microscope probe interactions. The associated light transmission of a single nanohole is enhanced when a LSP excitation of the nanohole itself is excited. Periodic arrays of nanoholes exhibit more complex behavior, with light transmission peaks exhibiting distinct minima and maxima that can be very well described with Fano lineshape models. This behavior is correlated with the coupling of SPP Bloch waves and more directly transmitted waves through the holes.

©2005 Optical Society of America

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Figures (10)
Fig. 1.
Fig. 1. Time-averaged |Ex |2 for an isolated d=200 nm diameter nanohole in a 100 nm thick gold film on top of a glass layer: (a) z=4 nm, x-y profile; (b) x-z cut for y=0 of result in (a); (c) same as (b) but for the case of no hole present; (d) result of subtracting the amplitudes in (b) and (c) and taking the absolute square of the result. The field shown is the Fourier transform at incident wavelength λ=532 nm of our FDTD result.

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Fig. 2.
Fig. 2. Profiles of scaled field components, Ex′=Ex kspp /(Aα) and Ez ′=Ez/A, along the incident polarization direction (x with y=0) just above (z=4 nm) the metal film. Symbols are the FDTD results and curves correspond to the Bessel function fits described in the text.

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Fig. 3.
Fig. 3. Comparison of theoretically estimated NSOM signal (solid red symbols) with the total intensity (dashed black line) and the intensity of parallel electric field component (solid blue line) on the metal surface of a single nanohole.

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Fig. 4.
Fig. 4. Transmission spectrum of a single d=200 nm nanohole in a 100 nm thick metal film on glass, treating the metal as gold (solid curve) and as a perfect electrical conductor (dashed curve). The metal film is sandwiched between glass and air, with the light incident from the glass side.

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Fig. 5.
Fig. 5. Transmission spectra for 2-D periodic square arrays of d=200 nm nanoholes with square lattice spacing D=600 nm in a 100 nm thickmetal film. (a) Treating the metal film as gold. (b) Treating the metal film as a PEC.

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Fig. 6.
Fig. 6. | Ez |2 for the 2-D square hole array in a gold film of Fig. 5(a). (a)–(f) correspond to λ=610 nm, 620 nm, …, 660 nm.

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Fig. 7.
Fig. 7. | Ex |2 for the 2-D hole array in the gold film of Fig. 5(a). (a)–(f) correspond to λ=610 nm, 620 nm, …, 660 nm.

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Fig. 8.
Fig. 8. |Ez |2 for the 2D hole array in (a) gold and (b) PEC films at wavelength 600 nm. The contrast has been increased by a factor of 3 comparing to other figures in order to show the weak Wood’s anomaly features.

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Fig. 9.
Fig. 9. Multiple resonance Fano model fit (solid curve) to the FDTD transmission data (symbols) for the 2D array of holes in a gold film.

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Fig. 10.
Fig. 10. Charge distribution of the (1,0)air mode at (a) the transmission minimum, and (b) the transmission maximum.

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Equations (9)

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ε A u ( ω ) = ε ∞ − ω D 2 ω 2 + i γ D ω
T ( λ ) = [ T tot ( λ ) − T film ( λ ) ] ⁄ ( I i n c π a 2 ) ,
k S P P ≈ ω c ( ε A u ε d ε A u + ε d ) 1 ⁄ 2
E S P P ≈ A ( z ̂ − i α k S P P ρ ̂ ) H 1 ( 1 ) ( k S P P ρ ) cos ( φ ) exp ( − α z ) exp ( − i ω t ) ,
H m ( 1 ) ( k S P P ρ ) = J m ( k S P P ρ ) + i Y m ( k S P P ρ ) .
H m ( 1 ) ( k S P P ρ ) ≈ ( 2 π k S P P ρ ) 1 ⁄ 2 exp ( i k S P P ρ ) exp ( − i 2 m + 1 4 π )
λ S P P = D ( n x 2 + n y 2 ) 1 ⁄ 2 ( ε A u ε d ε A u + ε d ) 1 ⁄ 2
T Fano ( ω ) − T b = T a ( ε + q ) 2 1 + ε 2 , ε = ω − ω r γ r ⁄ 2 .
T multiple ( ω ) − T b = T a ( 1 + Σ r q r ⁄ ε r ) 2 1 + ( Σ r ε r − 1 ) 2
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