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Role of metal film thickness on the enhanced transmission properties of a periodic array of subwavelength apertures

Xiang Shou, Amit Agrawal, and Ajay Nahata

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Abstract

We have measured the enhanced transmission properties of periodic arrays of subwavelength apertures fabricated in thin metal films as a function of the metal film thickness. In doing so, we determine the minimum metal film thickness for an array that exhibits resonantly enhanced transmission and observe the transmission properties as the metal film thickness is increased. The thickness range explored extends from δ/15, where δ is the skin depth, to approximately 2δ. Using terahertz time-domain spectroscopy, we measure both the amplitude and phase of the transmitted broadband THz pulses. Experimentally, we find that there is negligible transmission enhancement for metal films as thin as δ/15. As the film thickness increases, there is a sublinear increase in the enhancement until the film thickness is equal to the skin depth. For metal films thicker than one skin depth, there appears to be little additional enhancement at the resonant frequencies. We also observe that as the thickness of metal films increases, there is a corresponding increase in the resonance frequencies.

©2005 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. Experimentally observed time-domain waveforms for an array fabricated in a 350 nm thick aluminum film vacuum deposited onto a high resistivity silicon wafer (red) and the reference waveform measured for a blank high resistivity silicon wafer (black). The time-domain waveforms for the other aperture arrays fabricated in thinner metal films look similar, although the amplitudes of the damped oscillations are progressively reduced with decreasing metal film thickness.

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Fig. 2.
Fig. 2. Amplitude and phase spectra for six different periodic aperture arrays fabricated in thin aluminum films deposited on high resistivity silicon wafers. The array consisted of 400 μm diameter circular apertures periodically spaced by 1 mm. The spectra correspond to a metal film thickness of 10 nm (dashed red traces), 25 nm (dashed black traces), 50 nm (green traces), 100 nm (blue traces), 150 nm nm (solid red traces), and 350 nm (solid black traces), respectively. (a) Amplitude spectra for the six aperture arrays. With increasing thickness, each spectrum has been successively incremented by 0.1 for clarity. (b) Phase spectra for the six aperture arrays. With increasing thickness, each spectrum has been successively incremented by 0.5 for clarity. The vertical dashed lines are located at the frequencies corresponding to transmission maxima for the array fabricated in the 350 nm thick metal film and clearly demonstrate a frequency shift in the resonance frequency with metal film thickness.

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Fig. 3.
Fig. 3. Quantitative determination of transmission enhancement based on the magnitude of the dip in the phase spectrum for the lowest order resonance (~0.29 THz). For each phase spectrum in Fig. 2(b), we perform a linear fit. At the location of the phase minimum for the lowest order resonance, we measure the difference between the numerical value of the linear fit at that frequency the resonance minimum the corresponding value at the resonance minimum.

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Equations (3)

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ε m = ε ∞ − ω p 2 ω 2 + iωω τ ,
t ( ν ) = E array ( ν ) − ( 1 − f AFF ) E metal ( ν ) E reference ( ν ) = ∣ t ( ν ) ∣ exp [ iφ ( ν ) ] .
λ peak = P i 2 + j 2 n sp ≈ P i 2 + j 2 ε d ,
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