1. Introduction

In recent years there has been significant interest in structures that are periodically patterned on the scale of the wavelength of light, since they may be used to manipulate and control the propagation parameters of electromagnetic radiation. One specific example of such a structure that has elicited considerable interest recently is the demonstration of enhanced transmission through a periodic array of subwavelength apertures [1]. While numerous theories regarding the phenomenon have been put forward, there is a growing consensus that the phenomenon arises from a surface wave resonance supported by the periodic corrugations. Therefore, a necessary condition for enhanced transmission is that the array medium needs to support the low loss propagation of such surface propagating modes. For metal-dielectric interfaces, these waves are often referred to as surface plasmon-polaritons (SPPs) [2]. At optical frequencies, experimental and theoretical studies have shown that the optimal metal should exhibit a real component of the dielectric constant that is much larger in magnitude than the corresponding imaginary component [1–4]. Both silver and gold exhibit these characteristics. At long wavelengths, corresponding to the far-infrared and microwave spectral ranges, the imaginary component of the dielectric constant of most metals is orders of magnitude larger than the magnitude of the corresponding real component [5]. In this spectral range, the high conductivity of most metals (i.e. the large imaginary component of the dielectric constant) corresponds to extremely low attenuation factors for the propagating surface waves. Indeed, previous measurements suggest that the phenomenon may be observed using a broad range of metals [6]. Thus, even metals that are traditionally viewed as poor conductors should be acceptable for observation of the effect.

In an effort to more clearly understand the operational properties of the phenomenon, numerous studies have examined the role that the array pattern [4], aperture shape [7,8], and radiation polarization [9] plays in determining the observed transmission spectra. One issue that has only been partially addressed with regard to the enhanced transmission process is that of the dependence on the metal film thickness. Grupp et al. showed that when an existing aperture array is overcoated with a metal film of thickness greater than one skin depth at the relevant frequency, the transmission properties of the array are very similar to those obtained from an array formed simply from the overcoat metal medium [10]. More recently, there have been several experimental and theoretical studies examining the aperture transmission properties as a function of film thickness in the thick metal film regime [11,12]. In the majority of reported investigations, including the two cited above, the total metal film thickness is more than several skin depths typically. From a practical point of view, this is done to reduce the transmissivity of the metal layer.

There have been no studies, to our knowledge, examining the array transmission properties as the metal film thickness is reduced below a skin depth. There are two primary questions that we hope to address. First, what is the minimum metal film thickness necessary to observe enhancement in the zero-order transmission from a periodic array? In general, multiple physical processes must be considered to fully understand the enhancement phenomenon. Recently, we showed using time-domain analysis that surface defects act to couple broadband incident radiation to surface waves [13]. Other surface defects or apertures then radiate a fraction of these waves. Thus, the question may be rephrased to address the minimum thickness for the coupling and scattering processes. Second, as the metal film thickness increases progressively beyond this minimum thickness how do the spectral transmission properties evolve with increasing metal film thickness? Specifically, in the regime where the metal film thickness is approximately equal to or less than a skin depth, there is strong coupling between the electromagnetic fields on the two metal surfaces. It would be reasonable to assume that the associated transmission spectra for such thin films differ from arrays fabricated in very thick (>> skin depth) metal films.

In this submission, we examine the enhanced transmission properties of periodic arrays of subwavelength apertures fabricated in thin metal films as a function of the metal film thickness. The thickness range explored extends from δ/15, where δ is the skin depth, to approximately 2δ. At optical frequencies, the skin depth of silver is ~~25 nm, making studies over an equivalent thickness range technically challenging. Using terahertz time-domain spectroscopy, we measure both the amplitude and phase of the zero-order transmitted THz pulses. Experimentally, we find that there is negligible transmission enhancement for metal films as thin as δ/15, but that there is a discernable enhancement when the metal film thickness is approximately δ/6. As the metal film thickness is increased from one skin depth to more than two skin depths, there does not appear to be any significant increase in the level of enhancement. Furthermore, we find that as the thickness of metal films increases, there is a corresponding increase in the resonance frequencies.

2. Experimental details

As we have previously discussed, the conductivity of most metals is extremely large over the THz frequency range of interest. Thus, a broad range of metals may be used for measurements of enhanced transmission through periodic aperture arrays. In the present study, we fabricated the periodic aperture arrays in aluminum thin films that were vacuum deposited onto 500 μm thick high resistivity polished silicon (> 10 kΩ cm) wafers. A total of 6 sample sets were fabricated. For each set, one sample contained a periodic square array of subwavelength apertures consisting of 400 μm diameter circular apertures with a periodic spacing of 1 mm and a total array size of 5 cm × 5 cm. The arrays were fabricated using conventional lithographic and wet etching techniques. The second sample of each set consisted of a continuous (i.e. unperforated) metal film of identical thickness and was used for reference purposes. The use of these unperforated films was necessary, because an obvious issue with arrays fabricated in thin metal films is that a fraction of the incident electromagnetic radiation is transmitted not only through the apertures, but also through the metal film itself.

The dielectric properties of metals in the far-infrared has been well investigated. For a number of metals, including aluminum, the dielectric function can be well described by the Drude model [5]

where ε_∞ is the high frequency dielectric constant, ω_p /2π is the plasma frequency, and ω_τ/2π is the carrier damping frequency. While this function is valid over the entire THz spectral range, our primary emphasis in the array data discussed below is on the transmission resonance at 0.3 THz. At this frequency, the dielectric constant of aluminum is ε_Al (0.3 THz) = -3.4 ×10⁴ + i 2.2 ×10⁶. The corresponding skin depth at this frequency for aluminum is 150 nm. Based on this skin depth value, we fabricated 6 sample sets with a metal film thickness of 10 nm, 25 nm, 50 nm, 100 nm, 150 nm, and 350 nm, respectively. As mentioned above, Grupp et al have previously demonstrated that using metal film thickness greater than one skin depth provides negigible additional enhancement [10]. The 350 nm thick metal array was fabricated in order to verify this at THz frequencies.

We used a conventional time-domain THz spectroscopy setup [14] to characterize these aperture arrays. Photoconductive devices were used for both generation and coherent detection. The arrays and unperforated metal film samples were attached to a 75 mm diameter, 10 mm thick polished high resistivity silicon (> 10 kΩ cm) block, in order to remove the effect of multiple internal reflections within the measured time window and placed at the center of the two off-axis parabolic mirrors in the spectroscopy system. The 1/e THz beam diameter was approximately 30 mm, and therefore less than the spatial extent of the array, thereby minimizing edge effects due to the finite size of the array. The THz beam was normally incident of the aperture array and horizontally polarized, parallel to the aperture rows. Reference transmission spectra were taken with only the silicon wafers (10.5 mm total thickness) in place in order to normalize the measured transmission spectra.

These experimental parameters allow us to directly determine the absolute amplitude transmission coefficients. Furthermore, THz time-domain spectroscopy allows for the direct measurement of the THz electric field, yielding both amplitude and phase information. By transforming the time-domain data to the frequency domain, we are able to determine independently both the magnitude and phase of the amplitude transmission coefficient, t(ν). As noted above, the time domain waveform measured for an aperture array includes not only a contribution from the radiation arising from the interaction with holes, but also a contribution arising from simple transmission through the thin metal films. In order to correct for this, we numerically subtract a fraction, (1 - f_AFF), of the frequency-dependent THz electric field transmitted through the relevant unperforated metal film. Here, f_AFF is the aperture fill fraction, which for the present array is 0.125. The frequency dependent amplitude transmission coefficient, t(ν), may then be expressed as

In this expression, E_array (ν) and E_metal (ν), E_reference (ν) are the transmitted THz fields corresponding to the aperture array, the plane, unperforated metal film, and the reference silicon wafer, respectively, |t(ν)| and φ(ν) are the magnitude and phase of the amplitude transmission coefficient, respectively, and ν is the THz frequency.

3. Experimental results and discussion

Representative temporal waveforms of the transmitted THz pulses through a hole array fabricated in a 350 nm thick aluminum film on a silicon wafer and only the silicon wafer with no metal deposition are shown in Fig. 1. The waveforms are offset from the origin for clarity. The time-domain waveforms corresponding to the aperture arrays fabricated in thinner metal films are nominally similar to the upper waveform in Fig. 1, although the oscillations are of progressively lower amplitude with decreasing metal film thickness. The reduced amplitude corresponds to a lower level of enhancement at the resonant frequencies, as we discuss below.

Figure 2 shows the magnitude and phase of the amplitude transmission coefficient versus THz frequency obtained using Eq. (2) for the 6 different aperture arrays. We show only the spectra up to 0.6 THz, since higher frequency resonances exhibited reduced signal-to-noise characteristics. As discussed above, the aperture arrays are fabricated on high resistivity silicon wafers, so that the adjacent media on the two metal interfaces are air (ε_d = 1) and silicon (ε_d = 11.7). At normal incidence, the locations of the transmission peaks are approximately given by [1]

where P is the period spacing between the apertures, n_sp is the refractive index of the surface propagating wave, and i and j are integers. There are two distinct resonance peak locations associated with each combination of i and j, since both metal-dielectric interfaces will contribute to the observed transmission spectra.

 

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. 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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In general, numerous resonances in the transmission spectra should be observed within the frequency range investigated. However, within the signal-to-noise constraints of our spectroscopic system, we would expect to observe only the two lowest order resonances associated with each interface. From Eq. (3), the resonances associated with the silicon-metal interface are expected at 0.09 THz and 0.12 THz, corresponding to indices (i,j) equal to (±1,0) and (±1,±1), respectively. Similarly, the resonances associated with the air-metal interface are expected at 0.3 THz and 0.42 THz, corresponding to indices (i,j) equal to (±1,0) and (±1,±1), respectively. From Figure 2, it is apparent that the lowest order silicon-air resonance lies at a frequency below our detection sensitivity, while the next higher order (±1,±1) resonance is barely discernable in some instances. The two resonances associated with the air-metal interface are readily apparent in both the amplitude and phase spectra. In general, the observed resonances occur at slightly lower frequencies than predicted. This is not surprising, given that Eq. (3) is only approximately valid for a periodically perforated metal film.

There are several noteworthy points regarding the transmission resonances that appear in both the amplitude and phase spectra in Fig. 2. The transmission resonances in the magnitude spectra appear to be bipolar in character, particularly for the thickest metal films. This is in qualitative agreement with earlier measurements for comparable arrays fabricated in vacuum deposited thin metal films [15]. However, these resonance lineshapes appear to differ substantially in shape from the resonances obtained with thick metal free-standing foils [6,8]. In both the amplitude and phase spectra, the location of the transmission anomalies is progressively shifted to higher frequencies with increasing metal film thickness (see dashed vertical lines in Fig. 2). These effects may arise from the thin film nature of the metal film, where the electromagnetic fields on the two surfaces are strongly coupled. Further investigation is required. In the amplitude and phase spectra for the 3 thickest metal films in Fig. 2, we observe periodic oscillations on the low frequency side of the lowest order resonance. Such oscillations are similar to the fractional order surface plasmons reported by Qu at al. [16].

It is apparent that there is minimal enhancement in the transmission for the thinnest metal film, 10 nm, and that the enhancement level increases initially with increasing metal film thickness. In order to quantify this observation, we note two further observations regarding the phase spectra. In contrast to the resonances in the amplitude spectra, the resonances in the phase spectra appear to be largely unidirectional (i.e. dips). Furthermore, with the exception of the resonances themselves, the phase spectra associated with each aperture array is extremely linear with frequency. Using these observations, we perform a linear fit for each phase spectrum. At the location of the phase minimum for the lowest order resonance (~0.29 THz), we measure the difference between the numerical value of the linear fit at that frequency and the corresponding value at the resonance minimum. This data, shown in Fig. 3, depicts a sublinear increase in the magnitude of the enhancement dip, and correspondingly in the transmission enhancement factor for metal film thicknesses ranging from 10 nm to 150 nm. As the metal film thickness increases from 150 nm to 350 nm, there is minimal additional benefit, which is consistent with earlier measurements at optical frequencies [10].

 

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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4. Conclusion

In conclusion, we have examined the enhanced transmission properties of periodic arrays of subwavelength apertures fabricated in thin metal films as a function of the metal film thickness. The thickness range explored extends from δ/15, where δ is the skin depth, to approximately 2δ. Qualitatively, we find that the shape of the transmission resonances differ from those observed with arrays fabricated in very thick (free-standing) metal foils. As the thickness of metal films increases, there is a corresponding increase in the resonance frequency. Using the properties of the lowest order resonance from the phase spectra, we have found that there is negligible transmission enhancement for metal films as thin as δ/15, but that there is a discernable enhancement when the metal film thickness is approximately δ/6. 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.