1. Introduction

The ability to fabricate structures that exhibit periodicity on the scale of the wavelength of light has opened entirely new topics of study and, in some cases, led to a strong resurgence in topics that were believed to be well examined. As an example of this latter case, the electromagnetic transmission properties of a subwavelength aperture in a metal film have been studied extensively over the last century and can be modeled by conventional diffraction theory [1,2]. However, when a periodic surface structure surrounds the single aperture, the electromagnetic transmission can be strongly enhanced at frequencies related to the surface periodicity [3–8]. To date, studies within this subfield have focused almost exclusively on the transmission enhancement process [3–11].

Among these studies, primary attention has been paid to determining the optical properties of periodic arrays of subwavelength apertures [9–12]. In the optical frequency regime, the optimal metals are characterized by a real component of the dielectric constant that is much larger than the corresponding imaginary component. Based on observations in this frequency range, it was believed that this phenomenon would not be present for metal-based structures at long wavelengths [13], since the dielectric properties of metals approach that of ideal conductors [14]. Very recently, a number of studies have demonstrated that the enhanced transmission process through periodic arrays of subwavelength apertures can indeed be observed at significantly longer wavelengths [8,15–18]. In these demonstrations, there has been particular emphasis on the terahertz (THz) frequency range [15–18]. One consequence of this dramatic difference in the dielectric properties of metals in these two frequency ranges is that the transmission properties for appropriately scaled apertures arrays are not identical. The highly conductive nature of metals at THz frequencies can lead to the observation of spectral characteristics that simply are not present at optical frequencies [19,20].

In prior work studying periodic and aperiodic arrays of subwavelength apertures at THz frequencies, we found that there were two independent, yet phase-coherent, transmission processes that contributed to the transmitted time-domain waveform: a non-resonant transmission contribution related to simple transmission through subwavelength apertures and a resonant transmission contribution related to the interaction of the THz pulse with the periodic aperture array [19]. Based on this observation, we reasoned that by changing the phase properties of the periodic structure relative to the apertures, we could alter the phase relationship between these two contributions, which in turn would alter the transmission spectrum. It is not obvious how this can be accomplished using periodic aperture arrays, but it is possible if one utilizes a single aperture surrounded by a periodic surface corrugation (bullseye patterns).

In this submission, we demonstrate that profound changes in the spectral shape of the transmission resonance may be obtained by changing the phase properties of the surface periodicity relative to an individual subwavelength aperture. For example, we demonstrate that by simply inverting the surface corrugation pattern, the resonance feature can change from enhancement to suppression of the transmitted radiation. In general, more complex transmission resonance profiles can be generated.

2. Experimental details

We fabricated and analyzed a number of bullseye structures to test our hypothesis, as shown in Fig. 1. All of the structures were fabricated by chemical etching in freestanding 150 µm thick stainless steel foils. The bullseye structure consisted of 500 µm wide annular rings periodically spaced by 1 mm, with a total spatial extent of 50 mm. The typical annular groove depth was 100 µm. Circular apertures with a diameter of 490 µm were milled into the center of each bullseye structure, except for the structures used for Fig. 4, where the aperture position varied. The 1 mm annular groove periodicity corresponds to a transmission resonance at approximately 0.3 THz. For reference purposes, we fabricated 490 µm diameter bare apertures in the same metal foils. Since the metal thickness varied depending upon the specific surface corrugation pattern used, great care was taken to ensure that a reference bare aperture was fabricated in a metal foil of the same thickness profile.

 

Fig. 1. Schematic representation of the corrugation geometry of the bullseye structures relative to the central aperture. (A) Photograph of a typical in-phase bullseye structure used in the experiment. (B) Cross-sectional line diagrams of the four bullseye structures. The surface corrugation pattern in these structures is shifted relative to one another by a phase of π/2. The dotted lines in (B) represent the location of the circular aperture. The grooves in each structure have square cross-section. In all experiments, the THz pulses were incident on the corrugated surface at normal incidence.

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We used a conventional time-domain THz spectroscopy setup [21] to characterize the bullseye structures and bare apertures. Using this method, the time-domain properties of a single cycle electromagnetic transient transmitted through a structure can be measured using coherent detection with subpicosecond temporal resolution. In contrast to conventional optical measurements, where the transmitted optical power is measured, THz time-domain spectroscopy allows for the direct measurement of the THz electric field, yielding both amplitude and phase information. Although the phase spectrum carries important information about the transmission properties, we discuss only the transmitted amplitude spectrum. Photoconductive devices were used for both emission and coherent detection. An off-axis paraboloidal mirror was used to collect and collimate the THz radiation from the emitter to the samples. The THz beam was normally incident on the corrugated surface of the bullseye structures. The THz beam diameter was smaller than the aperture opening in the metal holder and the spatial extent of the bullseye structure, thereby minimizing edge effects due to the finite size of the surface corrugations. It is important to note that since the frequency content of the THz beam varies spatially, we do not normalize the transmission spectra associated with each structure by the spectral content of the incident beam. Furthermore, we have chosen not to divide the amplitude transmission spectrum corresponding to the bullseye structure by that of the appropriate bare aperture because of the noise in these spectra at low amplitude values. This ratio would yield the transmission enhancement versus frequency.

 

Fig. 2. Experimentally observed time-domain waveforms and corresponding amplitude spectra for the structures shown in Fig. 1. (a) Five time domain waveforms. The top trace corresponds to a bare aperture. The lower four traces correspond to the four bullseye structures. (b) The amplitude spectra obtained by Fourier transforming the time-domain waveforms. In each case, the spectra were normalized to the peak transmission value in an equivalently thick bare aperture.

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3. Experimental results and discussion

The measured temporal waveforms corresponding to the transmitted THz pulses through the structures described in Fig. 1 are shown in Fig. 2(a). The transmitted waveform for the reference bare aperture is characterized by a single cycle waveform. We found experimentally that the spectral content of the transmitted THz pulses through bare apertures in metal foils of different thickness was nearly identical, aside from a simple scaling factor. This is consistent with earlier measurements on bare apertures in metal films [22]. The transmitted time-domain waveforms for the four bullseye structures are more complex. In general, the waveforms are a superposition of a single cycle pulse and a damped oscillatory signal. The initial single cycle pulse, nearly identical in shape and magnitude to that for the bare aperture, is related to the simple transmission through the aperture. The damped oscillatory contribution is related to the interaction of the THz pulses with the periodic structure. Fourier transforming these time-domain waveforms yields the corresponding amplitude spectra shown in Fig. 2(b). The in-phase and out-of-phase bullseye structures differ by a π phase shift of the surface corrugation relative to the aperture. Correspondingly, we observe resonantly enhanced and suppressed transmission, respectively, for these two structures at the frequency corresponding to the surface periodicity. For the structures that are nominally π/2 and 3π/2 out of phase, the transmission resonance lineshape appears to incorporate both enhancement and suppression about the resonance frequency. In the case of the in-phase structure, the transmission of the THz electric field is enhanced by a factor of approximately 4 relative to the bare aperture at the resonance frequency of 0.29 THz. Correspondingly, the enhancement factor for the transmitted THz power is approximately 16 at the resonance frequency.

As we noted above, the measured time-domain waveforms consist of two independent contributions. The phase relationship between these two components leads to the variation in the transmission resonance lineshape. To further demonstrate that our hypothesis and explanation of the results shown in Fig. 2 are valid, we consider a simple numerical simulation. In Fig. 3(a), we show five time-domain waveforms. The top waveform consists only of a single cycle pulse, while the bottom four waveforms correspond to the superposition of a single cycle pulse and a damped sinusoid. The phase difference between these two signals in the latter four waveforms is 0, π/2, π, and 3π/2, respectively. Note that these waveforms were designed to approximate the time-domain waveforms in Fig. 2(a). The resulting amplitude spectra obtained from Fourier transforming the time-domain waveforms are shown in Fig. 3(b). These spectra are in good qualitative agreement with the amplitude spectra for the three bullseye structures shown in Fig. 2(b).

 

Fig. 3. Numerical simulations of time-domain waveforms and corresponding amplitude spectra. (a) Five time-domain waveforms. The top trace consists of a single cycle pulse, i.e., the principal pulse, which corresponds to the non-resonant transmission through a bare aperture. The lower four traces consist of a superposition of the single cycle pulse and a damped sinusoid. The phase difference between the single cycle pulse and the sinusoids is 0, π/2, π, and 3π/2, respectively. (b) The amplitude spectra obtained by Fourier transforming the time-domain waveforms. The simulation results are in good qualitative agreement with the experimental results shown in Fig. 2.

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As we noted above, a groove depth of 100 µm was used for all of the bullseye structures described here. Experimentally, we examined bullseye structures incorporating the four phase patterns discussed above with grooves depths ranging from 0 µm to 125 µm in 12.5 µm steps. In each case, we observed the basic temporal and spectral properties discussed above once the groove depth was 50 µm or greater. However, a groove depth of 100 µm was found to be optimal. This ratio of this optimal groove depth to period spacing is consistent with observations at optical frequencies [4].

To this point, we have utilized different surface corrugation patterns with centered apertures to obtain changes in the transmission spectrum. We now discuss how this same effect may be obtained with a single bullseye structure, simply by moving the single aperture relative to the pattern center. Numerous theoretical descriptions of the transmission enhancement process have been put forth in recent years. While there continues to be significant disagreement over the details of the underlying physical mechanism of this phenomenon, it is generally agreed that the basic features of the transmission spectra can be explained based on the coupling of incident radiation to surface waves [23]. In the context of single apertures surrounded by a periodic surface corrugation, this description yields a relatively simple description of the transmission resonance process. The periodic structure acts as a distributed reflector for these surface waves. The resulting standing wave pattern yields local maxima and minima in the field amplitude. By appropriately offsetting the circular aperture from the pattern center, the local maxima or minima can occur at the aperture, corresponding to transmission enhancement or suppression.

 

Fig. 4. Effect of offsetting the aperture from the center for the in-phase bullseye structure. (A) Cross-sectional line diagrams of the aperture placement. In each structure, the apertures were successively moved 0.25 mm further from the center corresponding to 0, 0.25, 0.5, 0.75, and 1 mm from the center. The dotted lines in (a) represent the location of the circular aperture. The grooves in each structure have square cross-section. (b) The amplitude spectra obtained by Fourier transforming the measured time-domain waveforms. In each case, the spectra were normalized to the peak transmission value in an equivalently thick bare aperture.

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Based on this simple description of the resonance phenomenon, it is reasonable to expect that the aperture location will impact the transmission properties of the bullseye structure. To demonstrate this, we fabricated and analyzed five separate bullseye structures. Instead of creating five distinctly different patterns with an aperture milled into the center of each pattern, we fabricated five identical in-phase bullseye structures (see Fig. 1). In each structure, the apertures were successively moved 0.25 mm further from the center, as shown schematically in Fig. 4(a). Thus, the apertures were located at 0, 0.25, 0.5, 0.75, and 1 mm from the center. Since the generated surface waves form a standing wave pattern with periodic maxima and minima, an aperture located at the surface maximum should lead to transmission enhancement, while an aperture located at the surface minimum should correspond to transmission suppression at the exact same wavelength, as we found above. The polarization direction of the incident THz radiation in these experiments is shown in Fig. 4(a). The measured time-domain waveforms transmitted through these five structures were Fourier transformed. The resulting amplitude spectra are shown in Fig. 4(b). These spectra are consistent with the results shown in Fig. 2(b). By using significantly smaller apertures, it should be possible to more easily discern resonance lineshape changes as incremental changes in the aperture placement are made.

In conclusion, we have demonstrated that the phase of the periodic surface corrugation relative to the single subwavelength aperture plays an important role in determining the lineshape of the transmission resonance. The effect arises from the fact that that there are two distinct, yet phase coherent, contributions to the measured far-field electric field: a contribution that corresponds to simple transmission through a subwavelength aperture and a contribution that arises from the interaction of the THz pulse with the periodic structure. Since these contributions are, to first approximation independent, the results suggest that further controlled changes to the surface corrugation may allow one to engineer the properties of the resonance lineshape.