Aperiodic aperture arrays as terahertz plasmonic metamaterials

While innumerable technologies exploit the various portions of the electromagnetic spectrum, the far-infrared or terahertz (THz) region has been largely neglected. Spanning frequencies from about 100 GHz to 10 THz, use of this spectral range has been hindered by the low brightness of incoherent sources and poor sensitivity of cryogenically-cooled detectors. Recent work has helped overcome these obstacles, and one technology eliciting renewed interest is plasmonics.¹ Surface plasmon-polaritons (SPPs) are electromagnetic waves coupled to collective charge oscillations at a metal-dielectric interface. Their use in a variety of applications, including photonics, is actively being pursued because they offer the prospect of new capabilities and miniaturization of existing technologies.²

In addition, it was recently demonstrated that a periodic array of subwavelength apertures in a metal film exhibits strong transmission resonances at wavelengths related to aperture periodicity.³ This has created great interest in developing new devices, including filters and modulators, and enabling applications from near-field imaging to high brightness displays. The resonances have been shown to arise from interference effects associated with SPPs at the metal surface. Extensive studies have analyzed the role of aperture size, shape, spacing, and metal-film thickness on the transmission properties of these metamaterials.^4–6

Figure 1. The real and reciprocal space representation of aperiodic aperture arrays with (a) 10-fold (Penrose type lattice) and (b) 40-fold rotational symmetry. The discrete peaks in reciprocal space exhibit the desired rotational symmetries. The reciprocal space representation is obtained using 2D Fourier transform and depicts the geometrical structure factor associated with the sample.

Although prior work assumed that periodicity in aperture spacing is crucial for strong transmission resonances through subwavelength aperture arrays, here we show that it is not critical. We demonstrate as much by measuring the terahertz transmission properties of subwavelength apertures, fabricated on free-standing metal films in two different classes of aperiodic arrays.

Quasiperiodic aperture array samples, fabricated using well-defined geometrical tiling rules and exhibiting long-range order (LRO) with unusual n-fold rotational symmetry (where n = 5, 8, 10 and 12), comprise the first class. Even though quasi-crystalline structures possess long-range positional order, standard physics developed for Bravais lattices, such as Bloch wave functions and Brillouin zone,⁷ cannot explain them. The second class of arrays involves approximate quasiperiodic structures specifically designed to exhibit n-fold rotational symmetry (where n = 18, 40, 120 etc.). This class does not possess LRO. These structures were developed using an inverse FFT numerical approach and have no associated geometrical tiling rules.⁸ In contrast to the first class, the approximate structures do not have well-defined nearest-neighbor distances across the array.

In both cases, we observed sharp resonances in the transmission spectra at frequencies matching the aperture array `structure factor.’ This numerical approach is not limited to the approximation of quasi-crystalline structures, but can be used to design any desired transmission spectrum, and hence is more general. Our finding that such patterns also exhibit anomalous transmission indicates that SPP excitations and interaction also occur in aperiodic structures.⁸

Figure 2. (a) Transmission spectra for Penrose-type quasi-crystalline structure. (b) Transmission spectra for approximate quasi-crystalline structure with 40-fold rotational symmetry. The peaks in the transmission spectra directly correspond to the bright spots in the reciprocal space representation of these structures.

Both the quasiperiodic and approximate structures were fabricated on 75 μm thick, ∼ 5×5 cm² free-standing stainless steel metal foils. The quasiperiodic structures possessed local 5-fold, 8-fold and 12-fold rotational symmetries. Aperture patterns were determined using established tiling rules. The approximate samples were, in contrast, fabricated to exhibit unusual local n-fold rotational symmetry (where n = 18, 40, 120 etc.) for which there exists no associated geometrical tiling rules. Aperture distribution in these structures was obtained using the inverse FFT algorithm.

We used a conventional THz time-domain spectroscopy (THz-TDS) setup to measure the transmission properties of both structures. A two-dimensional Fourier transform was applied to obtain the reciprocal space representation, and hence the geometrical structure factor for individual samples. Figure 1(a) shows a Penrose-type quasi-crystal with local 5-fold rotational symmetry, as is evident from the shaded regions together with its reciprocal space representation. The apertures in these samples were fabricated at the vertices of the geometrical tiles. Figure 1(b) shows the aperture array distribution for a 40-fold approximate quasi-periodic structure and its reciprocal space representation. As indicated in Figure 1, the geometrical structure factor possesses 10-fold and 40-fold rotational symmetries about the center, and contains a series of circular spots of differing intensities around the central spot. These correspond to specific reciprocal vectors associated with the real space representation of the quasi-crystalline sample.

Figures 2 (a) and (b) show the measured transmission spectra through the two samples from Figure 1. The multiple peaks correspond directly to the series of bright spots observed in the reciprocal space representation. It can also be seen in Figure 2 that the peaks in the transmission spectra are highly asymmetric and associated with sharp antiresonance features (depicted by AR_i). We interpret our results in terms of Fano-type interference between the discrete resonances caused by the diffraction from the aperture array structure and broad (continuum) transmission spectrum associated with the individual apertures. The sharp dips, or anti-resonance features, observed on the high frequency side of the resonant peaks are natural signatures of this interference mechanism.

In conclusion, we have shown that aperiodic aperture arrays act as tunable plasmonic metamaterials at terahertz frequencies. Importantly, the transmission enhancement behavior is possible through a broad range of arrays tailored to exhibit the desired resonances. Based on the design approach, the transmission enhancement can be tuned to occur at frequencies that directly correspond with the aperture array structure factor. This ability to purposely alter the transmission spectrum properties of aperture arrays opens new avenues in the development of optoelectronic devices for applications in the THz, a region of the electromagnetic spectrum currently devoid of usable devices.

This work was supported in part by the Army Research Office and the SYNERGY program at the University of Utah. Amit Agrawal acknowledges support from the University of Utah Graduate Research Fellowship.