Broadband enhanced transmission through the stacked metallic multi-layers perforated with coaxial annular apertures

This paper theoretically and experimentally presents a first report on broadband enhanced transmission through stacked metallic multi-layers perforated with coaxial annular apertures (CAAs). Different from previous studies on extraordinary transmission that occurs at a single frequency, the enhanced transmission of our system with two or three metallic layers can span a wide frequency range with a bandwidth about 60% of the central frequency. The phenomena arise from the excitation and hybridization of guided resonance modes in CAAs among different layers. Measured transmission spectra are in good agreement with calculations semi-analytically resolved by modal expansion method.

Extraordinary optical transmission (EOT) through metallic film perforated with subwavelength hole arrays has attracted considerable attentions since the pioneering study by T.W. Ebbesen and his coworkers 1 . Substantial efforts have been devoted to exploring the physical origin of EOT, both theoretically and experimentally, due to the appealing prospect in related applications [2][3][4][5][6][7] . Previous studies extensively investigated the EOT effects arising from the resonant tunneling of surface plasmon polaritons (SPPs) 8,9 through the perforated metallic film. The frequency of such an EOT peak is not only scaled to the period of hole arrays, but also very sensitive to the incident angle as the resonant tunneling occurs via the in-plane Bragg-scattering channels. Very recently, similar phenomena of the EOT through cascaded metallic multi-layers, which are perforated with one-dimensional gratings or twodimensional hole arrays, have also been brought into attention [10][11][12][13][14][15][16][17] . The resonant coupling among the SPP modes on different layers can be tuned by the spacing distance and lateral displacement of hole arrays between different layers, leading to tunable transmission peaks and zeros in spectra. It is worth noting that, when the slit size is very large or some kinds of specific apertures are adopted, the waveguide resonant modes of a slit or aperture can also give rise to the phenomena of EOT by allowing electromagnetic waves to propagate through the metallic slab. The cut-off wavelength of guided resonance modes 18-23 is primarily determined by the geometry of slits or apertures, and thus can be much longer than the array period. Under this circumstance, the EOT can also occur at a rather low frequency which is not scaled to the array periodand is robust against the structure disorder 24 . To the best of our knowledge, the EOT of metallic multi-layers arising from guided resonance modes has not yet been investigated before.
In this paper, we investigate the enhanced transmission of metallic multi-layers perforated with periodic arrays of coaxial annular apertures (CAAs). Modal expansion method (MEM) 23,25-27 is developed to semi-analytically deal with the electromagnetic properties of the multilayered system. We show that the hybridization of guided resonance modes of CAAs in adjacent layers dramatically extends an enhanced transmission peak into a broad passband that is nearly reflectionless. The passband gets more and more broadened with sharper edges when the system contains more metallic layers. In contrast, these results can not be observed when the wave propagation is dictated by evanescent coupling of SPP modes [10][11][12][13][14][15][16][17] . Measured transmission spectra are in good agreement with calculations for the model systems with different metallic layers. The broadening and varied fine structures of the passband with the increase of metallic layers,can be understood intuitively by a physical picture of mode splitting of coupled atoms. The passband of the enhanced transmission for a system with only two or three metallic layers, covering a wide frequency range with sharp band-edges, can be well estimated by calculated dispersion diagram under the assumption of infinite metallic layers.
A model system with n metallic layers perforated with square arrays of CAAs is of our interest. Figure 1 presents the top-view photo and schematic configuration of a sample with three thin metallic layers(n = 3) and two sandwiched dielectric space layers. The aperture arrays deposited on different layers are aligned with no displacement in xy plane.
The geometric parameters are the lattice constant p = 10mm of square arrays, the outer radius R = 4.8mm and inner radius r = 3.8mm of CAAs, and the thickness t = 0.035mm of metallic layer respectively. Each dielectric layer has a thickness of h = 1.575mm and a permittivity of ε r = 2.65.
Under assumption of perfect electric conductor (PEC) for metals, the electromagnetic wave fields within a metallic layer only exist in apertures. In cylindrical coordinate system, the radial and angular field components E ρ and E ϕ inside an aperture of the metallic layer can be analytically expressed as the superposition of guided resonance modes in the apertures where a l and b l are the coefficients of forward and backward guided waves inside the CAAs,  to n = 3, as shown in Fig. 4(b), depicts the evolution of the enhanced transmission feature from a single transmission peak to a broad passband. It is interesting that the passband between f b = 6.77GHz and f t = 12.7GHz shown in Fig. 4(a), predicting the passband of the n = 10 model quite well, is also a good measure of the bandwidth of the n=3 sample.
The total bandwidth is about 60% of the central frequency. In contrast, the EOT observed in multilayered systems of previous studies demonstrates a peak lineshape in spectra as it arises from the resonant tunneling of SPP modes among metallic films instead of guided resonance modes. And the broad passband we observed is not sensitive to the incident angle (not shown), while it is on the contrary when the SPP modes dominate. In summary, we present a first report on broadband enhanced transmission through stacked metallic multi-layers perforated with CAAs. Taking advantage of the excitation and interlayer coupling of guided resonance modes of CAAs, the enhanced transmission of such a system with only three metallic layers can span a wide frequency range covering about 60% of the central frequency. The broadband utility shall have enormous potential applications in optoelectronics, telecommunication and image processing.