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It is generally believed that, in the phenomena of extraordinary optical transmission, perfect transparency only occurs at a single or a multiple of discrete frequencies. This report presents for the first time that a stacked metallic multi-layered system, being perforated with coaxial annular apertures (CAAs), can be perfectly transparent in a broad frequency range. The phenomenon arises from the coupling of guided resonance modes in CAAs among different metallic layers. The transparency bandwidth is extended to about 40% of the central frequency with only 2–3 metallic layers. Measured transmission spectra in microwave regime are in good agreement with calculations which are semi-analytically resolved by modal expansion method.
© 2011 Optical Society of America
1. Introduction
Extraordinary optical transmission (EOT) through metallic films perforated with an array of subwavelength-sized holes was first observed in 1998[1, 2]. Since the discovery, substantial efforts have been devoted to exploring the physical origin of EOT as well as the related applications[3, 4, 5, 6, 7, 8]. The governing mechanism for EOT can be either the resonant tunneling of surface plasmon polaritons (SPPs) [9, 10], or the guided resonance modes of holes or specific apertures[11, 12, 13, 14, 15, 16, 17], alternatively. The mechanism of the first kind dictates when the size of holes is much smaller than the operational wavelength. And 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. While the mechanism of the second kind takes effect when the resonance modes of holes or specific apertures are excited as main channels for wave propagation[16]. In most of the previous studies, perfect transparency only occurs at a single or a multiple of discrete frequencies, no matter which mechanism is dominant. To the best of our knowledge, although a broadband response is usually desirable for both the fundamental research and applications, there is not any report on broadband transparency derived from EOT.
Here we demonstrate for the first time that broadband transparency can be achieved by employing a strategy of stacking metallic and dielectric layers alternately, in which the metallic layers are periodically perforated with arrays of coaxial annular apertures (CAAs). Calculated and measured results for various metallic layers show that broadband transparency arises from the hybridization of guided resonance modes of CAAs on adjacent metallic layers. The phenomenon can be intuitively interpreted with a physical picture of mode splitting of coupled atoms. The transparency band for a system with only two or three metallic layers covers a wide frequency range, which can be well estimated with the calculated dispersion by assuming the periodicity of metallo-dielectric multilayers. Very recently, similar strategy has been employed for the metallic multi-layered system perforated with one-dimensional gratings or two-dimensional hole arrays [18, 19, 20, 21, 22, 23, 24]. It is noticeable that, in these studies, transmission peaks are only observed at certain discrete frequencies and the governing mechanism is the resonant tunneling of SPP modes. In contrast, our study implies that the stacking strategy will give rise to broadband transparency when the guided resonance modes of apertures dictate the phenomenon of enhanced transmission. The results are heuristically revealed from the the distinct features in transmission spectra. In the former case, the EOT only occurs when the channels of in-plane evanescent Bragg scattering are triggered for the tunneling of SPP mode. Previous studies of this mode show a common characteristic of the transmission peaks being very narrow and sensitive to the incident angle. In this case, the stacking strategy cannot give rise to broadband transparency. While in the latter case, the stacking strategy is capable of dramatically extending a transparency peak of a single perforated metallic layer into a broad transparency band of the multilayered system. This is because the dominant channels for the interlayer coupling are the propagating and evanescent resonance modes of apertures instead.
2. Descriptions of model and modal expansion method
Our model system contains n metallic layers which are perforated with square arrays of CAAs. To see more clearly the role of metallic multilayers in the transparency band extension, transmission spectra are investigated for three models containing one, two and three metallic layers respectively. We also fabricate three samples with printed circuit board by etching and stacking technique. The samples each have the same geometric parameters as those of their corresponding models. Figure 1 presents a top-view photo and a 3D schematic of a sample comprised of three thin metallic layers(n = 3) and two sandwiched dielectric spacer layers. The aperture arrays on different metallic layers are aligned along the z direction with zero displacement in xy plane. The geometric parameters are the lattice constant p = 10mm of square array, the outer and inner radii R = 4.8mm, 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 ɛr = 2.65.
Fig. 1 (a) Top-view photo and (b) 3D schematic of our sample with three metallic layers (n = 3). The metallic layers are perforated with coaxial annular apertures(CAAs).
Under assumption of perfect electric conductor (PEC) for metals, a modal expansion method (MEM)[25, 26, 27, 28, 29] is developed to semi-analytically deal with the electromagnetic propagation through the multilayered system. The electromagnetic wave fields within a metallic layer only exist in apertures. In cylindrical coordinate system, the radial and angular components Eρ and Eφof electric field inside a CAA aperture can be analytically expressed as the superposition of guided resonance modes of the aperture
where al and bl are the coefficients of forward and backward guided waves inside the CAAs, and fl(ρ, ϕ) = jωμT [N′l (Tlr)J′l(Tlρ) − J′p(Tlr)N′l(Tlρ )] cos(lϕ) are the lth order modal functions of radial and angular components in aperture with Jl(x) and Nl(x) being the lth order Bessel and Neumann functions respectively, Tl refers to the root of the equation J′l(T R)N′l(Tr) − J′l(Tr)N′l(T R) = 0, βl is the z-component of the wavevector of the lth order modal functions. By adopting EQ. (1) as expressions of EM fields in metallic layers and plane-waves as those in dielectric layers, we applied the boundary continuum conditions for the tangential components of both the electric field and magnetic field at the metal-dielectric interfaces, and derived a MEM algorithm for the multilayer system. At the frequency range of our interest, all the l ⩾ 2 resonance modes are evanescent. More calculations show that the method is quickly convergent by adopting only 2 or 3 lowest guided resonance modes of CAA. This is because an evanescent resonance mode of higher order (l ≥ 3) is strongly localized with much shorter decay length along the z direction (βl is a purely imaginary number which is quite large), and contributes little to the interlayer coupling. This can be checked in EQ.(1) and the control calculations (not shown). Solid lines in Fig. 2 present calculated results by adopting only three guided resonance modes(l = 1,2,3) in the CAAs and 11 × 11 orders of plane-wave basis in the dielectric layers. We see that the calculations are in good agreement with the measurements (circular dots in Fig.2).Fig. 2 Transmission spectra through the models with (a) n=1, (b) n=2, (c) n=3, (d) n=10 metallic layers. Solid lines for calculated results by Modal expansion method(MEM), circular dots for measured results in microwave regime.
3. Broad transparent band
We see from Fig. 2(a) that there exists a perfect transmission peak for the n = 1 sample at fA = 8.7GHz due to the excitation of guided TE11 resonance mode in CAAs. We also see from Figs. 2(b) and 2(c) that there are two perfect transmission peaks at fB = 9.1GHz, and fC = 12.3GHz for the n = 2 sample, three peaks at fD = 8.2GHz, fE = 11.64GHz and fF = 12.35GHz for the n = 3 sample, respectively. It is quite obvious that, with the existence of these transparency frequencies, a broad transparency band emerges in each of the both figures. As we can see in Figs. 2(b) and 2(c), the transmittance between adjacent transmission peaks dips to as much as 25% for the sample with two metallic layers, and 40% for the sample with three metallic layers. Figure 2(d) presents the calculated transmission spectra of an n = 10 model system. With the increase of metallic layers, more transmission peaks emerge, resulting in more fluctuations in transmission spectra, but the transmittance is still above 50% at all frequencies within the pass-band. The feature implies that the system can be analogous to a chain of coupled atoms in some extent. It is also noticeable that for the n = 10 model the pass-band have very steep cut-off edges and the suppression outside the pass-band is perfect, the calculated transmittance outside the pass-band is very low (-20 -50 dB). The low-noise performance is also favored in potential applications. In contrast, for the multilayered systems governed by resonant tunneling of SPPs, nearly zero transmission usually occurs at a certain frequency between the frequencies of two adjacent transmission peaks as a result of in-plane evanescent Bragg scatterings which inevitably introduces both the strongly frequency-dispersive and the spatially dispersive signatures in transmission spectra.
4. The coupling and hybridization of guided resonance modes
More calculations show that, for the n = 2 sample, at an on-resonance frequency fB = 9.1GHz or fC = 12.3GHz of perfect transparency, the spatial distributions of electric field [see Figs. 3(a) and 3(b)] are symmetric or anti-symmetric about the xy plane, and the transmitted waves hold a phase difference of 0 (in phase) or π (out phase) with respect to the incident waves respectively. Therefore it is reasonable to say that the peaks at fB and fC arise from the excitations of the symmetric and anti-symmetric coupling modes for the two-layered model. The results unambiguously present a physical picture of mode splitting of coupled apertures (or meta-atoms). Similar results can be found for the n = 3 model. Figures 3(c)∼3(e) present the spatial field distribution at frequencies of the three transparency modes for the n = 3 model. Comparing the mode symmetry shown in Fig. 3(c)∼(e) and that shown in Figs. 3(a) and 3(b) of two-layered model. We can reasonably deduced that, the anti-symmetric mode at fC = 12.3GHz of the n = 2 model splits into two modes of the n = 3 model, one at fE = 11.64GHz is anti-symmetric [Fig. 3(d)], and the other at fF = 12.35GHz is symmetric [Fig. 3(e)], while the resonant mode at the lowest frequency fD = 8.2GHz inherits a symmetric feature in field distribution [Fig. 3(c)] from the symmetric mode at fB of the n = 2 model, it also applies an in-phase signature for the transmitted waves. It is worth noting that, the transparency band of the n = 3 sample becomes broadened as compared to the n = 2 sample, and the band edges are even sharper.
Fig. 3 Spatial distribution of electric fields in the xz plane at on-resonance frequencies of (a) fB = 9.1GHz, (b) fC = 12.3GHz for the n = 2 model, and (c) fD = 8.2GHz, (d) fE = 11.64GHz, (e) fF = 12.35GHz for the n = 3 model.
Figure 4(a) presents the dispersion relation of a bulk material by assuming that it is periodically constructed with layered CAAs. The band structure is calculated with MEM algorithm by assuming periodic boundary conditions along the z axis. The process of mode splitting shown in Fig. 4(b) depicts the evolution of the frequencies of transmission peaks from the n = 1 system to the n = 3 system. It is interesting to note that the pass-band between fb = 6.77GHz and ft = 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 transparency bandwidth shown in Figs. 2(b) and 2(c) is about 40% of the central frequency. It is also worth noting that, the transparency band we observed is not sensitive to the incident angle (not shown), which is contrary to the case when the resonant tunneling of SPP modes dominates the EOT of the system.
Fig. 4 (a) Dispersion relation of bulk material periodically constructed by layered CAAs. The inset shows a unit cell of the bulk material. (b) The frequencies of resonant modes (transmission peaks) for the n =1, 2 and 3 models. The thin lines denote the process of mode splitting. fA = 8.7GHz and f′A = 12.1GHz refer to the frequencies of the transmission peaks of the n = 1 sample with and without dielectric layer.
5. Conclusion
In summary, we investigate the transmission properties of stacked metallic multi-layers perforated with CAAs. Taking advantage of the excitation and interlayer coupling of guided resonance modes of CAAs, the transparency band of such a system with only three metallic layers can span a wide frequency range covering about 40% of the central frequency. In this study, we assume PEC for metals and perform experiments in microwave regime. In high frequencies especially the near-infrared and visble regimes, metals are dispersive and lossy and can not be treated as PEC. But the guided resonance modes of apertures can still take effect and dictate the EOT as revealed by a previous experimental study on EOT in near-infrared regime [13]. It is expected that our findings are applicable in the near-infrared and even visible regimes. Several hot research topics might benefit from our findings of broadband transparency derived from EOT. As a goal to be readily pursued in the fields of both plasmonics and metamaterials, broadband utility could have enormous potential applications in optoelectronics, telecommunication and image processing. This study might also extend the scope of fishnet metamaterials.
Acknowledgments
This work was supported by NSFC (No. 11174221, 10974144), CNKBRSF (Grant No. 2011CB922001), NCET ( 07-0621), STCSM and SHEDF (No. 06SG24).
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