1. Introduction

Metamaterials (MMs) draw intensive interests of many researchers recently, due to its versatility of controlling the incident electromagnetic (EM) waves, and possess properties which cannot be observed in nature, such as negative-index materials [1], extraordinary optical transmission [2], and classical analogue of electromagnetically-induced transparency [3]. Although MMs started to get spotlight by the fascinating negative-refractive-index properties [1, 4], the significance of concept of MMs is not restricted to only this [5–8]. MMs are characterized by the electric permittivity ε(ω) and the magnetic permeability μ(ω), which can be carefully adjusted for the impedance matching between MM and free space, and for a large imaginary part of the refractive index, to be qualified as MM absorber (MM-A), resulting in the minimal transmission and reflection, and, in turn, a large absorption [9]. Obviously, the MM-A with a single-band high absorption is inapplicable in some areas.

Among MMs, perfect-absorption (PA) MMs, which are useful to enhance the efficiency in capturing solar energy [10] and applied to plasmonic sensors [11], bolometers [12] and wireless power transfer [13], have been rapidly developed. Typical PA MMs contain the meta-atoms which induce high loss. The resonance established between inductive and capacitive portions of the “circuit” allows energy to be stored and subsequently dissipated via Ohmic and dielectric losses. In general, the dielectric loss in the dielectric is much larger than the Ohmic loss. Therefore, the magnetic resonance, which induces antiparallel currents, has been exploited to generate the dielectric loss significantly [11–14].

It is known that, a typical meta-atom, such as split-ring resonator [15] and cut-wire pair [16], shows two resonances by external magnetic and electric fields. On the other hand, the efforts to tame the higher-order magnetic resonance are noticeable. These results render the MM in larger scale, which is desirable in the fabrication of MMs operating in the optical range. A research on cut-wire pair to obtain the negative refraction at the third-harmonic resonance has opened the idea on the higher-frequency MMs [17]. The progressive exploitation of the third-harmonic resonance of meta-atom has promised to extend the application and the concept of MM.

In this work, we realized the polarization-independent dual-band PA by using only one kind of pattern. The high-frequency PA induced by the magnetic resonance at the third harmonic, of meta-atom and its polarization independence are also presented. By employing donut-type resonators, dual-band PA was realized at the third-harmonic as well as the fundamental magnetic resonances, and its polarization independence was also achieved.

2. Simulation and experimental setup

The polarization-independent PA structures, whose unit cells consist of a patterned metallic structure at the front and a metallic plane at the back separated by a dielectric substrate, were designed and fabricated, as shown in Fig. 1. The substrate was FR4 with a thickness of 0.8 mm, and a dielectric constant of ε = 4.3 and a dielectric loss tangent of 0.025. The lossy-metal model was used for copper with an electric conductivity of σ = 5.8 × 10⁷ S/m, and the thickness of metallic layer was t_c = 36 mm. The reflection spectra (|S₁₁|²) were measured in a microwave anechoic chamber using a Hewlett-Packard E8362B network analyzer connected to linearly-polarized microwave standard-gain horn antennas and calibrated by replacing the sample with a copper board of the same size as perfect reflector. Two horn antennas, which are 120 mm wide and 90 mm long, were used; one for illuminating the microwave beam on the sample and the other for receiving the reflected beam with an incident angle of 5°, which is the minimum angle in our system not to have the overlapping effect between incident and reflected waves, with a proper distance (sample to the middle point of two horn antennas: 2.0 m). The full-wave EM simulation has been performed by using CST Microwave Studio software. The unit cell was subject to the periodic boundary conditions in the x and y plane and open for the z direction in the environment of free space. Normally incident EM wave was polarized so that the electric and the magnetic fields were parallel to x and y axes, respectively (Fig. 1). The absorption is, in general, calculated by A(ω) = 1 - R(ω) - T(ω) = 1 - |S₁₁((ω)|² - |S₂₁(ω)|², where A, R, and T are absorptivity, reflectivity and transmittance, respectively, and S₁₁(ω) and S₂₁(ω) are the scattering parameters of reflection and transmission, respectively. Since the MM is backed by a thick (compared with the skin depth in the operating range) metallic layer, the EM wave is prevented or the transmission nearly vanishes. In this case, only the scattering parameter of reflection was considered, and the EM-wave absorption was calculated by using A(ω) = 1 - [S₁₁(ω)]².

 

Fig. 1 Unit cells for the MM absorbers of (a) disk-type and (b) donut-type structures. Photos of the fabricated samples with (c) disk-type and (d) donut-type structures.

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3. Results and discussion

Schematics for the two suggested MM-A structures, disk-type and donut-type, are shown in Figs. 1(a) and 1(b), respectively. The pattern is optimized for the disk-type structure with a fixed periodicity p = 19 mm. The optimum value for the radius turns out to be r = 6.5 mm. For the donut-type structure, the optimum value is 7 mm with the corresponding width of 4 mm, and the periodicity of 20 mm. Figures 1(c) and 1(d) show the photos of fabricated structures for the disk-type and the donut-type structures, respectively.

The absorption spectrum of disk-type absorber, whose meta-atoms are designed to facilitate the high-order magnetic resonances, is illustrated in Fig. 2(a) for a wide range of 4 ~18 GHz. Two high-absorption peaks are evident. The low-frequency peak (absorption of 94% at 6.22 GHz) is induced by the fundamental magnetic response and the other peak, i. e., the high-frequency peak (absorption of 93% at 17.38 GHz), results from the third-harmonic resonance of meta-atom. Figure 2(b) presents the absorption spectrum of donut-type absorber, displaying two stronger high-absorption peaks. The two peaks possess nearly perfect absorption, with the absorption of 99.6% at 5.10 GHz and 99.8% at 16.32 GHz. For the donut-type structure, the mechanism of the absorption is the same as that of the disk-type structure; the low-frequency peak is caused by the fundamental magnetic resonance and the high-frequency peak is induced by the third-harmonic magnetic resonance.

 

Fig. 2 (a) Simulated absorption spectra of the disk-type and (b) the donut-type absorbers.

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To understand the mechanism of the absorption at the third-harmonic resonance, the EM properties are explained in comparison with the fundamental mode of MM absorption. The anti-parallel currents of the front and the back plates are exhibited for both modes of PA [see Figs. 3(a) and 3(c)], manifesting that the absorptions at both peaks are induced by the magnetic resonance. Figures 3(b) and 3(d) present the distribution of surface currents of the metallic surface for disk- and donut-type structures, respectively. For the low-frequency peak a large portion of current flows along the edge of disk for the disk-type structure, while it flows along the central portion of the inner and the outer edges of donut for the donut-type structure. Rather different situation happens for the high-frequency peak: a significant amount of current flows are in the inner area of disk and the corresponding area of rear metal plane for the disk-type structure, and this current is missing in the donut-type structure. This difference is very important for the realization of PA for both peaks (see below).

 

Fig. 3 Induced surface currents for the disk-type [(a) and (b)] and the donut-type absorbers [(c) and (d)].

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To further compare the results of simulation with those of experiments, we have measured the absorption spectra in 4 ~7 and 12.4 ~18 GHz ranges. The experimental spectra are in good agreement with the simulations [Figs. 4(a) and 4(b)]. The absorption of the low-frequency peak for donut-type structure shows absorption of 99.1% at 5.06 GHz and of 99.6% at 5.10 GHz for experiment and simulation, respectively. On the other hand, the experimental high-frequency peak shows the absorption of 99.9% at 16.88 GHz.

 

Fig. 4 Simulated and measured absorption spectra for (a) disk-type and (b) donut-type structures.

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Another noteworthy aspect in the aforementioned Fig. 2 is that the absorptions of both peaks of the disk-type structure are lower than those of the donut-type structure. Our initial intention was to design high-frequency polarization-independent PA MMs which utilize the third-harmonic magnetic resonance. Since some of us already had an experience of designing MMs with left-handed behavior at the third-harmonic magnetic resonance [17] by employing a cut-wire structure, we decided to use the same concept. In order to modify this structure to be polarization-independent it is natural to replace the cut-wire with a highly symmetric one, circular disk. Therefore, we considered to design a disk-type PA MM. In the process that the unit-cell parameters were adjusted to obtain the optimum conditions for the disk-type PA, we noticed that, if we tried to adjust the structure to increase the absorption of the peak with lower absorption, then that of the other peak was lowered, implying that certain trade-off was inevitable.

To find the optimum conditions for the disk-type structure, we varied the periodicity p and the radius of disk. We found that r = 6.5 mm was the best choice for the radius. A systematic variation of the peak intensity was discovered. If the periodicity is increased (decreased), the absorption and the surface current of the low- (high-) frequency peak increase. Furthermore, there is a considerable amount of surface current in the inner area of the disk for the low-frequency peak when p = 14 mm, and this current decreases with increasing p and nearly disappears when p = 22 mm. The opposite is true for the high-frequency peak; a considerable amount of current in the inner area of the disk when p = 22 mm decreases with decreasing p and nearly disappears when p = 14 mm. To achieve PA for both peaks we reached a conclusion that the surface current near the center of the disk played an important role and removal of that portion of current was essential. Therefore, we replaced the disk with donut and successfully realized PA (higher than 99.6%) for both peaks. The surface current is mostly concentrated at the middle part of the inner and the outer edges of donut for both peaks with some portion of current flowing in the upper and the lower middle portions of donut for the high-frequency peak.

Discussion on another important aspect is continued. We also found that the magnitude of surface current plays a crucial role for PA. The higher the surface current the better the absorption. The surface current of the high- (low-) frequency peak of the donut-type structure is one-and-half times (twice) larger than that of the disk-type structure. This higher surface currents in the donut-type structure resulted in better absorptions for both peaks. Since the dielectric substrate has very small loss tangent, the dielectric loss is the dominant loss process. The dielectric loss is proportional to |E|² and electric field E is also proportional to the charge accumulated on the plates of capacitor. The front disk or donut and the rear metal plane form a capacitor, and the accumulated charge at the area where the surface current flows in or out is large if the induced surface current is large. Therefore, the electric field inside the dielectric substrate is strong for large induced surface current, resulting in a large dielectric loss. This is another reason for PA for both peaks of the donut-type structure. When periodicity p is increased (or decreased) by 2 mm (10% with respect to the unit-cell size) for the donut-type structure, the absorption is changed from 99.6 to 98.0% and from 99.8 to 96.5% for the fundamental resonance and the third-harmonic magnetic resonance, respectively. This indicates that p also affects the PA.

Finally, we measured the polarization dependence of the absorption spectra for the donut-type structure. Figures 5(a) and 5(b) present the simulated absorption spectra with α = 0, 15◦, 30◦ and 45◦, where α is the angle between the y-axis and the electric field of incident EM wave. In the simulation, the polarization independence of the spectra for both low- [Fig. 5(a)] and high-frequency [Fig. 5(b)] peaks is evidently displayed. The similar polarization independence is manifested in the experiments. The experimental low-frequency peak, however, exhibits some shift of the peak position with varying polarization. This slight shift might be attributed to the fact that the real zero incident angle is not 0 but 5°.

 

Fig. 5 (a), (b) Simulated and (c), (d) measured absorption spectra of donut-type absorber for various polarizations.

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4. Conclusions

We have designed and fabricated multi-plasmonic perfect absorbers, which consist of the arrangement of disk- and donut-type resonators and a metallic background plane, separated by a dielectric. The absorption spectra were measured in the microwave-frequency range and compared with the simulated ones. The third-harmonic magnetic resonance of PA MM, based on a simple structure, was numerically and experimentally investigated in comparison with the fundamental-resonance MM absorption. Although the single plasmon still works for the common MMs, our high-frequency PA is achieved by multi-plasmonic magnetic resonances. Moreover, the multi-plasmonic PAs for donut-type are polarization-independent. The designed PA MM could provide absorption higher than 98% at the third-harmonic magnetic resonance as well as the fundamental one, independently from polarization.