1. Introduction

Artificial materials are called metamaterials (MMs) whose electromagnetic (EM) properties are not available in nature, such as negative reflective index [1]. One of the representative properties of MMs is to control the real and the imaginary parts of electric permittivity ε(ω) and magnetic permeability μ(ω), which has been enough to attract many researchers world-wide. Although many scientists have investigated MMs for negative-reflective-index properties [1, 2] at the beginning, their interests have been extended to many other fields comprising perfect lenses [3–6].

MM absorbers (MM-As) mimics the blackbody through minimizing transmission and reflection. In order to maximize absorption, MM-As possess the same impedance as free space by adjusting the real and the imaginary parts of the ε(ω) and μ(ω) [7]. In general, MM-As consist of periodically-arranged meta-atoms which cause high loss. Electric-circuit interpretation of MM-As is that a designed structure is responsible for the resonance frequencies for given inductive and capacitive values, which make energy stored and extinguished through Ohmic and dielectric losses at these frequencies. The magnetic resonances, which are produced by induced antiparallel currents at metallic surfaces, produce significant dielectric loss. MM-As will be a useful in many applications, such as solar energy [8], plasmonic sensors [9], terahertz sensing [10], bolometers [11] and wireless power transfer [12].

For this reason, many MM-As have been proposed and demonstrated, such as cross-shaped resonator [13] and donut structure [14]. However, the sensitive conditions, which are relevant to optimization of the parameters of designed structure, make it difficult to fulfill the perfect absorption in broadband, on the other hand, and single-band high absorption by using MMs is easier to be prepared but patently inapplicable in some fields. Hence, recently many researchers on MM-As have focused on broadband and multi-band high absorption. They recently demonstrated multi-band [14] and broadband [15] by using several kinds of resonators, and even dual-bands by using only one kind of resonator [16]. Furthermore, Ding et al. already reported broadband MM-As with quadrangular frustum pyramids using multilayer process and milling method, which showed wide-band absorption in 8–14 GHz [15]. However, polarization-independent MM-A with wide-band high absorption at both low and high frequencies simultaneously has never been reported.

In this work, we realize the polarization-independent dual-wide-band MM-As by using cone-type multilayered structure. It should be noted that, in order to achieve the dual-wide-band absorber, we apply the concept of third magnetic resonance [16]. By comparing between simulation and measurement, the lower frequency band is in excellent coincidence, while the higher-frequency one is in slight discrepancy. The low-frequency absorption band turned out to be induced by the fundamental magnetic resonance and the high-frequency one due to the third magnetic resonance, and the polarization independence is presented. We also suggest that the the dual broadband is demonstrated even in the infrared and the visible ranges.

2. Simulation and experimental set-up

MM-As are usually made of the metallic patterns on one side and a metallic plane on the other side separated by a dielectric layer. However, multilayered sample was fabricated to have truncated cone-type resonators as unit cells through milling process on multilayered plate, which was piled of metallic layers (0.036-mm thick) and dielectric layers (0.182-mm thick) in sequence on dielectric substrate of thickness 2.2 mm with a metallic plate at the bottom by heat-pressing process. The employed metallic layer was the copper with an electric conductivity of 5.8×10⁷S/m, and dielectric layer was FR-4 with a dielectric constant of 4.2 and a loss tangent of 0.025. This sample, which was designed and fabricated, is shown in Fig. 1. We have used a commercial software, CST Microwave Studio, which is based on the finite-integration technique with which we have designed the model and got the simulation data. In the boundary-condition set-up, z direction and x-y plane are for the direction of propagation and the E-H field, and x and y axes are fixed to the unit cell and z axis is open. In simulation, the EM-wave absorption is defined as A(ω) = 1 – R(ω) – T(ω) = 1 – |S₁₁ (ω)|² – |S₂₁ (ω)|². A(ω), R(ω) and T(ω) are absorption, reflectance and transmittance, respectively. S₁₁(ω) and S₂₁(ω) are the scattering parameters of reflection and transmission, respectively. By the way, transmittance cannot exist owing to the back metallic plane. Therefore, the absorption of EM wave is determined by A(ω) = 1 – |S₁₁ (ω)|².

 

Fig. 1 (a) Perspective view and (b) side view side of the designed meta-atom. D₁ and D₂ are the top and the bottom diameters of circular structures. t₁ and h are the thickness of FR-4 and the height of truncated cone structure. (c) Photos of the fabricated sample.

Download Full Size | PDF

We calibrated the experiment by employing the copper board of the same size to obtain the reference perfect-reflection spectrum and measured the reflection spectra (|S₂₁ (ω)|²), in a microwave anechoic chamber by using Hewlett-Packard E8362B network analyzer linked to two linearly-polarized microwave standard-gain horn antennas, whose width and height are 120 and 90 mm, respectively. The microwave incident angle of 10° was set together with a proper distance between two antennas, to prevent the interference between incident and reflected waves.

3. Results and discussion

The schematic drawing and the photo of fabricated structure, truncated cone structure, were already shown in Fig. 1. The truncated cone structure includes circular structures with different diameters, and is repeated with periodicity p = 23.8 mm. The optimum values for the bottom and the top diameters come to be D₁ = 21.8 mm and D₂ = 13.8 mm, respectively. Height h is 6.3 mm, and the number of the metallic and dielectric pair-layers is 29. The diameters (D₁ and D₂) turn out to determine the starting and the ending frequencies for broadband, and the slope of truncated cone corresponds to the width of absorption band.

The simulated absorption spectrum of truncated cone structure, which is designed to demonstrate dual-broadband absorption, is illustrated in Fig. 2 for a range of 3–18 GHz. The absorption spectrum shows that absorption is over 90% in both 3.93–6.05 and 11.64–14.55 GHz. There are 29 absorption peaks in 3.93–6.05 GHz according to the number of dielectric layers between two neighboring metallic layers, but these absorption peaks are connected to be a wide band due to the fact that the intervals between neighboring peaks are very small [15]. The fundamental magnetic response induces the low-frequency absorption band, and the third-harmonic resonance makes additionally the high-frequency absorption band. Likewise with the fundamental magnetic response, the third-harmonic resonance is induced by the same resonators in the sample. The range of absorption band by the third-harmonic resonance is analyzed with the distribution of induced surface current to be 11.5–17.5 GHz, but the absorption over 90% turns out to be in 11.64–14.55 GHz. The detailed analysis will be described later.

 

Fig. 2 Simulated absorption spectrum of the truncated cone-structure absorber.

Download Full Size | PDF

In order to understand the absorption mechanism of the low-frequency absorption band, we employ the distributions of induced electric field, induced magnetic field and surface current at specific frequencies, which are shown in Fig. 3. At 4 GHz, the induced electric field, the induced magnetic field and the surface current are located in the bottom of truncated cone. It should be mentioned that the induced electric field is formed at the sides, on the other hand, the induced magnetic field is located at the center. Since the induced surface current doesn’t flow though dielectric layer, which exists between two metallic layers, naturally the induced electric field is strong at the sides of dielectric layer in terms of equivalent oscillating-current resonant circuit. The induced magnetic field, which is caused by the antiparallel surface currents at two neighboring layers, is located at the center due to the fact that surface currents at the center is stronger than that at those side. Figure 3 shows that the absorption band of multilayered structure is made only by the magnetic resonance. The electric field, the magnetic field and the surface current are not only induced at 4 GHz, but at other frequencies in 3.93–6.05 GHz such as 4.5, 5, 5.5 and 6 GHz. The positions of the induced electric and magnetic fields are shifted continuously to the top of truncated cone according to frequency. The resonant frequency shifts to higher frequency with the upward movement of field position because of the smaller-size disk at the top of truncated cone structure. In general planar type of MMs concentric resonators, broadening of the fundamental resonance band is enhanced by decreasing the inductance [17]. In comparison between multilayered structure and the planar type, the wide band of truncated cone structure is induced by the antiparallel surface currents in different diameters due to the fact that different diameters of multilayered structure play role of various inductances.

 

Fig. 3 Simulated electric and magnetic field distributions at the central cross section of unit cell at 4.0, 4.5, 5.0, 5.5 and 6.0 GHz. Left and center columns are for the electric and the magnetic fields, and right one show the induced surface current.

Download Full Size | PDF

Figure 4 presents the induced surface current at 12, 13 and 14 GHz in order to understand why absorption is over 90% from 11.64 to 14.55 GHz in Fig. 2. At 12 GHz, Fig. 4(a) shows that the induced surface currents at the third-harmonic resonance do not flow only in the bottom layers, but in the middle ones. The layers for induced surface currents at 13 and 14 GHz turn out to be even in the top as well as in the middle, as in Figs. 4(b) and 4(c), respectively. It should be noted that two groups of layers have a specific spatial interval in order to reveal the absorption over 90%. The induced surface currents in the upper and the lower layers make a dielectric loss, which is proportional to the square of the electric field between the two groups of involved layers. The accumulated charges on the metallic plates of capacitor are proportional to the electric field. The upper and the lower metallic disks act as metallic layers of capacitor. The accumulated charges are plenty on the area where the surface current flow is strong. The electric field in dielectric layer between upper and lower metallic planes is large, and the dielectric loss is enhanced as a result [16]. The absorption rapidly declines, owing to the fact that the induced surface currents in the upper layer evanesce over 14 GHz. This proves that at the third-harmonic resonance two layers are needed so that the absorption is higher than 90%. The upward movement of active layers according to resonant frequency was analyzed in detail, as in Fig. 4(d), which shows the positions of active layers from the top of FR-4 substrate vs. frequency. Both upper and lower active layers turn out to move up linearly with the same slope of 1 dielectric layer per 0.2 GHz, since the change in position is accompanied by the change in radius of the truncated cone, and the induced surface currents, which are divided into 3 sections along the axis of electric field, flow in both upper and lower layers.

 

Fig. 4 Simulated surface current in the unit cell at specific frequencies: (a) 12.0, (b) 13.0, and (c) 14.0 GHz. (d) Heights of active layers from the top of FR-4 substrate in the truncated cone (denoted as position) according to frequency.

Download Full Size | PDF

We have measured the absorption spectra in ranges of 3.5–6.5 and 9.0–14.5 GHz to compare the simulation results in Fig. 5. In the experimental data, the low-frequency absorption band over 90% emerges in 3.88–6.08 GHz, which is nearly coincident with the simulated one. On the other hand, the experimental results at high frequencies show two absorption bands whose absorption is higher than 90%) : band A in 9.95–10.46 GHz and band B in 11.86–13.84 GHz. Absorption band A is similar to the simulation, but the absorption is higher with respect to the simulation. For absorption band B, the experimental spectrum is in good agreement with the simulation. To provide the absorption according to polarization angle, we simulated and measured the absorption spectra of polarization independence in 3.5–6.5 and 9.0–14.5 GHz.

 

Fig. 5 Simulated and measured absorption spectra in (a) 3.5–6.5GHz and (b) 9.0–14.5GHz.

Download Full Size | PDF

Figures 6(a) and 6(c) are the simulated absorption spectra for polarization of 0, 30°and 45°, and Figs. 6(b) and 6(d) are those of experiment. Figures 6(a) and 6(b) indicate that change of the polarization angle doesn’t influence greatly the absorption band. However, the low-frequency absorption band is slightly red-shifted in Fig. 6(b) by increasing the polarization angle. On the other hand, the high-frequency absorption band is inversely blue-shifted slightly in Fig. 6(d). The absorption is experimentally reduced more or less in 9.95–10.46 GHz. These slight differences occur owing to non-zero incident angle in order to avoid the interference between incident and reflected EM waves in the experiment, and slightly changed values for dielectric constants between simulation and experiment. Synthetically, the simulated and the experimental spectra turn out to be similar.

 

Fig. 6 (a), (c) Simulated and (b), (d) measured absorption spectra in 3.5–6.5 and 9.0–14.5 GHz.

Download Full Size | PDF

In order to expand the application area, we designed and simulated another similar absorber for the THz regime (shown in Fig. 7). The materials and the parameters of the designed structure are optimized. The dielectric layers are silicon with a thickness of each layer of 40 nm, and gold is used for the metal with an electric conductivity of σ = 4.56×10⁷ S/m and a thickness of each layer of 5 nm. This meta-atom is repeated with periodicity p = 400 nm. The optimum values for the bottom and the top diameters come to be D₁ = 320 nm and D₂ = 240 nm, respectively. Total height h is 180 nm, and the number of metallic and dielectric pair-layers is 4. Figure 7(c) shows that absorption is over 90% in both 198–201 and 443–546 THz, which include red to green light, and independent of polarization angle similar to the GHz regime.

 

Fig. 7 (a) Perspective view and (b)side view of the designed meta-atom for the infrared and the visible. D₁ and D₂ are the top and the bottom diameters of circular structures. h is the height of truncated cone structure. (c) Simulated absorption spectrum of the truncated cone-structure absorber in 100–650 THz.

Download Full Size | PDF

4. Conclusion

We designed and fabricated dual wide-band MM absorber where truncated-cone meta-atoms, which consist of alternately-piled metallic and dielectric disks, are periodically arranged. The experiments have been proceeded, based on the simulation results, in microwave-frequency range, and we compared elaborately the spectra of simulation and measurement. For this structure, we understood how the fundamental and the third-harmonic resonance frequencies move. The absorption of designed MM-A was measured to be above 90% broadly in 3.88–6.08, 9.95–10.46 and 11.86–13.84 GHz. In addition, it is independent of polarization angle because of the multilayered disk structure and possible to be scalable to smaller devices for the infrared and the optical regimes.