1. Introduction

Metamaterials (MMs) are artificial, effectively homogeneous electromagnetic (EM) structures consisting of dielectrics and highly conducting metals, which are periodically arranged. The major advantage of MM over natural materials is that the unit-cell parameters can be tailored to have desired macroscopic properties. Although MMs started to get spotlight by fascinating the negative-refractive-index properties [1, 2] in the beginning, the significance of concept of MMs is not restricted to only this [3–6]. MMs are characterized by the electric permittivity ε(ω) and the magnetic permeability μ(ω), whose real and imaginary parts are adjusted to match the impedance of MM to that of free space, and to possess a large imaginary part of the refractive index to be qualified as MM absorber (MM-A) by engineering the structure and considering the material. Therefore, both transmission and reflection are minimized and a large loss results in [7]. Obviously, the MM-A single-band high absorption is inapplicable in some areas. Therefore, the research on broadband or multi-band high-performance MM-A is necessary. Hence, it is not easy to combine multi-band MM-As with high efficiency, since the sensitive perfect absorption conditions are easy to be broken. Therefore, the achievement is still a significant issue in the MM-A researches. In spite of numerous studies, many issues remain to be explored, for example, to relax the working conditions and to increase the number of absorption peaks and the absorption bandwidth [8–24], as well as to switch the absorption properties [14, 25] from microwave to infrared frequencies, because of significant impact in the field of solar cells [26], photodetectors [27], sensors [28], imaging devices [29] and thermal emitters [30].

There were several nice attempts to fabricate the MM-A with multiple bands and wide-range absorption peak. Shen et al. [10, 11] fabricated a polarization-insensitive, wide-angle, triple-band MM-A. Ding et al. [12] prepared an ultrawide-band MM-A. To add new information in the area of MM-A, we suggest another design of multi-band MM-A which is composed of donut-type resonators. By the suitable arrangement and the proper parametric study, we achieve the absorption conditions for multi peaks which are even not sensitive to the polarization condition of incident EM wave. Both experiment and simulation were performed, and it is found that the results of simulation are in good accordance with those of experiment.

2. Simulation and experimental setup

The samples were fabricated by the conventional printed-circuit-board process with copper patterns (0.036 mm thick) on one side and the other side was backed by a copper layer with the same thickness and a size of 15 × 30 cm². The substrate was FR4 with a thickness of 1.2 mm, and a dielectric constant of 4.3 and a dielectric loss tangent of 0.024. The lossy-metal model was used for copper with an electric conductivity of σ = 5.8 × 10⁷ S/m. 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, respectively, 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° with a proper distance (sample to the middle point of two horn antennas: 2.0 m). By varying the incident angle of EM wave, not only the distance between sample and middle point of two horn antennas but also the tilting angle of two horn antennas were established properly for each case. A computational study was performed for the MM-A with a commercial program, CST MICROWAVE STUDIO^TM. Unit-cell boundary conditions were used in x and y direction, and plane wave was incident downward on the MM-A with the electric field polarized along the y direction as the excitation source. Because the proposed structure is backed by a metallic sheet, the EM wave cannot transmit, and thereby the EM wave absorption is determined by A = 1 - |S₁₁|² - |S₂₁|² with |S₂₁| = 0 where S₁₁ and S₂₁ are scattering parameters relevant to reflection and transmission, respectively.

3. Results and discussion

Actually, polarization-independent triple-band MM-A has been reported in [10, 11] with a simple design. On the other hand, the realization of close-set perfect-absorption multi-peaks is very difficult only by using the structure proposed by Shen et al. [10, 11], owing to the large differences in size among resonators. Here, we propose a new type of resonant absorbers to realize quad-band MM-A by adjusting the aforementioned arrangement and utilizing the idea in the previous study. The advantage of the highly-symmetrical shape for the polarization of incident light is well known: as far as the k direction is maintained to be perpendicular to the plane of structure, the absorption properties are nearly unchanged with polarization. By considering the difficulty of fabricating squares, structures with sharp corners, especially when the structure is intended to be used in mid- or near-infrared, we choose donut-type resonators. In addition, the most important advantage of our suggestions is narrow interval of absorption peaks. Furthermore, by adjusting the width of rings, we can enhance the absorption of each peak close to unity.

The schematic drawing of suggested MM-A is shown in Fig. 1(a). The optimized pattern is composed of 3 donut-type structures which have different radii with a periodicity p = 25 mm. The radii (r₁, r₂ and r₃) represent those for the outer circles of donuts. The optimum values for the radii come to be r₁ = 5.0 mm, r₂ = 4.7 mm and r₃ = 4.5 mm, and the corresponding width is 1.8 mm for all. Although the size of unit cell is relatively large, the sizes of resonators, which determine the resonance frequency, are still suitable for deep sub-wavelength concept. We define 3-donut structures as donut 1, 2 and 3 in compliance with the same numbering for the radius. Each group of donuts are distinguished by virtue of position of the central point of donut, in other words, that of r₁, r₂ or r₃ matches with the center, the corner or the middle of boundary line of the square unit cell, respectively. As shown in Figs. 1(b) and 1(c), 2 types of sample were fabricated for realization of 2 peaks (donuts 1 & 2) and 3 peaks (donuts 1, 2 & 3).

 

Fig. 1 (a) Schematic of the proposed structure of MM-A. Photos of the fabricated samples with (b) 2 types and (c) 3 types of structure.

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The aforementioned donut structures are added one by one to realize the multiple absorption bands. Figure 2 presents progress of the combination at α = 0 where α is the angle between the y-axis and the electric field of incident radiation. In the simulation [Fig. 2(a)], we can clearly see triple absorption peaks at 6.5, 7.0 and 7.6 GHz with absorption of 99%, 98% and 99%, respectively. The experimental results also reveal multiple peaks at 6.51, 7.0 and 7.61 GHz with absorption of 98%, 98% and 98%, respectively, and any appreciable alteration by varying the polarization of EM wave was not detected [Fig. 2(b)]. It is confirmed that both simulation and experiment are in excellent coincidence. We might ascribe the minor difference between simulation and experiment to the imperfect fabrication. When donut 2 was positioned with donut 1 [Fig. 2(a)], the corresponding 2 peaks appear nearly independently. We kept adding donut 3 to the system of donuts 1 and 2 (Fig. 2). Because of little interaction between them, the slight peak shift was shown in progress of the combinations. As aforementioned, the absorption band is significantly narrower than that in [10, 11].

 

Fig. 2 (a) Simulated and (b) measured absorption spectra for the combinations of donuts.

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The expression of the absorption is A(w) = 1 – R(w) – T(w), where A(w), R(w) and T(w) are the absorption, the reflection, and the transmission as a function of frequency w, respectively. The frequency-dependent T(w) and R(w) are determined to be dependent on the complex index of refraction $n(w)=\sqrt{\epsilon (w)\mu (w)}=n_1+i{n}_2$ and the impedance $z(w)=\sqrt{\mu (w)/\epsilon (w)}=z_1+i{z}_2$ . It is possible to absorb both the incident electric and magnetic fields remarkably by properly tuning $\epsilon (w)$and $\epsilon (w)$ and to achieve perfect impedance matching with the free space [$z(w)=\sqrt{\mu (w)/\epsilon (w)}=1$]. In [31], the retrieved impedance equation is given as follow;

Both real and imaginary parts of relative impedance are shown in Fig. 3(a). At each absorption frequency, the real relative impedance is near unity [z(w) ≈1]. By the free-space impedance matching of MM-A, electric and magnetic fields might be localized in the copper-FR4-copper structure. The evidence for magnetic resonance, which is related with the effective permeability, can be manifested by the anti-parallel surface currents in two metallic layers, and each metal structure participates in the effective permittivity [Fig. 3(b)]. The surface currents on the two sides are strongly associated with a dipolar response which contributes to the effective $\epsilon \left(w\right)$[7], eventually attenuating the power of wave to be very low. It is clearly seen that most of the power loss takes place in the upper and the lower parts of donut, and that the dielectric losses occur in between the two metallic plates [Fig. 3(c)].

 

Fig. 3 (a) Simulated effective surface impedance of the triple-band absorption. (b) Distribution of the normalized induced current at a resonance frequency (6.5 GHz). (c) 3-dimensional distribution of the power loss density at each resonance frequency.

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Previously, a theoretical interpretation based on interferences, among multiply reflected beams between two metallic layers, without considering the antiparallel arrangements of induced currents was proposed [11, 32]. To analyze the effect of interferences among the multiple-reflection beams between two metallic layers, we need 4 coefficients – 2 reflection coefficients (air-to-air and dielectric-to-dielectric), and the transmission coefficients (air-to-dielectric and dielectric-to-air) – and 4 phase shifts associated with the aforementioned coefficients. The rear metal plate functions as a reflector with reflection coefficient ~-1. According to the interference theory [11, 32], not only the phase difference but also the amplitude of the coefficients play the key role for absorption mechanism. To adopt the multiple-reflection theory for our structure and to exclude the magnetic resonance, we removed the rear metal plate from the structure of Fig. 1(a) (decoupled system) and investigated the reflection and the transmission coefficients because the magnetic resonance can be taken into account between the resonator array and the rear metal plate (coupled system). Differently from the results in [11], only a single dipole resonance of the array of donut resonators, as indicated by the deep transmission drop at 12.2 GHz [Fig. 4(b)], was observed even though 3 kinds of metallic components were present. Distribution of the normalized induced current at a resonance frequency is presented in Fig. 4(c). It is shown that existence of the rear metal plate significantly affects the absorption mechanism of suggested MM-A. Therefore, we can safely argue that the multiple-reflection theory is not suitable for elucidation of the absorption mechanism of our structure.

 

Fig. 4 (a) Schematic diagram for multiple-reflection theory with associated parameters. (b) Amplitude of the reflection and the transmission coefficients at the air-dielectric interference for the system of only resonator array and dielectric (decoupled model). (c) Normalized surface current distribution of the decoupled model at 12.2 GHz.

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Another schematic drawings of MM-A with 4 absorption peaks are shown in Fig. 5. The optimized pattern is composed of 4 donut-type structures which have different radii with a periodicity p = 16 mm. The radii (r₁ ~r₄) represent those for the outer circles of donuts. The optimum values for the radii come to be r₁ = 4.5 mm, r₂ = 4.0 mm, r₃ = 3.5 mm and r₄ = 3.0 mm, and the corresponding widths are w₁ = w₂ = 0.5 mm and w₃ = w₄ = 1.0 mm, and the sizes of resonators are still in the range that the MM concept is still applicable. As previously started, we define 4-donut structures as donut 1 ~donut 4 in compliance with the same numbering set of radii and widths.

 

Fig. 5 Schematics of the proposed structure of MM-A for quad peaks (left) and photos of the fabricated sample (right).

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The black dotted data in Fig. 6 show the simulated [Fig. 6(a)] and the measured [Fig. 6(b)] absorption spectra with α = 0, where α is the angle between the y-axis and the electric field of incident radiation. In the simulation, we can clearly see four absorption peaks at 6.45, 7.4, 9.1 and 11.0 GHz with absorption of 97%, 98%, 98% and 98%, respectively. The experimental results also present multiple peaks at 6.5, 7.4, 9.2 and 11.0 GHz with absorption of 97%, 97%, 98% and 98%, respectively, which indicates that both simulation and experiment are in excellent coincidence. We might ascribe the minor difference between simulation and experiment to the imperfect fabrication which can lead to, for instance, the minute disparity in the width of ring. Compared with [10], the realized absorption peaks are relatively concentrated in a certain frequency range with more number of bands. Any appreciable alternation by varying the polarization of EM wave was not detected, as shown in Fig. 6.

 

Fig. 6 (a) Simulated and (b) measured absorption spectra of quad-peak MM-A according to polarization.

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Figure 7(a) shows the absorption spectra of single-donut structure by varying r, with w = 0.5 mm and p = 16 mm. It is seen that the absorption frequency is inversely proportional to r, but the absorption is not changed, similar to [33]. This is related to the fact that the magnetic-resonance frequency (f_m) of structure is shifted by r without significant change of the intensity $\left(f_m=\text{1}/\left(\text{2}\pi \sqrt{LC}/2\right)\sim 1/r_i\right)$ [34]. The aforementioned donut structures are added one by one to realize the multiple absorption bands. Figure 7(b) presents progress of the combination. When donut 2 was positioned with donut 1 [data for donuts 1 & 2 in Fig. 7(b)], the corresponding 2 peaks appear nearly independently. It was found that the coupling effect of donuts 1 and 2 was enhanced as p decreased (not shown in the Fig.). When p was overly increased to avoid the coupling effect, free-space impedance-matching condition was affected owing to a great reduction of the metal density. We kept adding donuts 3 and 4 into the inside of donuts 1 and 2, respectively [Fig. 7(b)]. Actually, the nested design was mentioned in previous reports with the fact that neighboring edges of inner and outer donuts have antiparallel directions of currents induced by external electric field [10, 35, 36]. By increasing the spacing between them, the coupling effect was reduced and the high-efficiency multi-peaks could be realized [10]. The lacking point here is that the absorption peaks are more dispersed by increasing the gap between concentric donuts. In the structure, the facing edges of inner and outer donuts are influenced owing to the proximity. As shown by the data for donuts 1, 2, 3 & 4 (w₃ = w₄ = 0.5 mm) in Fig. 7(b), 4 absorption peaks are produced, but the absorption of 2 peaks produced by donuts 3 and 4 are below 90% because the donuts in each pair are too close, whereas the resonances of outer donuts seem not to be affected much by the existence of inner elements. Indeed, the antiparallel surface currents on the inner and the outer elements interrupt each other by induced electromotive force. On the other hand, the induced current on the outer element is more intensive than that on the inner one owing to difference in the number of free electrons, and the inner element gets influenced more by the outer one when the coupling happens. Interestingly, when the width of inner donut is increased, the absorption is enhanced together with a blue shift [the data for donuts 1, 2, 3 & 4 (w₃ = w₄ = 1.0 mm) in Fig. 7(b)]. This behavior can be explained by the fact that the increased number of free electrons in the inner donut affects not only the magnitude of induced surface current but also the full-charging time in the edge area, which is related to the capacitance of structure [34]. It was reported that, compared with the anti-parallel surface currents in two metallic-layer structure, the coupling effect between neighboring donuts came to be weaker [10].

 

Fig. 7 (a) Simulated absorption spectra of single-donut structure by varying r, with w = 0.5 mm and p = 16 mm. (b) Absorption spectra for the combination of donuts

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The coupling effect was also noticed, which has space dependence between each resonator. To understand the effect of coupling between the element at the center of unit cell and that at the corner, we simulated the absorption spectra by varying the periodicity. The results were presented in Fig. 8, based on donuts 1 and 2 only. As in Fig. 8(b), for p = 16 mm 2 peaks appear to be independent, similarly to the data for donuts 1 & 2 in Fig. 8(b). When both structures become closer (p = 14 mm), however, not only the absorption but also the resonance frequency are changed, similar to the case of [35]. It means that the MM-A does not have the ideal effective parameters any more for the free-space impedance matching at a certain frequency, even each though individual resonator can perform high absorption. For better understanding, the surface-current distributions were obtained when the central structure was highly excited. Although the main contribution to the low-frequency peak comes from donut 1 due to the larger radius, we are able to detect clearly the surface current of donut 2 induced by donut 1, because of the closeness [Fig. 8(c)]. By increasing the separation between them, the interaction is diminished and the pure resonant mode of each structure appears. If p is outsized to avoid this coupling effect, the periodicity of inner-positioned elements (donuts 3 and 4) is influenced and, in turn, the high multiple absorption peaks are not realized. Therefore, the controlling space between each element should be tuned carefully when the MM-A is designed.

 

Fig. 8 (a) Unit cell only with donuts 1 and 2. (b) Absorption spectra for 2 different p's. (c) and (d) Normalized surface current distributions at low-frequency peak.

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Finally, we examine the dependence of absorption on the incident angle. Figures 9(a) and 9(b) display the dependence of the simulated absorption spectra for the TE and the TM polarizations, respectively. We also measured the dependence for the TE polarization [see Fig. 9(c)]. Due to the experimental limitation, that is, not only fixation of the polarization but also uncontrollable tilting up or down of the receiving horn antenna, we were unable to measure the dependence for the TM polarization. The experimental results agree well with the simulations for the TE polarization. It is evident that the absorption is nearly independent of the incident angle up to 45°. This can be explained by the fact that the position of magnetic-resonance peak is not changed much by increasing the angle of incidence [34]. In the TM mode, minor shifts of the absorption peaks were observed. As the contact area of copper layer by the electric field decreases upon increasing the angle of incidence, it is rather difficult to drive the magnetic resonance. Therefore, the resonance frequency changes slightly, resulting in more change of absorption [34]. Although the suggested parametric conditions of MM-A were selected because of the experimental limitation, if the proportion between the width of donuts and the thickness of FR4 is adjusted carefully, more stable absorption properties would be achieved. In addition, the suggested MM-A can be realized even in the optical range by scaling down.

 

Fig. 9 Dependence of the simulated absorption spectra on incident angle for (a) TE mode and (b) TM mode. (c) The corresponding measured absorption spectra for TE mode.

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4. Conclusions

We have designed and fabricated multi-band MM-As, which consist of a delicate arrangement of donut-shape resonators in different sizes and a metallic background plane, separated by a dielectric. The absorption spectra were measured in the microwave-frequency range and compared with the calculated ones. The agreement between experiment and simulation was good. By employing the delicate arrangement, the absorption of dual-, triple- and quad-peaks turns out to be not only unaffected by the polarization condition of incident EM wave owing to its own symmetry, but also comes to be nearly perfect (higher than 97%). In addition, compared with the previous studies, the realized absorption peaks are relatively concentrated in a certain frequency range with more number of bands. Moreover, the designed MM absorber could achieve the absorption higher than 90% over a wide range of incident angle for both TE and TM polarizations. It was confirmed that the multiple-reflection theory is not suitable for explaining the absorption mechanism of our investigated structure. With simple design and geometrical scalability, the suggested MM absorber might operate at higher frequency with perfect absorption and be modified to reveal other capabilities relevant to the practical applications.