1. Introduction

Near-perfect absorption is a budding field in metamaterial (MM) studies. Since Landy et al. proposed MM absorber [1] to obtain near unity absorption (A(ω)), the design, analysis and experiment of MM absorber have attracted increasing attention [2–7]. MM absorber is constructed by two portions: the metallization and the dielectric. The role of the metallization is well known to provide necessary resonant elements, also to consume energy due to the existing of the imaginary part of the metal’s permittivity. The influence of the dielectric is considered to arise from the real part (Re(ε _d)) of its permittivity. It is well analyzed that Re(ε _d) can modulate the capacitance of the resonant system [4] in MM absorber. This modulation changes the magnetic response, resulting in variation of A(ω). While, the influence of the imaginary part (Im(ε _d)) of the dielectric on the resonant system has not been fully investigated. Partly because the main function of Im(ε _d), in previous works [1–4], is only understood as a source to introduce loss. In this paper, a MM is proposed to achieve near 100% A(ω). The microwave experiments in a full absorption environment are carried out, showing minimum transmission (T(ω)) and reflection (R(ω)) at the same frequency. Compared with simulated results, a slight larger R(ω) is observed in experiments, which is also noticed in previous work, but not fully analyzed [4]. The parametric investigation shows that Im(ε _d) of the dielectric is the primary contributor to the mismatch. We find out that the absorption increases to near unity when Im(ε _d) increases from zero to an optimum value, but decreases to a constant when Im(ε _d) is further increased. By investigating the effective electromagnetic parameters, we figure out the unexpected variation is dominated by the dependence of the electric and magnetic resonances on Im(ε _d). This result demonstrates that Im(ε _d), not only has responsibility for the loss in MM absorber, but also has influence on the strength of the electric and magnetic resonances in MM absorber.

2. Structure and experimental results

Figure 1(a) shows the elementary cell of the MM absorber which includes two metallic elements: a top split-cut-wire and a bottom cut-wire. The double cut-wires design is analogous with the conventional cut-wire pair [8,9]. The metallic portion is copper with conductivity of 5.8 × 10⁷ S/m. CST microwave studio (CST 2006B) was used to theoretically investigate the proposed MM absorber. Figure 2(a) shows the optimum results. T(ω) and R(ω) are simultaneously suppressed to near zero at 4.87GHz, which result in A(ω) about 98.6% (A(ω) = 1-T(ω)-R(ω)). In simulations, the metal has standard thickness of 0.035 mm. The substrate is set to be FR4 board with standard thickness of 0.53 mm and measured permittivity of 4.1 (between 4 and 6GHz, the imaginary part cannot be accurately detected in a large area due to the limitation of our microwave measurement’s precision) to keep consistent with the following experiments. The optimum results are obtained when Im(ε _d) of FR4 board is set to be 0.03 and MM absorber has the dimensions of: P _y = 16 mm, P _x = 32 mm, w = 8 mm, l = 30 mm and d = 1 mm.

 

Fig. 1 (Color online) (a) Schematic drawing of the unit cell, the inset shows the polarization direction of the incident wave. Different incident directions are realized by tuning the angle (θ). (b) and (c) Top and bottom structures of the sample used in experiments, respectively.

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Fig. 2 (Color online) (a) Measured and simulated spectra of the MM absorber. Standing waves are observed in the spectra. (b) Absorption with different incident angles. The solid curve and the discrete red dots represent the simulated and measured results, respectively. The inset demonstrates the method used in the reflection measurement. The normal R(ω) is approximated by the oblique R(ω) with a small angle (θ = 5 degree).

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To experimentally verify the performance of the MM absorber, the sample is fabricated as following way: FR4-S1141 circuit board is chosen to be the substrate. The top and bottom metallic structures are respectively printed on the two sides of the board, as shown in Fig. 1(b) and (c). The geometric parameters of the sample are same with that used in simulations (smaller than 0.005 mm error, little influence is observed). In experiments, two microwave horns are used as the transmitting and receiving ports. Both horns have the same cross section of 109.3 × 54.8 mm², the same effective frequency band from 4.05 to 5.99 GHz and the same vertical polarization direction. A vector network analyzer (AV3629) is utilized as an electromagnetic wave source to produce microwaves in the range of 4 to 6 GHz. The sample is placed in such way as shown in Fig. 1(a) to realize the effective electromagnetic responses. The distance between the transmitting\receiving horn and the sample is set to be 500 mm, which is a long enough space to obtain the near plane wave radiation. All equipments are located into an environment decorated with high absorption materials around, whose ability reaches −38 dB to eliminate the influence of the unwanted scattering. T(ω) and R(ω) are obtained by measuring the complex S(ω) parameters, including S ₂₁(ω) and S ₁₁(ω), of the sample.

The experimental results (T(ω) = |S ₂₁(ω)|² and R(ω) = |S ₁₁(ω)|²) are also shown in Fig. 2(a). It can be observed that a sharp R(ω) drop about −13 dB (linear value 5%) and a T(ω) drop about −28 dB (linear value 0.16%) simultaneously exist at the same frequency (4.87GHz), which result in a high A(ω) about 94.84%. While there exists an obvious disagreement between the simulated and measured results, especially the two R(ω) values at 4.87GHz, although the frequency point in experiments matches well with that in simulations. This disagreement also exists when incident wave is oblique. The simulated A(ω) decreases when the incident angle changes from 5 to 60 degree as shown in Fig. 2(b). The measured values have the analogous behavior, but are always smaller than the simulated ones.

3. Discussions

In experiments, all measurable parameters are the same with those in simulations. While, due to the limitation mentioned above, Im(ε _d) is the uncertain parameter. Thus, in our opinion, it may be the major contributor to the disagreement between simulations and experiments. Figure 3 show the simulated influence of Im(ε _d) on A(ω). The absorption has two different behaviors: a rapid enhancement and a gradual decrease. First, It can be seen that only 21.5% energy is absorbed when Im(ε _d) ideally equals to zero (the dielectric is absolutely lossfree). All absorbed energy is consumed in metal. Then, the absorption is rapidly enhanced to a maximum value 98.6% when Im(ε _d) increases from zero to 0.03. Second, the absorption gradually decreases to a constant about 27% when Im(ε _d) is further increased. In the two distinct situations, both larger (0.05) and smaller (0.02) value of Im(ε _d) can suppress the simulated absorption to match well with the measured value. It can be easily understood that a larger Im(ε _d) produces a larger loss in dielectric, resulting in good performance of the MM absorber. While the unexpected point is the falling down of the absorption when Im(ε _d) exceeds over the optimum value. It means that larger Im(ε _d) does not always imply more loss in the dielectric and higher absorption. There exists the additional influence of Im(ε _d) on the MM absorber.

 

Fig. 3 (Color Online) (a) Absorption with different Im(ε _d) of the dielectric. The inset shows the amplified picture marked by the blue rectangle.

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In order to figure out the additional influence, we analyze the electromagnetic parameters, including the effective permeability (μ) and permittivity (ε), of the MM absorber. Figure 4 show the retrieved real parts of μ and ε (Re(μ) and Re(ε)). Two variations of Re(μ) and Re(ε) are observed. First, the oscillation of Re(μ) is very large when Im(ε _d) equals to zero, which indicates the strongest magnetic response. Then it is suppressed with increasing Im(ε _d), and finally disappears when Im(ε _d) equals to 0.13. This result demonstrates that the strength of the magnetic resonance in the MM absorber is much influenced by Im(ε _d) when other relevant parameters are constant. In fact, in the magnetic resonance supported by the cut-wire structures, the participation of the bottom cut-wire into the magnetic resonance is gradually restricted when Im(ε _d) increases, even fully eliminated when Im(ε _d) has a big enough value, such as 0.13. Thus, although both the magnetic resonant elements and outside source exist, the magnetic resonance is fully turned off. Likewise, the oscillation of Re(ε) is also tuned by Im(ε _d), which indicates the influence of Im(ε _d) upon the electric resonance supported by the spilt-cut-wire. This behavior is analogous with the dynamical electric response realized by an active control over the dielectric in MM [10,11].

 

Fig. 4 (Color online) Variations of Re(μ) and Re(ε) of the MM absorber with increasing Im(ε _d).

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Additionally, Re(μ) and Re(ε) come closer when Im(ε _d) increases from zero to 0.03. This indicates the impedance of the MM absorber is closer to unity. Especially, Re(μ) and Re(ε) have the same values in the range of 4.8 to 4.9 GHz when Im(ε _d) equals to 0.03, which indicates impedance matching between the MM absorber and the outside space.

The dependence of the MM absorber’s electromagnetic responses on Im(ε _d) can also be seen in the T(ω) and R(ω) spectra with different Im(ε _d), as shown in Fig. 5 . The T(ω) drop gradually disappears when Im(ε _d) increases. It indicates that stronger magnetic resonance brings deeper T(ω) drop. If there is no magnetic resonance, then no T(ω) drop is observed. R(ω) has a minimum when Im(ε _d) equals to 0.03. However, the impedance of the MM absorber is mismatched again when Im(ε _d) gradually moves away from 0.03, resulting in the increasing R(ω) as shown in Fig. 5(b).

 

Fig. 5 (Color online) (a) Transmission and (b) Reflection spectra with increasing Im(ε _d).

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At the end of the paper, as a necessary supplement, we discuss the energy into MM absorber. In other MM absorber which utilizing localized or un-localized surface plasmon (SP) coupling [6,7,12], almost all absorbed energy is consumed in metal. Figure 6 compares the two absorption rates of the proposed MM absorber when dielectric is lossy (Im(ε _d) = 0.03) and lossfree (Im(ε _d) = 0), respectively. It shows that about 77% energy is collected and consumed in dielectric when the MM absorber has maximum absorption. Thus, compared with the absorber based on SP coupling, the large dielectric absorption indicates the potential advantage of the MM absorber in some domains where energy needs to be collected by dielectric.

 

Fig. 6 (Color online) Absorption spectra when Im(ε _d) equals to 0.03 and zero. About 77% energy is consumed in dielectric.

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4. Conclusions

In conclusion, a design of MM absorber constructed by cut-wire structures is theoretically and experimentally presented in this paper. An obvious mismatch is found between the measured and simulated absorption. This phenomenon is explained by investigating the role of the imaginary part of the dielectric in absorber. Our results show that the imaginary part of the dielectric has considerable influence on the resonant system in MM absorber. It not only behaves as a source to introduce loss, but also is seen as an effective element which can be utilized to tuning the strength of the electric and magnetic resonances. Our results are helpful to analyze the maximization of the MM absorber’s ability in capturing electromagnetic energy.