1. Introduction

In the recent years, the metamaterials (MMs) have been the highlighted field for many research groups and scientists in the world. MM is well-known as an artificial material that possesses many unusual electromagnetic (EM) behaviors, and high benefits for practical applications such as sub-diffraction imaging, electromagnetically induced transparency, and invisible cloaking [1–4]. In 2008, by simultaneous optimization of the perfect impedance matching and the fundamental magnetic resonance in the sandwiched-MM structure, the elimination for both reflection and transmission of EM radiation from MM is firstly discovered by Landy et al. [5]. Henceforth, a new branch: metamaterial perfect absorber (MPA) has been intensively raised owing to the fact that it can consume totally energy of incident electromagnetic waves. A new generation of MPA had a thickness of only λ/30, much smaller than the traditional absorbers [6]. Remarkably, the simulated and measured absorptions of their absorber can be reached as A ≈99% and 88% at 11.48 GHz, respectively. By artificially arranging unit-cell structure, moreover, the operational frequency can be selected flexibly from the radio to the optical region [7–15]. Since MPAs have compatibility with peripheral devices, they are becoming to be promising candidates for future devices such as bolometers [16,17], thermal imagers [18,19], solar cells [20,21], and bio-sensors [22–24].

In order to expand the practical-application areas of MPAs, the topics on multi- and/or broadband absorption have been investigated intensively. There are many effective resolutions which have been proposed for enhanced bandwidth of MPA structures, for instance, stacked layers [25,26], resistive films [27], lumped elements [28,29] and multiple resonance resonators [30,31]. For these models, to eliminate reflection, one can tune the effective parameters ε(ω) and μ(ω) of front-patterned resonator to match the effective impedance Z of ambient environment. Otherwise, no transmission can be accomplished by the third layer of a continuous metallic plate, which completely blocks all incident EM waves. Since the ground metallic layer reflects simply all incoming EM waves, it has a passive role in these common MPAs. In this work, we introduce an efficient model to realize wide-band MPA by the active role of the continuous metallic plate, which leads us to the idea of a small, flat and hybrid MPA. By integrating the low-conductivity material on the ground metallic layer (made by perfect conductor), the dual perfect absorption is achieved inside an effective unit-cell size in the microwave band. Moreover, our proposed MPA is expected to satisfy the practical requirements, which demand a wide range of incident angle of the incoming EM wave and the polarization-independent behavior.

2. Structure design, simulation and experiment

The 3-dimensional schematic for a single unit cell (periodicity of a) of planar MPA, which involves three layers (metal-dielectric-metal), is shown in Fig. 1(a). The top meta-surface is designed by two coaxial circular resonators (radii of r₁ and r₂). The ground plate is continuous metallic layer with a circular cutout in the center (diameter of d₀), where low-conductivity material is entirely filled. The optimized geometrical parameters of MPA are a = 20, r₁ = 4.2, r₂ = 6.0, w = 1.4 and d₀ = 2r₀ = 15.0 mm. The dielectric layer (FR-4) has a thickness of t = 0.4 mm. The low-conductivity circular patch (a commercial paste using the conductive polymer, polypyrrole) and metallic layers (copper) have a same thickness of 0.036 mm, and are designed with electric conductivity of σ = 0.015 and 5.8 × 10⁷ S/m, respectively. The key idea of this design is a combination of the optimized meta-surface and lossy interconnects at the bottom MPA in order to enhance the bandwidth of dual-intrinsic resonances in association with perfect impedance matching simultaneously. Figure 1(b) presents the real sample of wide-band absorber. The wide-band MPA is fabricated with a size of 30 mm $\times$ 45 mm $\times$ 0.4 mm, which is large enough to adequately include the main beam of transmitting antenna in the measurement. The meta-surface and the lossy material were precisely fabricated by the printed-circuit-board technique (photolithography and laminate processes).

 

Fig. 1 (a) Three-dimensional arrangement of the unit cell for wide-band MPA with the polarization of EM wave. (b) Fabricated sample and its magnification for the front and the back layers of 2 × 2 unit cells. (b) Illustrated arrangement for the experimental configuration.

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Our simulations were conducted on a commercial software package, CST Microwave Studio [32]. The absorption can be calculated as A = 1 - │S₁₁(ω)│² - │S₂₁(ω)│², where S₁₁ (ω) and S₂₁ (ω) are the reflection and the transmission parameters, respectively. Because the back plane is made by a continuous metallic and lossy-metal materials, S₂₁(ω) = 0, therefore, the absorption is simply expressed as A = 1 - │S₁₁(ω)│². The experiment was performed in a microwave anechoic chamber as shown in Fig. 1(c). The Hewlett-Packard E8362B network analyzer was used for our measurements. In detail, two linearly-polarized microwave standard-gain horn antennas were arranged at an appropriate distance (2.0 m from the sample to the location of two antennas) in order to radiate the incident EM waves and receive the reflected EM waves from the MPA sample for incident angles from 5° to 50°. This range of incident angle was finely established through simultaneously controlling the aperture of two horn antennas and the distance between midpoint of these two antennas to MPA sample.

3. Results and discussions

Basically, the unit cell of sandwiched MPAs can be designed by an electric inductor-capacitor (LC) circuit resonator. For proposed MPA, by optimizing this LC equivalent circuit, the dual-absorption frequency can be approximately adjusted by $f\approx 1/2\pi \sqrt{L_m{C}_m}$(m = 1, 2 corresponding to inner and outer resonant structure, respectively), which is inversely proportional to the square root of total corresponding effective inductance (L_m) and capacitance (C_m) [33–35]. In principle, each effective inductance is strongly depended on shape of resonator while the effective capacitance can be controlled by the coupling between top and bottom layers. For the inner disk (m = 1) and the outer ring (m = 2), respectively, the effective capacitance can be approximately given by:

In case of lossy conductors, for the LC equivalent circuit model, we add a series resistance R to take into account the power loss energies inside the MPA. The mirrored inductances on the continuous metallic layer (L₁, L₂) are inversely depended on the total series resistance (R_m) as follows [36]:

To obtain the perfect absorption, intrinsic resonance inside the MPA is simultaneously required to associate with the perfectly-matched impedance condition,$Z=\sqrt{\mu (\omega )/\epsilon (\omega )}=1$. Based on the reflection and the transmission parameters, the effective impedance can also be given by [37]:

Both extracted real and imaginary parts of the relative impedance are plotted in Fig. 2(a). It is clearly observed that the effective impedance of MPA approaches to be 1.0 and zero for its real and imaginary parts (around 6.5 and 8.2 GHz), respectively. In other words, there is no reflected wave between the MPA and the surrounding environment. This yields wideband absorption over 90% (as shown in orange area) from 5.4 to 9.1 GHz (fractal bandwidth FBW = 51.0%). It is noteworthy that, as reported in the Refs [38,39], when the back layer of MPA is metal completely, only separated and narrow absorption peaks are observed. Therefore, the integrated low-conductivity material in back layer is very important, which enhances the absorption from the separated and narrow peaks to a broadband region. Interestingly, the thickness of MPA are very thin with respect to the operation wavelength: λ/82 (where λ is the smallest resonant wavelength). This value is smaller than those reported in previous works [9–11].

 

Fig. 2 (a) Calculated effective impedance of the proposed MPA. (b) Combination of inner-disk and outer-ring structures resulting in wide-band absorption. The orange area shows the frequency band with an absorption over 90% for the proposed MPA. Distributions of the induced surface currents on front and back layers at resonant frequencies for the same unit cell, which contains only (c) outer ring and (d) inner disk.

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To gain the overall insight of the underlying mechanism of wideband MPA, the dependence of absorption on each resonator is separately investigated in Fig. 2(b)-2(d). It is clearly seen that the wideband absorption spectrum (blue curve) is replaced by single peak at 6.5 GHz (absorption of 98%) or 8.2 GHz (absorption of 85%) in case of outer ring or inner disk structure, respectively. Obviously, due to the appearance of low-conductivity component on the back plate, the bandwidth of absorption spectrum for each case is significantly enhanced (red and green curves) to be wider than the other common MPAs. In detail, those dependences of bandwidth on the loss components (R_m) of LC circuits can be understood by Eqs. (3) and (4). Therefore, it can be concluded that the overlap of two fundamental absorption peaks originates the wide-band absorption. In particular, from the distribution of surface currents in Figs. 2(c) and 2(d), the anti-parallel surface currents, which indicate two magnetic resonances, are induced within the structure constructed from only outer ring and inner disk resonators. In other words, the wideband of good absorption is caused by two magnetic resonances where the perfect impedance matching arises simultaneously at 6.5 and 8.2 GHz.

The dependences simulated absorption frequencies on geometrical components r₀ and t are shown in Fig. 3. When r₀ is increased from 7.0 to 8.0 mm, while other parameters are unchanged, both the low and the high absorption peaks are red-shifted from 6.83 to 5.76 GHz, and from 8.43 to 8.5 GHz, respectively. The slight difference in shifting of these two peaks leads to the change of FBW from 40.5% (at r₀ = 7.0 mm) to 68.7% (at r₀ = 8.0mm). Similarly, in case of varying t from 0.2 to 0.7 mm, while the radius r₀ is fixed to be 7.5 mm, the red-shift also causes more separation between two absorption peaks [Fig. 3(b)]. It can be noted that when we can control the absorption feature of proposed MPA by varying the radius of low-conductivity disk or thickness of dielectric layer, from Eqs. (1)-(3). The increased values of r₀ or t causes the enhancement of total effective inductance or capacitance in the equivalent circuit LC, respectively. These changes originate the red-shift of absorption frequencies as observed in Fig. 3.

 

Fig. 3 Simulated absorption frequencies according to (a) the radius of low-conductivity disk (r_o) and (b) the thickness of FR-4 (t).

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In general, almost the recent wideband MPAs are strongly depend on the incident and polarization angle of the incoming EM wave. To evaluate the preeminent advantage of the proposed MPA, we also explored the dependence of absorption on the incident angle (θ) for both TE and TM polarization as presented in Fig. 4. By changing the incident angle for TE polarization, the simulated absorption spectrum indicates that the FBW = 51% (at θ = 0) is slightly reduced to be 32.8% at θ = 50° [Fig. 4(a)]. In particular, Fig. 4(b) confirms a good agreement for the evolution of measured absorption data of the fabricated sample with the simulated ones. When θ = 50°, the measured absorption reaches over 90% from 5.7 to 9.1 GHz (FBW = 46%). Since θ = 50°, the absorptions are remained to be 90% from 6.07 to 8.41 GHz (FBW = 32.3%). It can be noted that the scattering from imperfections in the fabricated sample and the scattering between the two horn antennas caused by their relatively-large aperture [40], might cause the small deviations between measured and simulated absorption spectra. Interestingly, in case of TM polarization, the simulated FBW is kept increasing to be higher 76% at incident angle up to θ = 50°, as presented in Fig. 4(c).

 

Fig. 4 Performance of the wide-band MPA in wide range of incident angle. (a) Simulated and (b) measured absorption spectra according to the incident angle of EM wave for the TE polarization. (c) Simulated dependence of absorption on the incident angle of EM wave for the TM polarization.

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In particular, by exploiting the symmetrical structure, the MPA exhibits polarization-insensitive properties as shown in Fig. 5. For the normal-incident wave, the simulated wideband absorption spectra are unchanged with respect to polarization angle from 0 to 90°. In other words, the 51%-FBW is conserved for all polarization angles of EM wave as shown in Fig. 5(a). Correspondingly, the measured absorptions were also detected above 90% from 5.7 to 9.1 GHz (FBW = 46%) for the polarization angles of 0, 45° and 90° [Fig. 5(b)]. To be more firm, the influences of polarization angles for some arbitrary incident angles (θ = 20°, 40°, and 50°) are also simulated as in Fig. 6. Although there are slight changes of absorption spectra at high frequencies above 9.5 GHz, the high-absorption region is still polarization-independent for both TE and TM modes. It can be concluded that these Omni-directional wide-band and polarization-insensitive absorption properties ensure the practical capability of the proposed MPA.

 

Fig. 5 (a) Simulated and (b) measured polarization-independent behavior of the wide-band MPA.

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Fig. 6 Simulated polarization-behaviors of the wide-band MPA for incident angles of 20°, 40°, 50° under TE and TM modes.

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4. Conclusions

We have demonstrated the good-absorption features for a new type of thin MPA by combining two fundamental magnetic resonances in the hybrid structure. For the wide-band target, the unit cell of proposed absorber is efficiently miniaturized to be 20 × 20 × 0.4 mm³ (corresponding to periodicity of 0.6λ and thickness of 0.012λ) at 9.1 GHz. By exploiting the high-loss property of low-conductivity material, the FBW of MPA (absorption over 90%) can be practically enhanced to be 46% and entirely stable for a wide range of the incident angle (up to 50°) for TE and TM polarizations. Particularly, wide-band absorption is polarization-independent at the normal incidence of EM wave and nearly polarization-independent at arbitrary one. Thus, we believe that our subwavelength structure is promising candidates to be applied for future meta-devices in the microwave band.