Recoverable Broadband Absorption Based on Ultra-Flexible Meta-Surfaces

Abstract

In this work, we demonstrated a tunable metamaterial perfect absorber (MPA) with broadband absorption by tuning the different states of flexible sandwiched structures (graphene conductive ink/rubber/metallic layers). The broadband absorption spectrum was tuned mechanically by changing the concave-up/down states of flexible hemispherical unit-cells. When the unit-cell was concave-up, our proposed MPAs played as a broadband absorber with a fractal bandwidth (FBW) of 107% (since an absorption over 90% ranges from 5.28 to 17.6 GHz) at the normal incidence; at the same time, this broadband absorption feature could remain well at large incident angles up to 40 deg. and regardless of polarization of the incoming electromagnetic waves. In the case of the concave-down state, a narrow FBW of only 6.8% was noticed. These results could promote great application potential, such as regarding advanced stealth devices, advances in the biomedical and the communication fields, and more.

1. Introduction

More than a decade ago, the challenge of perfect absorption for all incoming electromagnetic (EM) waves was intensively explored by using a structure with sub-wavelength unit-cells, and first produced by Landy et al., in 2008. The structure was artificial and came to be the so-called metamaterial perfect absorber (MPA), in which the effective impedance was controlled flexibly to be equal to that of the surrounding environment, around the electric/magnetic resonances [1]. With the advantages of reduced size, wide adaptability, and increased effectiveness, MPAs have gained much attention and become candidates for many applications, such as emission [2,3], sensing [4,5,6,7,8], wireless communication [9,10], and energy harvesting [11,12,13]. To date, studies on MPAs have been carried out in different frequency regions, including MHz [14,15], GHz [10,16], THz [16,17,18,19], and visible range [20], to yield remarkable advantages of high absorption [21], polarization insensitivity, incident-angle stability [22], multi-/broadband [22,23,24,25,26,27,28], and, especially, the possibility of a switchable absorption bandwidth.

In general, recent tunable MPAs can be constructed only with three-layer (metal–dielectric–metal) or multilayer structures. On the other hand, their bandwidths are hard to tailor for independent cancellation or recovery, since their resonant properties are immutable after fabrication [13,14,15,16,17]; therefore, MPAs are limited in practical applications, especially in the case of smart electronic devices which demand multi-function performance. To overcome this shortcoming, some progress has been achieved in the realization of tunable metamaterials, such as hybridization with functional materials: graphene [29,30], vanadium dioxide (VO₂) [3,31,32], liquid crystals [33,34], and water-based objects [35,36]; however, to control the desired EM properties of MPA, the corresponding external-source activation (electricity, heat, or light) is always required and with strict conditions [37,38,39]; therefore, the mechanical-tuning approach can be effective in adjusting the tailored bandwidth of recent MPAs. For example, Kim et al., proposed a mechanically-actuated frequency-reconfigurable metamaterial absorber in which an air substrate with tunable thickness was applied. When the air substrate thickness was changed from 17 to 26 mm, the peak shifted from 6.96 to 5.79 GHz [40]. Xu et al., also designed stretchable parabolic-shaped metamaterials, and achieved resonant tuning ranges of 0.55 and 0.32 THz by stretching the width and length of the unit-cell [41]. Remarkably, Li et al., demonstrated experimentally a reconfigurable metamaterial for chirality switching and selective intensity modulation. It could be achieved by switching among non-chiral, single-band-chiral, and dual-band-chiral states by a simple folding strategy [42]. It can be noted that, in the latest literature, the tunable/recoverable broadband absorption of MPAs has concentrated mostly on external activation where wide absorption bandwidth, low cost, and ability to construct simple structures without masks are still the challenges; moreover, another limitation is apparent from this experimental confirmation and that is the difficulty of measuring at different modulations owing to the complicated and/or expensive techniques for broadband MPAs.

In this paper, we designed a simple MPA structure which enabled flexible control of EM-wave absorption properties. The proposed MMA was based on a flexible rubber sheet which has hollow hemispheres, arranged periodically. These can be changed from concave-down (CD) to concave-up (CU), and vice versa, simply by injecting different volume ratios of air. A layer of graphene ink was coated on the hollow hemispheres. When they are in the concave-up state, the absorption spectrum becomes broadband, covering the WiMAX/LTE to X band. When all hemispheres are set to be in the concave-down state, the absorption spectrum is changed to show low absorption at low frequencies. These states of recoverable broadband-absorption performance were tested by both simulation and experimentation for different resistivities of graphene ink.

2. Materials and Methods

Figure 1 shows a schematic of the proposed metamaterial absorber in the concave-down and concave-up states. Each unit-cell consists of continuous copper film, a silicone rubber layer, and hemispheres based on graphene ink. The resistivity of graphene ink was chosen to be approximately 100 Ω/sq. at a thickness of t_i = 0.1 mm. The other geometrical parameters are optimized to be a = 20.0, t_r = 0.6, r = 6.2, t_d = 7.4, and t_m = 0.035 mm. The dielectric layer is constructed of silicone rubber, which is ultra-flexible, and easily exchanged between CD and CU, as shown in Figure 1.

The simulation process was carried out by CST software. The unit-cell was set to periodic boundary conditions in the x(H)-y(E) plane, and the z(k) axis was set to be open. To fabricate the recoverable MPA, the rectangular wall of commercial silicon rubber (a size of 12 × 18 unit-cells) was bounded on the continuous copper layer to be concave-down, as in Figure 1b. In order to switch flexibly between CD and CU states for the sample, the air was inhaled or exhaled inside the wall-bound volume with a capacity of 215 cm³.

In simulation, the absorption (A) of CU and CD states can be estimated from the reflectance and transmittance coefficients: R = |S₁₁|² and T = |S₂₁|², A = 1 − R − T = 1 − |S₁₁|² − |S₂₁|². In our structure, due to the continuous copper layer, the transmission is canceled to be zero (T = 0); therefore, the total absorption is estimated as A = 1 − R = 1 − |S₁₁|². From the extracted scattering parameters, the effective impedance for CD and CU states can also be expressed by [15]:

$$Z=\sqrt{\frac{{(1+{\mathrm{S}}_{11}(\omega ))}^2-{\mathrm{S}}_{21}^2(\omega )}{{(1-{\mathrm{S}}_{11}(\omega ))}^2-{\mathrm{S}}_{21}^2(\omega )}}=\sqrt{\frac{{(1+{\mathrm{S}}_{11}(\omega ))}^2}{{(1-{\mathrm{S}}_{11}(\omega ))}^2}}$$

(1)

The recoverable performance for the proposed MPA is evaluated through the fractional bandwidth (FBW):

$$FBW=\frac{2\left(f_{high}-f_{low}\right)}{f_{high}+f_{low}},$$

(2)

where f_low and f_high are denoted as the frequencies at an absorption of 90%. The measured absorption spectra were obtained by using a ZNB-20 Vector Network Analyzer (1–18 GHz), as shown in Figure 1c, where the free-space method was carried through a pair of horn antennae.

3. Results and Discussion

First, we simulated the broadband absorption behavior of the proposed MPA at the normal incidence for the CU state. As shown in Figure 2a, three absorption peaks at 6.6, 14.5, and 16.2 GHz are induced with absorption of 96.0%, 99.7%, and 99.1%, respectively. From Equation (2), a broadband absorption of FBW_CU = 107% is obtained in a frequency range of interest. The effective characteristic impedance is the key quantity to understand the absorption mechanism in metamaterial structures; particularly, to develop the high absorption, the transmission and reflection should be minimized. The first requirement is fulfilled by the back continuous metallic layer, leading to no transmission through the metamaterial. The second requirement is obtained when the impedances of metamaterial and air are similar, leading to no reflection back from the metamaterial. It can be observed that, in Figure 2b, near-perfect impedance matching occurs, since Re[Z] and Im[Z] of the effective impedance tend toward one and zero, respectively, in a range from 5.3 to 17.6 GHz (where absorption is more than 90%); meanwhile, when the meta-surface is switched to be in the concave-down state, the absorption peaks are decreased to below 70%, 86%, and 89%, respectively, owing to impedance mismatching. The value of FBW is also reduced correspondingly to be only 6.8%, as shown in Figure 2a. Second, the results are confirmed experimentally. The measured FBW of 114% (from 4.9 to 18 GHz, in Figure 2a) is recovered from FBW_CD = 6.3% (from 16.9 to 18.0 GHz, in Figure 2a) by changing all unit-cells from the CD to CU state. There are small nonconformities between measured and simulated absorption spectra which might be due to the slightly higher conductivity of graphene ink. This can be changed more or less after the drying progress of fabrication.

To understand the mechanism of recoverable broadband-absorption properties, the distributions of induced surface currents on the graphene-ink and metallic layers were simulated at resonant frequencies of 6.6, 14.5, and 16.2 GHz, as plotted in Figure 3. It can be observed that, in Figure 3a, the top and bottom surface currents at a frequency of 6.6 GHz are anti-parallel. This phenomenon confirms the fundamental magnetic resonance as the common effect [43,44].

Due to the role of the hemispherical shape, the induced surface-current distribution at 16.2 GHz can be regarded as third-order magnetic resonances, as shown in Figure 3c. In other words, the induced currents at the top and bottom surfaces of the structure are mainly divided into three distinct regions and have opposite directions. In particular, the hemisphere structure plays an important role in developing a characteristic lattice resonance (LR) [45,46,47], which is due to the large periodicity of the unit-cell. Consequently, the near-field coupling between the third-harmonic peak and LR results in another absorption peak at 14.5 GHz, as presented in Figure 2a. By merging the fundamental and high/coupling-ordered absorption peaks, the dynamical absorption spectrum is enhanced to be broad, as shown in Figure 2a. This feature is the main difference from flat meta-surface structures [43,44]; thereafter, the surface loss densities for these three absorption peaks, as presented in Figure 3, turn out to be enhanced mostly on the graphene low-conductive ink layer.

In the CD state, as shown in Figure 4a, there are only two absorption peaks that can be activated at 17.7 and 14.0 GHz, which correspond to, respectively, the third-order magnetic resonance and the near-field coupling between third-harmonic peak and LR. These peak positions are shifted slightly to higher frequencies because of the increased effective thickness of the MPA in the CD state. The consumed energy is also dissipated mainly in the hemispherical shape, as revealed by the magnitude of surface loss density in Figure 4b. It can be found that the varying CD and CU states result in canceling or activating the fundamental magnetic resonance; consequently, the recoverable broadband absorption of proposed MPA was triggered by the flexible switching of fundamental magnetic resonances.

In general, the absorption behavior depends strongly on the incident angle of EM waves. As presented in Figure 5, the broadband absorption feature is inversely proportional to the incidence angle in the case of both transverse–electric (TE) and transverse–magnetic (TM) polarization. Obviously, the FBW_CU of 107% remains to be relatively stable while increasing the incident angle up to 40° for the TE and TM modes. When the incident angle becomes more than 50°, the multi-band absorption peaks can be excited because of the mismatched impedance in the area surrounding the strong magnetic resonances, as shown in Figure 5a,b; furthermore, at the normal incidence, the absorption spectra are independent of the polarization angle (the FBW_CU of 107% is conserved for the changed polarization angles from 0° to 45°) by using the symmetric structure of the hollow hemispheres. For the proposed MPA, the CU state well supports the high FBW in a large range of incident angles and in an overall range of polarization angles of incoming EM waves.

4. Conclusions

In this work, we designed and investigated an effective model to recover the broadband absorption feature of MPA by changing the resonant states of flexible unit-cells. Having flexible rubber material as the dielectric layer allows the FWB of the absorption spectrum to be switched flexibly from an FWB_CD = 6.3% to FWB_CU = 114% (in the measurement). In the CU state, the proposed structure exhibited three peaks at 6.6, 14.5, and 16.2 GHz with absorption of 96.0%, 99.7%, and 99.1%, respectively, with a fractional bandwidth of 114%. When the meta-surface was switched to the CD state, there were only two absorption peaks at 17.7 and 14.0 GHz with absorption of 88% and 99%, respectively, and the fractional bandwidth was reduced to 6.3% with an absorption of more than 90% covering from 16.9 to 18.0 GHz. These further results clarify that the induced fundamental/third/coupling-ordered magnetic resonances are the critical mechanism in the proposed structure. This surface-control technique can be effective for large incidence and various polarization angles of EM waves; furthermore, these obtained results are useful for relevant potential or immediate applications, such as telecommunication filters, sensors/detectors, and energy harvesters.