# Ultra-wideband and Polarization-Insensitive Perfect Absorber Using Multilayer Metamaterials, Lumped Resistors, and Strong Coupling Effects

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## Abstract

We theoretically and experimentally proposed a new structure of ultra-wideband and thin perfect metamaterial absorber loaded with lumped resistances. The thin absorber was composed of four dielectric layers, the metallic double split ring resonators (MDSRR) microstructures and a set of lumped resistors. The mechanism of the ultra-wideband absorption was analyzed and parametric study was also carried out to achieve ultra-wideband operation. The features of ultra-wideband, polarization-insensitivity, and angle-immune absorption were systematically characterized by the angular absorption spectrum, the near electric-field, the surface current distributions and dielectric and ohmic losses. Numerical results show that the proposed metamaterial absorber achieved perfect absorption with absorptivity larger than 80% at the normal incidences within 4.52~25.42 GHz (an absolute bandwidth of 20.9GHz), corresponding to a fractional bandwidth of 139.6%. For verification, a thin metamaterial absorber was implemented using the common printed circuit board method and then measured in a microwave anechoic chamber. Numerical and experimental results agreed well with each other and verified the desired polarization-insensitive ultra-wideband perfect absorption.

## Keywords

Metamaterial absorbers Polarization Subwavelength structures Ultra-wideband## Abbreviations

- EM
Electromagnetic

- MDSRR
Metallic double split ring resonators

- PBCs
Periodic boundary conditions

- PMA
Perfect metamaterial absorber

- SRR-I
Split ring resonator-I

- SRR-II
Split ring resonator-II

- TE
Transverse electric

- TEM
Transverse electromagnetic

- TM
Transverse magnetic

## Background

As an artificially engineered material, metamaterial has attracted significant interest because it exhibited fantastic electromagnetic properties unusual or difficult to obtain over the last decade [1, 2, 3]. With the rapid development, metamaterial with dynamical mass anisotropy has been applied to develop acoustic cloaks, hyperlenses, perfect absorbers, gradient index lenses [4, 5, 6, 7], metalense, optofluidic barrier, polarization convertor, etc. [8, 9, 10, 11, 12, 13, 14, 15, 16]. In particular, the perfect metamaterial absorber (PMA) with ultrathin profile and near-unity absorption was firstly proposed by Landy et al. [6]. Relative to conventional absorbers, metamaterial absorber, which offers great benefits of thin profile, further miniaturization, increased effectiveness, and wider adaptability, has become promising applications of metamaterials. Later, researchers make several efforts on PMA to achieve wide incident angle absorption [17, 18, 19], multi-band absorption [20, 21], polarization-insensitive absorption [22, 23, 24], and the tunable absorption [25, 26]. However, absorbers with narrow bandwidth limit their applications in practice. Hence, it is necessary to design the ultra-broadband, polarization-insensitive, and thin metamaterial absorber.

To increase the absorption bandwidth, several methods such as by using the multi-resonance mechanism [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], the fractal structures [39], the multilayer [40, 41, 42, 43, 44], the magnetic medium [45, 46], and loading the lumped elements [47, 48, 49] have been proposed in the design of gigahertz and terahertz metamaterial absorbers. For instance, a broadband polarization-insensitive perfect absorber exhibiting a bandwidth of 9.25 GHz has been designed in a single layer based on the double octagonal-ring metamaterials and lumped resistances [50]. Additionally, a gigahertz perfect metamaterial-inspired absorber was proposed which was composed of three-layer substrates, double split-serration-rings, and a metal ground [51]. Although a relative bandwidth of 93.5% was obtained, the absorption bandwidth is still insufficient for applications, such as electromagnetic protection, stealth, and electronic warfare.

Different from the previous metamaterial absorbers, we proposed a thin and ultra-wideband perfect metamaterial absorber by combining the resonant and resistive absorptions using strong coupling effects. The absorber was composed of four dielectric layers, two metallic double split ring resonators (MDSRR) and several lumped resistors. The characteristics of polarization-insensitive and wide-incident absorption had been verified both numerically and experimentally. This perfect metamaterial absorber is promising for many practical applications such as radar cross scatter reduction, stealth, and electromagnetic protection in different flight platform.

## Methods

*d*

_{1},

*d*

_{2},

*d*

_{3}, and

*d*

_{4}. The dielectric constant and the tangent loss angle of the residual substrates are all 4.2 and 0.02 (ε

_{r}= 4.2, tanδ = 0.02) respectively. As given in Fig. 1(d), the first MDSRR (F-MDSRR) microstructure with four lumped resistances is on the second substrate. The metallic split ring resonator-I (SRR-I) and split ring resonator-II (SRR-II) are respectively on the third and bottom substrate which make up the second metallic DSRR (S-MDSRR) microstructure. The F-MDSRR and S-MDSRR microstructures are copper with the conductivity of 5.8 × 10

^{7}S/m and thickness of 0.036 mm. The length of the meta-atom for the proposed PMA is

*P*= 8.4 mm. As shown in Fig. 1 (b) and (c), the lengths of SRR-I and SRR-II are

*a*

_{1}and

*a*

_{2}. Their widths are

*w*

_{1}and

*w*

_{2}. The lengths and widths of F-MDSRR, as given in Fig. 1(d), are represented by

*a*

_{3},

*a*

_{4},

*w*

_{3}, and

*w*

_{4}. The resistances loaded on the inner and outer split rings are denoted by

*R*

_{1,2}and

*R*

_{3,4}. And

*s*denotes the length of the splits for F-MDSRR and S-MDSRR. The proposed PMA is designed, analyzed, and optimized in simulation. A full-wave electromagnetic simulation is performed by using the finite-element analysis-based ANSYS Electro-magnetics Suite 15.0. The proposed absorber is simulated and optimized with parameters of

*d*

_{1}= 2 mm,

*d*

_{2}=

*d*

_{3}= 1 mm,

*d*

_{4}= 1 mm,

*w*

_{1}=

*w*

_{2}=

*w*

_{3}=

*w*

_{4}= 0.8 mm,

*P*= 8.4 mm,

*R*

_{1,2}= 60 Ω,

*R*

_{3,4}= 180 Ω,

*a*

_{1}= 7.8 mm,

*a*

_{2}= 6.6 mm,

*a*

_{3}= 5 mm,

*a*

_{4}= 3.4 mm, and

*s*= 1.2 mm.

*A*(

*f*), we could minimize the transmission

*T*(

*f*) (

*T*(

*f*)

*= |S*

_{21}

*|*

^{2}) and the reflection

*R*(

*f*) (

*R*(

*f*)

*= |S*

_{11}

*|*

^{2}) simultaneously. The absorptivity could be calculated by

*A*(

*f*) = 1 −

*R*(

*f*) because the presented PMA was blocked by the metallic plate without patterns on the bottom layer (so the transmission was zero,

*T*(

*f*)

*= |S*

_{21}

*|*

^{2}= 0). Hence, the absorptivity of the presented PMA could be calculated by

*A*(

*f*) ≈ 100%) when the reflection is close to zero (

*R*(

*f*) ≈ 0). It is necessary to note that the S

_{11}components include the reflection of co-polarized EM waves and the reflection of cross-polarized EM waves [56, 57, 58]. So the

*S*

_{11}components can be expressed as:

*xx*and

*xy*denote the co-polarization and cross-polarization. In the proposed PMA design, the

**|***S*

_{11}

*comprises the components of the co-polarization and the cross-polarization. Furthermore, the reflection of PMA at normal incidence is given by [6, 21]:*

**|***η*

_{0}, about 377 Ω, represents the free space impedance.

*z*

_{eff}(

*f*) is the effective impedance of PMA. The effective impedance includes the lumped resistances in proposed PMA, the surface impedance which is to obtain a large resonant dissipation and the substrate impedance due to the high tangent. By substitution of (5) in (4), the absorptivity

*A*could also be written by:

*z*

_{eff}(

*f*)] and Im [

*z*

_{eff}(

*f*)] are respectively the real part and the imaginary part of

*z*

_{eff}(

*f*). When the proposed PMA is at the resonant modes, the absorption is near to one (

*A*= 1). From the expression of (6), we know that when

*A*= 1, Re [

*z*

_{eff}(

*ω*)] and Im [

*z*

_{eff}(

*ω*)] can be calculated as:

It is found that the absorption is close to 100%, when the real part and imaginary part of the effective impedance are respectively close to 377 Ω and 0. The absorptivity is enhanced because of the different resonant modes. Generally, the excellent absorption could be obtained as the effective permittivity was equal to effective permeability. So the broadband absorption would be achieved by modulating the effective parameters.

The ultra-wideband metamaterial absorber was simulated by employing the commercial software, Ansoft High Frequency Structure Simulator (HFSS 18.0), which was based on the finite-element analysis method. In the calculation, a plane electromagnetic wave with the electric field along the direction of *x*-axis was used as the incidences, which was perpendicularly irradiated to the resonance structure along the direction of the *z*-axis (shown in Fig. 1). The frequency range from 1.0 to 30 GHz of the incidences had been used in simulation. The size of the incidences should be slightly larger than that of the presented period of the structure; at the same time, enough simulation times and the suitable boundaries (periodic boundaries in directions of *x*- and *y*-axis and perfectly matched layers in direction of *z*-axis) should be utilized for ensuring the accuracy of calculation results.

## Results and Discussion

*S*

_{11}, absorption, effective impedance, and reflection components of the cross-polarization from 1 to 30 GHz are shown in Fig. 2. As shown in Fig. 2a, it can be seen that the proposed PMA exhibited ultra-broadband lower reflection from 4.5 to 25.5 GHz than that of the PMA using the same microstructure without lumped resistances. Especially, the differences between the microstructure with and without lumped resistances were evident from 9 to 14 GHz and from 19 to 21 GHz. In Fig. 2b, we could see that the ultra-broadband absorption from 4.52 to 25.42 GHz with absorptivity larger than 80% could be obtained for the proposed PMA and the absorption would deteriorate for proposed microstructure without lumped resistances obviously. The real and imaginary parts of effective impedance were respectively close to 377 Ω and 0 for the proposed PMA at the resonance frequency of 5.13, 14.49, 19.05, 20.77, and 25.42 GHz in Fig. 2c. The more the absorptivity near to 100%, the more the real and imaginary parts of effective impedance were respectively close to 377 Ω and 0. From Fig. 2d, the reflection components of cross-polarization were about zero for the proposed absorber from 1 to 30 GHz. It was necessary to note that the reflection components

**|***S*

_{11,xy}

**|**^{2}of cross-polarization was about 0.35 at 2.8 GHz for the proposed microstructure without lumped resistances. This phenomenon was caused by the unsymmetrical structure and the weak resonator modes at the frequency. Therefore, the lumped resistances were important for the ultra-broadband PMA design. From Fig. 2b, d, the real part and imaginary part of the effective permittivity were respectively approximated to that of the effective permeability for the proposed PMA from 4.52 to 25.42 GHz. The imaginary part of refractive index was more than zero in this band. Consequently, the ultra-broadband can be exhibited for the presented PMA.

A parametric study was carried out by ANSYS HFSS Solver. In this study, it was main objective to achieve ultra-broadband absorption. According to this goal, some parameters of the lumped resistances *R*_{1,2} and *R*_{3,4} in the inner and outer split rings, the cell length *P* of the PMA, the length *s* of the splits for F-MDSRR and S-MDSRR, the thickness *d*_{1} of the antireflection coating substrate, and the thickness *d*_{2} were selected in the study.

*R*

_{1,2}= 50 Ω, 60 Ω, 100 Ω, 150 Ω. By adopting

*R*

_{1,2}, the absorption was improved obviously from 19 to 25 GHz. While as

*R*

_{1,2}shifted from 50 to 150 Ω, the lumped resistances had slightly effect on absorption in low frequency. Hence, by selecting a proper value for

*R*

_{1,2}= 60 Ω, the proposed PMA obtained the ultra-broadband absorption. As shown in Fig. 3b, the

*R*

_{3,4}mainly affected the absorption in the range of 6~17 GHz and 21~23 GHz. For wideband absorption,

*R*

_{3,4}was chosen to be 180 Ω. The length was another critical parameter. The case with different lengths of PMA cell and splits in for F-MDSRR and S-MDSRR was studied. Figure 3c shows that the absorption from 21 to 25 GHz was very sensitive to the length

*P*of PMA cell. To achieve wideband absorption, we selected

*P*= 8.4 mm. In Fig. 3d, it was clear that the PMA had wideband absorption at low frequency and the bandwidth was influenced by

*s*which was shifted from 0.6 to 1.5 mm. According to the standard of absorptivity more than 0.8,

*s*= 1.2 mm was selected to obtain wideband absorption for the proposed PMA. The effects of the antireflection coating substrate thicknesses

*d*

_{1}are illustrated in Fig. 3e. It was obvious that the thickness

*d*

_{1}influenced the wideband absorption from 7 to 30 GHz and

*d*

_{1}= 2.0 mm was chosen for broadband PMA design. The absorption results with different

*d*

_{2}are given in Fig. 3f. It was clear that

*d*

_{2}was the key parameters for wideband PMA in high frequency. To achieve the ultra-broadband absorption, the optimized

*d*

_{2}of 1.0 mm was selected in PMA design.

From Figs. 2 and 3, it could be seen that the absorption bandwidth of the proposed PMA was sensitive to the thicknesses of *d*_{1} and *d*_{2}, and the values of lumped resistances. Moreover, the splits in the F-MDSRR and S-MDSRR were necessary for achieving the wideband absorption in our design. Hence, the thicknesses and the lumped resistances needed to be optimized for ultra-broadband absorption.

*A*

_{1},

*A*

_{2},

*A*

_{3},

*A*

_{4},

*A*

_{5},

*A*

_{6},) near to the origin point with strong density. These physical phenomena were all illustrated by the coupling effects and high-order modes for the proposed ultra-broadband PMA. Consequently, the coupling effects between the different microstructures and the high-order modes were the crucial component to design the broadband PMA.

*R*

_{34}was distinctly more than that of

*R*

_{12}at 5.13 GHz. The difference would decrease at 14.49 GHz. At 19.05 GHz and 20.77 GHz, the VLD of

*R*

_{34}was faintly less than that of

*R*

_{12}. When it was 25.42 GHz, the volume loss densities of

*R*

_{34}and

*R*

_{12}were both less than that of other frequencies. It was obvious that the ohmic losses with the range from 1 × 10

^{5}w/mm

^{3}to 1 × 10

^{7}w/mm

^{3}were more than the dielectric losses with the range from 100 w/mm

^{3}to 1 × 10

^{7}w/mm

^{6}. Consequently, the ohmic and dielectric losses were important for this proposed ultra-broadband absorber from Figs. 3(e) and (f) and 7.

### Fabrication and Measurement

*ε*

_{r}= 4.2 and tanδ = 0.02) with thickness of 2 mm, 1 mm, 1 mm, and 1 mm. Two linearly polarized standard-gain horn antennas as the transmitter and receiver were connected to the Agilent Vector Network Analyzer (VNA, N5230C). To eliminate the interference of environment, the function of time-domain gating in the Network Analyzer was adopted in experiments. The devices were placed vertically in the center of a turntable to ensure that the EM wave could be similar to a plane wave on the front of device. The distance between the antennas and the devices under test satisfied the far-field condition.

*θ*) shifted from 0 to 45°. The measured results illustrated that the angular absorption decreased sluggishly as the incident angle increased from 0 to 45° in the

*x*- and

*y*- polarized incidences. When the incident angle was zero (

*θ*= 0), the ultra-broadband absorption from 4.48 to 25.46 GHz could be achieved with absorptivity larger than 80% not only in

*x*-polarized incidence but also in

*y*-polarized incidence. Moreover, when the incident angle was 45°, the relative bandwidth of 136%, from 4.76 to 25.03 GHz, would be obtained with absorptivity larger than 60% for

*x*- and

*y*-polarized incident waves. From Fig. 9a, b, it was obvious that the absorptions in

*x*-polarized incidences were same with that in

*x*-polarized incident waves. Hence, the characteristic of polarized-insensitivity were exhibited for the proposed PMA. It was necessary to note that the absorption would exacerbate for the oblique incidence, especially with the incident angle of 45°. To improve angular absorption, the stereometamaterial structure and the substrate integrated cavity could be the beneficial candidate [22, 35]. Compared with Figs. 2(b), 6 and 9, it was clear that the experimental results agreed well with the simulated results and the presented PMA exhibited the ultra-broadband, polarized-insensitivity, and wide-incident absorption.

## Conclusion

In conclusion, we have proposed, designed, and fabricated an ultra-wideband perfect metamaterial absorber with polarized-insensitivity and wide-incident absorption. The angular absorption spectrum, surface current, and near electric-field distributions were explored to validate the excellent characteristics of the proposed perfect metamaterial absorber with strong coupling effects. The fabricated metamaterial absorber device was fabricated, measured, and analyzed. The experimental results indicated that the ultra-broadband absorption from 4.48 to 25.46 GHz could be achieved with absorptivity larger than 80% with normal incidences for *x*-polarization and *y*-polarization. For the oblique incidences with the incident angle of 45°, the perfect metamaterial absorber exhibited the relative bandwidth of 136% with absorptivity larger than 60% for different polarized incidences. This perfect metamaterial absorber device with the innovation is promising for many practical applications such as radar cross scatter reduction and electromagnetic protection in different flight platform.

## Notes

### Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61501494, 61471389, 61671464, and 61701523, in part by the Natural Science Foundational Research Fund of Shaanxi Province under Grant No. 2017JM6025, in part by the Young Talent fund of University Association for Science and Technology in Shaanxi, China (No.20170107), in part by the Key Program of National Natural Science Foundation of Shaanxi Province under grant No.2017KJX-24, National Defense Foundation of China (2201078), and Aviation Science Foundation of China under No. 20161996009. They also thank the reviewers for their valuable comments.

### Availability of Data and Materials

All date are fully available without restriction.

### Authors’ Contributions

SJL conceived the research and wrote the manuscript. PXW, YLZ, and JFH conducted the simulations and analyses. HXX, XYC, and LMX supervised the whole work. CZ and HHY completed the whole measurement and assisted in processing the data and figures. All authors read and approved the final manuscript.

### Competing Interests

The authors declare that they have no competing interests.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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