 Nano Express
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Ultrawideband and PolarizationInsensitive Perfect Absorber Using Multilayer Metamaterials, Lumped Resistors, and Strong Coupling Effects
Nanoscale Research Letters volume 13, Article number: 386 (2018)
Abstract
We theoretically and experimentally proposed a new structure of ultrawideband 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 ultrawideband absorption was analyzed and parametric study was also carried out to achieve ultrawideband operation. The features of ultrawideband, polarizationinsensitivity, and angleimmune absorption were systematically characterized by the angular absorption spectrum, the near electricfield, 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 polarizationinsensitive ultrawideband perfect absorption.
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 nearunity 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], multiband absorption [20, 21], polarizationinsensitive 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 ultrabroadband, polarizationinsensitive, and thin metamaterial absorber.
To increase the absorption bandwidth, several methods such as by using the multiresonance 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 polarizationinsensitive perfect absorber exhibiting a bandwidth of 9.25 GHz has been designed in a single layer based on the double octagonalring metamaterials and lumped resistances [50]. Additionally, a gigahertz perfect metamaterialinspired absorber was proposed which was composed of threelayer substrates, double splitserrationrings, 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 ultrawideband 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 polarizationinsensitive and wideincident 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
The metaatom of proposed ultrawideband PMA consists of four dielectric layers, double metallic DSRR microstructures, and the lumped resistances in Fig. 1. To obtain the destructive interference, the top (first) dielectric spacer with a dielectric constant of 4.4 and a tangent loss angle of 0.02 is required as an antireflection coating substrate to enhance absorption bandwidth. The thicknesses of the four dielectric layer are 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 (FMDSRR) microstructure with four lumped resistances is on the second substrate. The metallic split ring resonatorI (SRRI) and split ring resonatorII (SRRII) are respectively on the third and bottom substrate which make up the second metallic DSRR (SMDSRR) microstructure. The FMDSRR and SMDSRR microstructures are copper with the conductivity of 5.8 × 10^{7}S/m and thickness of 0.036 mm. The length of the metaatom for the proposed PMA is P = 8.4 mm. As shown in Fig. 1 (b) and (c), the lengths of SRRI and SRRII are a_{1} and a_{2}. Their widths are w_{1} and w_{2}. The lengths and widths of FMDSRR, 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 FMDSRR and SMDSRR. The proposed PMA is designed, analyzed, and optimized in simulation. A fullwave electromagnetic simulation is performed by using the finiteelement analysisbased ANSYS Electromagnetics 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.
To explore the absorption mechanism for the proposed ultrawideband PMA, the periodic boundary conditions (PBCs) and Floquet port were applied to simulate the infinite periodic cells. The electromagnetic (EM) wave would be gradually absorbed by the absorber according to the antireflection conditions. Both magnetic and electric resonances would be independently aroused, which could confine the wave into the PMA cell. The wave could be gradually absorbed by the dielectric loss. It could achieve that the magnetic permittivity equaled to the electric permittivity, resulting in the perfect absorptivity for incident EM waves. In more direct perspective, absorptivity was defined as [52,53,54,55]
In order to maximize absorptivity 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
From the Eq.(2), it is obvious that the absorption is near to 100% (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 copolarized EM waves and the reflection of crosspolarized EM waves [56,57,58]. So the S_{11} components can be expressed as:
Accordingly, based on the Eq.(3), the Eq.(2) could be evaluated by
where the xx and xy denote the copolarization and crosspolarization. In the proposed PMA design, the S_{11} comprises the components of the copolarization and the crosspolarization. Furthermore, the reflection of PMA at normal incidence is given by [6, 21]:
where 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:
where Re [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 ultrawideband metamaterial absorber was simulated by employing the commercial software, Ansoft High Frequency Structure Simulator (HFSS 18.0), which was based on the finiteelement analysis method. In the calculation, a plane electromagnetic wave with the electric field along the direction of xaxis was used as the incidences, which was perpendicularly irradiated to the resonance structure along the direction of the zaxis (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 yaxis and perfectly matched layers in direction of zaxis) should be utilized for ensuring the accuracy of calculation results.
Results and Discussion
The simulated amplitude of S_{11}, absorption, effective impedance, and reflection components of the crosspolarization from 1 to 30 GHz are shown in Fig. 2. As shown in Fig. 2a, it can be seen that the proposed PMA exhibited ultrabroadband 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 ultrabroadband 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 crosspolarization 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 crosspolarization 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 ultrabroadband 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 ultrabroadband 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 ultrabroadband 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 FMDSRR and SMDSRR, the thickness d_{1} of the antireflection coating substrate, and the thickness d_{2} were selected in the study.
Figure 3a shows the simulated absorption, when the proposed PMA adopted the lumped resistances of 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 ultrabroadband 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 FMDSRR and SMDSRR 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 ultrabroadband 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 FMDSRR and SMDSRR were necessary for achieving the wideband absorption in our design. Hence, the thicknesses and the lumped resistances needed to be optimized for ultrabroadband absorption.
To explore the mechanism for ultrabroadband absorption, the surface current distributions and the near electric fields distributions of the PMA had been given in Fig. 4 at the resonance frequency of 5.1, 14.5, 19.1, 20.8, and 25.4GHz. The exquisite resonance absorbing effect in Fig. 4a had been exhibited which were primary attributed to the SRRI for SMDSRR microstructure and the outer split rings for FMDSRR microstructure at 5.13 GHz. The strong coupling between the SMDSRR and FMDSRR microstructures leaded to the resonance absorption. From Fig. 4c, it could be seen that the absorption peak at 14.49 GHz for proposed absorber would be obtained due to the FMDSRR microstructure with four lumped resistances and the strong coupling in the FMDSRR microstructure. As given in Fig. 4e, the present ultrabroadband PMA achieved absorption resonance resulting from the inter split rings for FMDSRR and the coupling effects between the SRRII and SRRI. At 20.77 GHz, the absorption peak was mainly caused by the inter split rings for FMDSRR in Fig. 4g. The strong coupling effects between the outer split rings for FMDSRR and the SRRII for SMDSRR microstructure had been achieved from Fig. 4i. It was necessary to note that the dipole resonance, the equivalent inductance and capacitance resonance, and the coupling resonance were of primary importance for achieving the ultrabroadband absorption. From Fig. 4b, d, f, h, and j, it could be found that the near electric fields of 5.13 GHz in the upper space were different from that of other response frequency due to the stronger coupling effects between the SRRI and the outer split rings. The type of the resonance absorption at 14.49, 19.1, and 20.8 GHz were same with each other, and their absorption peaks were both achieved by the FMDSRR microstructure. It can be found that the more density of the PMA exhibited, the better absorption of the PMA achieved. As shown in Fig. 4j, there were six space points (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 highorder modes for the proposed ultrabroadband PMA. Consequently, the coupling effects between the different microstructures and the highorder modes were the crucial component to design the broadband PMA.
The simulated absorption results of the present PMA with different angles of theta and phi are discussed in Fig. 5 for the transverse electromagnetic (TEM) incident waves. From Fig. 5a, we could see that the proposed PMA exhibited the high absorptivity from 4.5 to 25 GHz with theta = 0°. as the angle of phi shifted from 0 to 360°. It was obvious that the absorption decreased drastically for the angle increased from 70 to 80° or decreased from − 70 to − 80° in Fig. 5b. Generally, the ultrabroadband and wide angle absorption could be obtained for the proposed PMA with the angle of theta shifted from − 70 to 70° and the angle of phi increased from 0 to 360°. To illustrate the excellent absorption, the simulated absorption results at the resonance frequency of 5.13, 14.49, 19.05, 20.77, and 25.42 GHz are given with − 90° < theta< 90° and 0° < phi< 360° in Fig. 5c–g. From these figures, we clearly observed that the outstanding absorption at 14.49 GHz could be obtained for the PMA with − 90° < theta< 90° and 0° < phi< 360° due to the symmetrical FMDSRR microstructure with four lumped resistances and the strong coupling effects between the inner and outer split rings. The PMA at 19.05 GHz and 20.77 GHz respectively retained high absorbing efficiency with wide absorption in Fig. 5e, f. These phenomena were proved that their absorption peaks were all achieved by the symmetrical FMDSRR microstructure. Because the resonance of the PMA at 5.13 GHz was determined by the unsymmetrical SMDSRR microstructure, the absorption results at this frequency were not unsymmetrical in Fig. 5c. As shown in Fig. 5g, it was necessary to point out that the absorption at 25.42 GHz was inconstancy due to the coupling effects between the FMDSRR and SMDSRR microstructures and the highorder modes for the proposed ultrabroadband PMA. From these figures, we could see that the proposed PMA exhibited the wide angle absorption for the electromagnetic waves with different incident angles.
To interpret the polarizedinsensitivity of the ultrabroadband PMA for transverse electric (TE) and transverse magnetic (TM) polarized incidences, we presented the oblique absorption, the surface current distributions at 12 GHz and the near electric fields at 12 GHz in Fig. 6. From Fig. 6a, b, it is obvious that the oblique absorption results in TM polarized incidence were same with that in TE polarized incidence. The same oblique absorptions with different incidences were attributed to the absorption mechanism and the present microstructure. For example, the surface current distributions and near electric fields at 12GHz with TE and TM polarized incidences were further explored to illustrate polarizedinsensitivity of the ultrabroadband PMA in Fig. 6c–f. It was reported that the presented PMA exhibited the same surface current distributions and near electric fields with different polarized incident waves. Consequently, the characteristic of polarizedinsensitivity could be achieved for this ultrabroadband PMA.
In order to elaborate the dielectric and ohmic losses, Fig. 7 shows the volume loss density (VLD) of the substrates and lumped resistances for the proposed PAM at 5.13, 14.49, 19.05, 20.77, and 25.42 GHz. From Fig. 7a, we could observe that the VLD increased as the resonance frequency shifted from 5.13 to 25.42 GHz. The different modes could be achieved from the ohmic losses of the lumped resistances in Fig. 7b. The volume loss density of 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 ultrabroadband absorber from Figs. 3(e) and (f) and 7.
Fabrication and Measurement
In order to verify the characters, two 900cell (30 × 30) devices of the proposed ultrabroadband PMA are fabricated and illustrated in Fig. 8. The device had been measured by employing the freespace test method in a microwave anechoic chamber. The ultrabroadband PMA sample was fabricated using an optical lithographic processes on three substrates (ε_{r} = 4.2 and tanδ = 0.02) with thickness of 2 mm, 1 mm, 1 mm, and 1 mm. Two linearly polarized standardgain 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 timedomain 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 farfield condition.
The experimental results of angular absorption for the proposed PMA sample are given in Fig. 9 when the incident angle (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 ultrabroadband absorption from 4.48 to 25.46 GHz could be achieved with absorptivity larger than 80% not only in xpolarized incidence but also in ypolarized 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 ypolarized incident waves. From Fig. 9a, b, it was obvious that the absorptions in xpolarized incidences were same with that in xpolarized incident waves. Hence, the characteristic of polarizedinsensitivity 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 ultrabroadband, polarizedinsensitivity, and wideincident absorption.
Conclusion
In conclusion, we have proposed, designed, and fabricated an ultrawideband perfect metamaterial absorber with polarizedinsensitivity and wideincident absorption. The angular absorption spectrum, surface current, and near electricfield 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 ultrabroadband absorption from 4.48 to 25.46 GHz could be achieved with absorptivity larger than 80% with normal incidences for xpolarization and ypolarization. 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.
Abbreviations
 EM:

Electromagnetic
 MDSRR:

Metallic double split ring resonators
 PBCs:

Periodic boundary conditions
 PMA:

Perfect metamaterial absorber
 SRRI:

Split ring resonatorI
 SRRII:

Split ring resonatorII
 TE:

Transverse electric
 TEM:

Transverse electromagnetic
 TM:

Transverse magnetic
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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.2017KJX24, National Defense Foundation of China (2201078), and Aviation Science Foundation of China under No. 20161996009. They also thank the reviewers for their valuable comments.
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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.
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Correspondence to SiJia Li.
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Keywords
 Metamaterial absorbers
 Polarization
 Subwavelength structures
 Ultrawideband