Simulation of angle-insensitive microwave metamaterial absorbers operating at transmission mode

 Communications in Physics, Vol.31, No. 2 (2021), pp. 211-217
 DOI:10.15625/0868-3166/15382
 SIMULATION OF ANGLE-INSENSITIVE MICROWAVE METAMATERIAL
 ABSORBERS OPERATING AT TRANSMISSION MODE
 TRAN VAN HUYNH1,2,3, VU DINH LAM1,2 AND NGUYEN THANH TUNG1,2,†
1Institute of Materials Science, Vietnam Academy of Science and Technology,
 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
2Graduate University of Science and Technology, Vietnam Academy of Science and Technology,
 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
3Department of Basic Sciences, University of Fire Prevention and Fighting, Vietnam
 E-mail: †tungnt@ims.vast.ac.vn
 Received 15 August 2020
 Accepted for publication 29 October 2020
 Published 05 January 2020
 Abstract. Metamaterial absorbers with the resonator/dielectric/metallic-mirror conventional de-
 sign are often angle-dependent and completely reflective outside the absorption band. Herein we
 have proposed a novel solution to achieve an angle-insensitive bidirectional absorber operating
 at transmission mode using a simple metamaterials system. The proposed system is composed of
 two symmetric disk-pair layers, called the disk-pair dimer, that exhibited two identical but coupled
 magnetic resonances at the same frequency. This unique design allows to absorb the electromag-
 netic energy at the transmission mode, which is rarely achieved in the conventional modes. By
 optimizing the coupling strength between two disk-pair layers, a total absorptivity could be en-
 hanced up to 90%.
 Keywords: perfect absorbers; metamaterials; transmission mode.
 Classification numbers: 81.05.Xj; 78.67.Pt.
 I. INTRODUCTION
 Independent manipulation of the electric and magnetic responses through structural engi-
 neering for a frequency-selective absorption, which is usually not available in natural occurring
 materials, is an important advance of metamaterials [1–3]. Since the first introduction in 2008,
 the novel concept of metamaterial absorbers (MMAs) has gained a huge attention and rapidly
 ©2021 Vietnam Academy of Science and Technology
212 SIMULATION OF ANGLE-INSENSITIVE MICROWAVE METAMATERIAL ABSORBERS OPERATING ...
developed not only for fundamental knowledge but also for the desire of using advanced materi-
als in sensing, energy harvesting, and radiation probing based applications [4–6]. Generally, the
interactions of light with MMAs can be described in terms of transmission, reflection, and ab-
sorption. The absorption can be defined as A( f ) = 1 − R( f ) − T( f ), where A, R, and T are the
absorption, reflection, and transmission as functions of frequency f , respectively [1]. An absorp-
tion as high as possible can only be achieved by minimizing R( f ) and T( f ) at the same time.
A simple design, which is composed of a three-functional-layer structure, has been proposed for
MMAs to simultaneously satisfy both above-mentioned requirements. The structure usually in-
cludes periodically-arrayed metallic resonators on top, a dielectric spacer in the middle layer, and
a metallic ground plane on the back. First, to diminish the reflection, the effective impedance of
metallic resonators is matched to that of the free space through tuning the geometrical parameters
of the top resonators. Meanwhile, the metallic ground plane is used as a electromagnetic mirror
to quench all incoming waves, resulting in a zero transmission. The absorbed energy is mainly
attributed to the dielectric loss generated by the induced coupling between the resonators and the
mirror [7–9]. The simplification of this structure in fabrication and characterization makes it most
commonly used for existing MMAs in the current literature so far.
 Nevertheless, there are still barriers to overcome before the MMAs can be utilized in the real
applications. A certain number of studies have been carried out to push the operating frequency
of MMAs to either higher regimes, i.e. millimeter waves [10, 11], THz [12, 13], infrared [14, 15],
and visible range [16,17], or lower regimes, i.e. MHz range [18]. Different geometrical structures
have been proposed and investigated to improve the polarization and incidence-angle dependence
of the MMAs [16, 19]. Together with attempts to diversify operating frequencies, many efforts
have been paid for advancing the MMA functionalities through real-time controlling their ab-
sorption band [11] and frequency tunability [20, 21]. But the most unpleasant disadvantage of
the resonator/dielectric/metallic-mirror motif lies in the fact that it only operates at the reflection
mode, sending back all signals at frequencies outside of the absorption range while many applica-
tions of absorbers are required to be transparent [22].
 Recently, a potential solution has been reported operating at the transmission mode without
the metallic mirror [23]. The desired absorption peak is obtained by matching the electric and
magnetic resonant losses at the same frequency range while allowing the waves to be transmitted
outside the absorption band. Unfortunately, the magnetic and electric resonant frequencies have
shown different sensitivities to the incident waves and the resonant superposition lasts only for the
incident angles less than 5 degrees. The high absorption behavior hence can only be observed at
the normal incident angle, putting an unfortunate limitation on their promising applicability [23].
In order to bridge this gap, we propose a disk-pair (DP) dimer that can exhibit an angle-insensitive
bidirectional high absorptivity at transmission mode. The total absorptivity can be achieved up
to 90%, resulting in an effective approach to the quasi-omnidirectional frequency-selective ab-
sorber. The scattering and dispersive parameters are simulated to get insight into the underlying
physics of the hybridized absorption. Finally, an incident-angle sensitivity analysis is performed
to characterize the absorption behavior of the proposed metamaterials.
II. COMPUTATIONAL METHOD
 A computational unit cell of the DP dimer structure is illustrated in Fig. 1(a). The structure
consists of two aligned DPs along the k-direction. Each pair contains two identical disks arranged
 TRAN VAN HUYNH et al. 213
symmetrically and separated by a dielectric spacer. In our study, the dielectric material is assumed
to be FR4 with a dielectric constant of 4 + i0.008. The disk-shaped elements are made of copper
for microwave-fabrication compatibility. The thicknesses of copper and FR4 are chosen as 0.036
and 1.2 mm, respectively. The disk diameter is fixed at 16.5 mm while the periodicity of the
unit cell in the x-direction and the y-direction is kept at 29 mm. The scattering parameters and
field distribution are calculated by using the finite integration simulation technique embedded in
CST Microwave Studio [24]. To minimize the number of calculations, the periodic boundary
conditions are applied in the x-y plane. The standard retrieval method was utilized to extract the
effective permittivity and permeability from simulated transmission and reflection [25].
 Fig. 1. (a) The computational structure of a disk-pair dimer and its geometrical parame-
 ters. (b) The second-hybdrization scheme.
III. RESULTS AND DISCUSSION
 The electromagnetic behavior of the DP dimer structure can be described by an analog of
molecular orbital theory [26]. We first discuss the electromagnetic responses of an isolated single
DP monomer metamaterials. Under a normal excitation, the plasmonic response is stimulated
in each individual copper disk (the elemental unit). The electromagnetic response, including the
magnetic and the electric resonance, of the DP monomer, results from a hybridization of two
individual elemental plasmon modes [27]. According to the hybridization scheme, there are two
stimulated eigenmodes with opposite current directions. The antisymmetric mode corresponds
214 SIMULATION OF ANGLE-INSENSITIVE MICROWAVE METAMATERIAL ABSORBERS OPERATING ...
to the magnetically-driven oscillations, (|w−i), and the symmetric (|w+i) mode corresponds to
the electrically-driven oscillations. The energy level of each mode depends on the size, shape,
and composition of the hybridized system. While the symmetric mode operates as two identical
electric dipoles, the antisymmetric mode with antiparallel currents behaves as magnetic resonance.
The energetic splitting of two modes is larger if the distance between two disks in a pair (td)
is smaller [28]. In this study, we focus on the use of the magnetic resonance (mode |w−i) to
create the high absorption in metamaterials as shown in Fig. 1(b). The reflection, transmission,
and absorption spectra at the magnetic resonant mode (|w−i) of a single DP are shown in the
left panel of Fig. 2. The magnetic resonance frequency is determined as about 5 GHz, where
the transmission and the reflection are strongly fluctuated. A transmission gap appeared at the
magnetic resonance reflecting the negative nature of the magnetic permeability that does not allow
waves to propagate [29]. The recorded absorption of a single DP is about 45%, in line with
previous results [3].
 Fig. 2. Computed reflection, transmission, and absorption of the single DP and DP dimer
 structure with k = 0.5.
 The electromagnetic response of a DP dimer is more interesting. Along with the intrinsic
charge interactions within each DP, the additional interactions between two DPs (the back disk
of the first DP and the front one of the second DP) also result in Coulomb forces, giving rise to
two degenerated magnetic modes corresponding to the second-order antisymmetric |w−+i and the
second-order symmetric resonances |w−−i [30]. This level of interactions can be illustrated by
the second-order hybridization scheme in Fig. 1(b). While the spacer thickness td responds for
the internal coupling between two disks in a DP monomer, the distance d along the k-direction
governs the external one between two DPs in a dimer. It has been shown that by properly selecting
the ratio k of d to td one can achieve the best effectiveness of the second-order hybridization
for a dual-band negative permeability [30]. Unfortunately, the effect of enhanced absorption and
the possibility of using the second-order hybridization for the desired absorption have not been
explored in earlier studies. In this work, after performing the optimization procedure a value of
0.5 is chosen for k to achieve the best absorption performance. The reflection, transmission, and
absorption of a DP dimer with k = 0.5 are presented in the right panel of Fig. 2. It can be seen
that the transmission gap corresponding to the negative band of permeability is significantly wider
 TRAN VAN HUYNH et al. 215
due to two degenerated magnetic resonances |w−−i and |w−+i. While the transmission gap of
degenerated resonances is extended, their corresponding absorption peak is greatly enhanced from
45% to 90%. The full width at half maximum of the absorption peak also increases from 0.22 GHz
for a single DP structure to 0.40 GHz for DP dimer structure. In order to validate the magnetic
nature of the observed resonances in the single DP and DP dimer metamaterials, we simulate
the distribution of the magnetic and the electric field in each structure at 5 GHz. The results are
presented in Fig. 3. In the magnetic resonance, the surface currents between two disks in a pair are
antiparallel. The currents travel back and forth along the vertical direction of the external electric
field and vice versa, resulting in the strong induced electric field at the top and bottom edges of
the disks. The antiparallel currents induce a magnetic field between two paired disks along the
horizontal direction of the external magnetic field as seen in Fig. 3. Both the single DP and DP
dimer show exactly the same electric and magnetic field distribution, confirming their magnetic
origin at 5 GHz.
 Fig. 3. The simulated E-field and H-field distribution induced in the single DP and DP
 dimer metamaterials at 5 GHz.
 As discussed in Section 1, the previously proposed metamaterial absorber operating at the
transmission mode is angle-fragile. Since its high absorption strength relies on the overlap of the
magnetic and electric resonant frequencies whose sensitivities to the incident waves are strongly
different, the resonant superposition lasts only for very small incident angles. The main advantage
of our design is that the proposed DP dimer does not only absorb the electromagnetic waves at the
216 SIMULATION OF ANGLE-INSENSITIVE MICROWAVE METAMATERIAL ABSORBERS OPERATING ...
transmission mode but it also operates at large incident angles. Figure 4 presents our computed
results on the absorption intensity of the DP dimer for TE and TM modes at incident angles from
0 to 80 degrees. It is confirmed that the absorption strength is nearly unchanged if the incident
angles were up to 70 degrees. It means that the DP dimer can be considered as a 3D quasi-
omnidirectional absorber. At larger incident angles, the absorption strength rapidly decreases
because the external electric and magnetic field become perpendicular to the sample plane for
TE and TM mode, respectively. On the other hand, the DP dimer absorber will allow in-plane
electromagnetic waves to propagate through.
 Fig. 4. The computed absorption strength of DP dimer metamaterials according to dif-
 ferent incident angles: (left) TE polarization and (right) TM polarization.
IV. CONCLUSIONS
 In summary, we have proposed a simple metamaterial absorber and demonstrated that this
absorber can operate at the transmission mode with a wide range of incident angles. The meta-
material absorber consists of two hybridized DP structures. The transmission, reflection and ab-
sorption were calculated along with the simulated field distribution to interpret the essence of the
absorption peak. The obtained results showed that the high absorption strength of the DP dimer
metamaterials originated from a second-order hybridization of magnetic resonances. The insen-
sitivity of absorption intensity to incident angles was examined and this demonstrated its high
potential for a wide field of applications. The obtained results can be considered as supplementary
valuable information to design advanced metamaterial devices.
ACKNOWLEDGEMENT
 This work is supported by Vietnam National Foundation for Science and Technology De-
velopment under grant number FWO.2017.103.01.
 TRAN VAN HUYNH et al. 217
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