This article presents a thin and flexible artificial electromagnetic absorber with two absorption peaks at frequencies of 28 and 39 GHz for 5G communication. Copper and a flexible FR4 substrate are used in a pyramid-shaped layered configuration, achieving absorption rates exceeding 99% at 28 and 39 GHz. The thickness of the proposed structure is only 0.34 mm, which is ∼1/32 and 1/23 of the corresponding free-space wavelengths at the absorption frequencies. Due to its symmetric structure, the absorber is polarization-insensitive. Furthermore, the proposed structure exhibits over 90% absorption within the incident angle range of −45° to 45°. To investigate its absorption mechanism, the electric field and magnetic field distributions at the absorption frequencies were analyzed. Then a 150 × 150 mm2 sample was fabricated using printed circuit board manufacturing techniques. This sample was placed on flat or curved surfaces and tested under normal or oblique incidences. The experimental results were consistent with the simulated results, confirming the feasibility of the design. This absorber can be applied in 5G communication and millimeter-wave imaging.

Artificial electromagnetic (EM) materials, commonly termed metamaterials, are custom-engineered structures fabricated at sub-wavelength scales.1 Compared with natural materials, metamaterials exhibit unique electromagnetic properties such as a negative refractive index,2 the capability for perfect imaging,3 and the inverse Doppler effect,4 which is controllable by modifying their periodic structure and unit cell composition.5,6 Owing to these distinctive characteristics, metamaterials have enabled a variety of fantastic applications, including electromagnetic (EM) cloaking,4 ultra-sensitive detection,7 energy conversion,8,9 and absorption.10–14 Especially, absorptive devices crafted with metamaterials are of great significance in both defense and civilian applications, which have attracted many researchers.

The concept of metamaterial-based absorbers was pioneered in 2008 by Padilla at Boston College, USA.15 His approach involved a dielectric layer interposed between metallic strips and dual-split ring resonators, which interact with the magnetic and electric fields, respectively. This configuration achieved a complete impedance match with free space, thereby eliminating reflection at the operational frequency and facilitating the absorption and dissipation of incident waves within the material. Prior absorbers attained an absorption efficiency exceeding 88% at 11.5 GHz. This progression led to the development of devices with absorption capability at single,16 dual,17 and multi-frequency ranges.18 

In recent times, millimeter-wave technology has emerged as a focal point in the scientific and engineering research of radar, imaging, and wireless communication. The widespread issue of electromagnetic interference in these applications requires effective solutions to preserve the quality of high-speed data. Metamaterial-based millimeter-wave absorbers, renowned for their thin, compact, and efficient design compared to traditional absorbers,20 are instrumental in mitigating such interference, thus significantly enhancing system performance.19 Current research is mainly focused on metamaterial absorbers with rigid substrates.21,22 However, applications involving curved surfaces, conformal installations, and wearable technologies necessitate the development of flexible absorbers,23,24 which is still a great challenge in the design with millimeter-wave metamaterials.25 

In this work, we present a metamaterial absorber designed on a flexible FR4 substrate, optimized for high absorption at millimeter-wave frequencies of 28 and 39 GHz. These frequency bands are required by applications in 5G communication and millimeter-wave imaging. Efficient absorption of undesired millimeter waves significantly improves the signal-to-noise ratio (SNR) in these systems, reducing signal loss due to reflection and scattering and thereby bolstering the received signal strength. Here, we introduce an absorber design that is compact, ultra-thin, lightweight, flexible, and easily manufactured using printed circuit board (PCB) technology. The innovative design of unit-cells enables the dual-band metamaterial absorber to achieve high absorption rates, even under a wide incident angle range. Simulation results demonstrate absorption peaks exceeding 99% at both 28 and 39 GHz. The absorber’s symmetric structure ensures insensitivity to varying polarizations. In addition, the absorber maintains an absorption rate of above 90% under the illumination of transverse-electric (TE) and transverse-magnetic (TM) waves at an incident angle of 45°.

To verify the absorber’s performance, a prototype composed of 40 × 40 unit-cells was fabricated, whose experimental results coincided with the simulation results. The flexible configuration of this absorber indicates that it is suitable for non-planar and conformal applications.

Figure 1 depicts the schematic diagram of the metamaterial absorber and the geometric layout of a unit cell. The absorber consists of two layers of dielectric substrates (yellow regions) sandwiched by three layers of copper patterns (brown regions). The flexible FR4 substrates serve as the dielectric layers with a thickness of h1 = h2 = 0.1 mm, whose relative permittivity is 4.35 and loss tangent is 0.0202. The pattern layers are made of copper with a thickness of 0.018 mm, whose conductivity is 5.8 × 107 S/m. The bottom pattern is an entire copper sheet, while the middle and upper patterns are periodic square copper patches with varying side lengths w1 and w2. Incident electromagnetic waves interact with these sub-wavelength copper patches. At resonant frequency, intense coupling and dissipation of electromagnetic energy occur within the dielectric substrates, leading to energy absorption. Due to the bottom copper sheet, energy transmission through the sample is prevented. At non-resonant frequencies, the absorber reflects incident waves without absorption.

FIG. 1.

(a) Schematic diagram of the metamaterial absorber; (b) geometry of a unit cell.

FIG. 1.

(a) Schematic diagram of the metamaterial absorber; (b) geometry of a unit cell.

Close modal

The absorber was designed and simulated using the finite-difference time domain (FDTD) electromagnetic simulation method. Each unit-cell with homogeneous structural parameters was simulated using periodic boundary conditions. From the simulation of the absorber, its optimized structural parameters are displayed in Table I.

TABLE I.

The parameters of the absorber.

ParameterValue (mm)
3.75 
w1 2.38 
w2 1.78 
h1 0.1 
h2 0.1 
ParameterValue (mm)
3.75 
w1 2.38 
w2 1.78 
h1 0.1 
h2 0.1 

The simulated power reflection coefficient R (R = reflected power/incident power) and power transmission coefficient T (T = transmitted power/incident power) are calculated from the simulated S-parameters: R=S112 and T=S212. The power absorption coefficient A is determined by A = 1 − R − T. Moreover, due to the bottom copper sheet, the electromagnetic waves cannot pass through the device. Therefore, the transmission coefficient is almost zero, simplifying the calculation of the absorption rate as A = 1 − R. Figure 2(a) presents the absorption curve of the proposed absorber under normal incidence. The proposed absorber exhibits absorption rates exceeding 99% at 28 and 39 GHz. Figure 2(b) displays the absorption curves of the proposed absorber structure at different polarization angles. It can be observed that the absorber maintains consistent absorption across polarization angles from 0° to 90°. Therefore, the proposed absorber is polarization-insensitive to incident electromagnetic waves.

FIG. 2.

(a) Simulated absorption spectra at normal incidence; (b) absorption spectrum for different polarization angles.

FIG. 2.

(a) Simulated absorption spectra at normal incidence; (b) absorption spectrum for different polarization angles.

Close modal

Furthermore, angle insensitivity played a crucial role in the performance of the absorber as electromagnetic waves can impinge on the absorber surface at any incident angle. Therefore, it is essential to analyze the angular stability of the proposed absorber under different incident angles. As shown in Fig. 3, the absorption rate decreased gradually with the increase in the incident angle. This decrease may be attributed to the reduction in the horizontal component of the electric field intensity. Consequently, the effectiveness of the induced circulating currents generated by the incident electric field gradually diminishes. However, when the incident angle θ reaches 45°, the absorption rates at 28 and 39 GHz still remain over 90%. Hence, the stability of the absorber at absorption frequencies within the incident angle range of −45° to 45° can be proved.

FIG. 3.

Simulation results of the artificial electromagnetic metamaterial absorber: (a) and (b) the absorption performance when the incident angle varies from normal incidence to 60° oblique incidence.

FIG. 3.

Simulation results of the artificial electromagnetic metamaterial absorber: (a) and (b) the absorption performance when the incident angle varies from normal incidence to 60° oblique incidence.

Close modal

To further investigate the mechanism of electromagnetic wave absorption, Fig. 4 illustrates the normalized electromagnetic field distributions within the absorber at 28 and 39 GHz. As shown in Figs. 4(a) and 4(b), the electromagnetic wave at this frequency is mainly localized between the copper patches and the bottom copper sheet, forming a waveguide-like structure. The incident wave at 28 GHz is excited as a slow wave mode with a group velocity of zero in this waveguide. The electric field mainly distributes on the sides of the waveguide, while the magnetic field is concentrated at the center of the waveguide. In this case, the electromagnetic waves cannot be reflected or transmitted. The lossy medium in the middle of the waveguide will dissipate the electromagnetic waves localized within the waveguide by converting the energy into heat. As the number of metal film layers increases, the dimensions of the waveguide progressively decrease, concurrently leading to a progressive increase in the frequency of the electromagnetic waves it can “capture.”

FIG. 4.

Normalized electromagnetic field distributions for different simulated frequencies in artificial electromagnetic dielectric structures: (a) and (c) the electric field distributions at 28 and 39 GHz; (b) and (d) the magnetic field distributions for the corresponding frequencies.

FIG. 4.

Normalized electromagnetic field distributions for different simulated frequencies in artificial electromagnetic dielectric structures: (a) and (c) the electric field distributions at 28 and 39 GHz; (b) and (d) the magnetic field distributions for the corresponding frequencies.

Close modal

In order to further analyze the mechanism of the proposed absorber, we retrieved the permittivity and permeability of its periodic structure. Because of the small thickness of the absorber designed in this paper, it is considered as a metasurface to extract its permittivity and permeability under normal incidence.27,28 The permittivity and permeability are calculated using Eq. (1), where d is the thickness of the proposed absorber. k0 is the wavenumber in free space.

The frequency response of the extracted real and imaginary parts of ε and μ is shown in Figs. 5(a) and 5(b), respectively. The real and imaginary parts of the retrieved ε and μ at 28 and 39 GHz shown in Table II at two distinct frequencies of absorption are nearly equal, which satisfy the condition of absorption,29 
ε=1+2jk0dS111S11+1,μ=1+2jk0dS11+1S111.
(1)
FIG. 5.

Extracted constitutive parameters of the proposed structure: (a) real part and imaginary part of ɛ; (b) real part and imaginary part of μ.

FIG. 5.

Extracted constitutive parameters of the proposed structure: (a) real part and imaginary part of ɛ; (b) real part and imaginary part of μ.

Close modal
TABLE II.

Constitutive parameters of the proposed structure at the peak absorption frequencies.

Frequency (GHz)Real (ɛ)Real (μ)Imaginary (ɛ)Imaginary (μ)
28 2.17 −0.03 −13.93 −12.26 
39 2.20 −0.04 −10.05 −8.70 
Frequency (GHz)Real (ɛ)Real (μ)Imaginary (ɛ)Imaginary (μ)
28 2.17 −0.03 −13.93 −12.26 
39 2.20 −0.04 −10.05 −8.70 

To validate the effectiveness of the designed absorber, an absorber prototype is implemented using PCB manufacturing technology. This prototype is composed of 40 × 40 unit cells with a total dimension of 150 × 150 mm2, as shown in Fig. 6(a). In order to better show the flexibility of the absorber, it is rolled up and adhered to a cylindrical surface with a diameter of 110 mm, as shown in Fig. 6(b). The absorption performance under these conditions is assessed using the free-space method, ensuring the absorber’s functionality is maintained even in a non-planar shape.

FIG. 6.

(a) Fabricated absorber prototype; (b) flexible absorber attached to a 110 mm diameter cylinder.

FIG. 6.

(a) Fabricated absorber prototype; (b) flexible absorber attached to a 110 mm diameter cylinder.

Close modal

To better explain the performance of the absorber, an experiment setup schematic is depicted in Fig. 7(a). A pair of horn antennas was connected to a vector network analyzer (Agilent N5244 A) to measure the reflection spectra of the sample. Another sample of the same size without the patterned layer is also measured to obtain the referenced reflection spectra. Then the actual reflection of the sample was calculated by subtracting the measured reflection power of the reference sample from that of the sample under test.26  Figure 7(b) shows the measured absorption rates of the sample, which are 99% and 94.2% at 27.92 and 38.95 GHz, respectively. The measured absorption rates show good agreement with the simulation results. The little deviations between the measured and simulated results can be attributed to manufacturing tolerances, differences in the dielectric constant of the substrate layer, and the introduction of a 0.08 mm adhesive layer between the dielectric layer and the copper patches in the actual sample. In addition, the precision during fabrication may not be aligned sufficiently, resulting in a non-perfect pyramid shape of the copper patches. These factors collectively contribute to the slight shift of the absorption peak frequency.

FIG. 7.

(a) Schematic diagram of the experimental setup; (b) simulated and measured absorption at normal incidence; (c) the absorption of TE polarized waves from forward to 60° oblique incidence; (d) the absorption of TM polarized waves from forward to 60° oblique incidence.

FIG. 7.

(a) Schematic diagram of the experimental setup; (b) simulated and measured absorption at normal incidence; (c) the absorption of TE polarized waves from forward to 60° oblique incidence; (d) the absorption of TM polarized waves from forward to 60° oblique incidence.

Close modal

The absorption characteristics of the designed absorber under different oblique incident angles for TE and TM waves could be better understood. As shown in Figs. 7(c) and 7(d), the absorption intensity gradually decreases as the incident angle increases from 0° to 60° for both TE and TM polarized waves. This decrease can be attributed to the impedance mismatch that occurs with increasing oblique incident angles. For the TE-polarized wave, the tangential component of the magnetic field decreases with the increasing incident angle, whereas the electric field orientation remains constant. For the TM polarized wave, the behavior of magnetic and electric fields is reversed. These findings verify the absorber’s effectiveness across a wide range of incident angles.

To demonstrate the high flexibility of the absorber, Fig. 8 displays the absorption spectra of the absorber adhered to different cylindrical surfaces with diameters of 66, 82, 110, 132, and 162 mm. It can be observed that the absorber maintains similar absorption rates across different diameters, which is crucial for conformal applications. Moreover, it is clearly proved that a highly flexible absorber can maintain a good performance under large bending angles.

FIG. 8.

Absorption spectra of absorbers affixed to cylinders of different diameters.

FIG. 8.

Absorption spectra of absorbers affixed to cylinders of different diameters.

Close modal

In conclusion, this work introduces a thin and flexible artificial electromagnetic absorber characterized by two significant absorption peaks. The absorber’s ultra-thin profile, with a total thickness of merely 0.34 mm, is ∼1/32 of the freespace wavelength at the lower absorption frequency. It maintains an absorption rate exceeding 90% for a wide incident angle range from −45° to 45° and exhibits structural symmetry, ensuring insensitivity to polarization. The absorber’s performance is validated through the fabrication and measurement of a sample with a 40 × 40 unit-cell. The high absorption rates under a wide incident angle range and under different bend conditions make the absorber an ideal candidate for applications requiring a wide incident angle range and conformal shapes, such as shielding structures for 5G communication and millimeter-wave imaging technologies.

The authors have no conflicts to disclose.

Jianfei Zhu: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Writing – review & editing (equal). Guoliang Gao: Data curation (equal); Formal analysis (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Weien Lai: Methodology (equal); Writing – review & editing (equal).

The data that support the findings of this study are available upon reasonable request from the corresponding author, Weien Lai.

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