1. Introduction

With the prompt development of electronic equipment and fifth-generation wireless communication technology, the ever-increasing electromagnetic interference (EMI) and electromagnetic compatibility (EMC) issues have not only interfered with their regular service but have also threatened human health [1,2]. In particular, the operating frequency of current electronic instruments is mainly in the S (2–4 GHz), L (1–2 GHz), and even lower bands; thus, EM pollution from this region has become a serious concern [3]. In addition, for high angular resolution and long-distance detection, an ultra-low frequency radar is widely employed in military applications [4–6], resulting in a sharp increase in demand for anti-reconnaissance measures. However, existing EM absorbers, including conventional absorbing materials (AMs) and metamaterial absorbers (MMAs), cannot easily satisfy such requirements because of the ultra-long wavelength of the incident EM waves. Evidently, it is also challenging to simultaneously consider high-frequency properties.

To address these problems, considerable effort has been made on developing low-frequency EM absorbers with high efficiency and wide relative bandwidth; however, studies focusing on below the L band are lacking. With regard to conventional AMs, the incident EM energy can be dissipated through magnetic [7,8] or dielectric loss materials [9–12]. However, they have drawbacks such as large thickness, high density, and narrow effective bandwidth because of their inherent limitations [13]. For example, Liu et al. developed a yolk-shell-structured Co-C/Void/Co₉S₈ ternary composite, enabling only a narrow absorption peak within the S band [14]. Other similar designs can be found in Refs. [15,16]. To balance the low-frequency and broadband, Lv et al. [17,18] proposed a core-shell-structured absorber as an alternative scheme, where the absorption peak could be tuned in the region of 2.0–8.0 GHz by controlling the carrier mobility and excitable carriers using a voltage control system. However, this absorber cannot operate alone without precisely detecting the incoming frequency, making it impractical.

Recently, MMs have attracted considerable attention for their exotic properties such as negative refraction [19], reversal of Cherenkov radiation [20], and inverse Doppler shift [21], providing a promising way to resolve some of the aforementioned issues. Since the proposal of the first perfect MMA by Landy et al. [22], significant efforts have been made toward the development of MMAs, aiming at realizing low-frequency and broadband absorption [23–28]. For instance, Zhou et al. designed an ultra-wideband EM absorber (ranging from 3.74 to 18.5 GHz) based on the concept of metasurface Salisbury screen, which features low profile, light weight, simple configuration, and robust angular performance [26]. Shen et al. demonstrated a sandwich structure that can achieve broadband absorption with reflection less than –10 dB in the frequency range of 2.6–21.0 GHz [27]. Compared with conventional AMs, MMAs are undoubtedly the right choice for improving the working bandwidth; however, they cannot meet the demand because of their inadequacy in the L and S bands.

Evidently, MMAs are faced with the challenge of enhancing the absorption efficiency in the ultra-low-frequency range, which is exactly what the conventional AMs do well. Therefore, by integrating AMs with MMAs, we could perhaps take advantage of their synergistic effect to overcome the existing problems. To date, although several such attempts have been made, most studies concentrated on the performance improvement in the S band [29–33].

Herein, to overcome this limitation, we propose a hybrid MMA [HMMA, Fig. 1(a)] with a multi-resonance feature for the first time, whereby 90% of the normally incident EM energy can be absorbed within the operating bands of 0.79–20.9 GHz and 25.1–40.0 GHz. Considering the intense atmospheric attenuation, the K band from 18.0 GHz to 26.5 GHz is neglected in our design, because it is hardly used for long-range applications such as detection and wireless communication [34,35]. In our design, graphene films with outstanding mechanical properties and a type of conventional magnetic AM (MAM; density of approximately 3850 kg/m³) are assembled to extend the absorption bandwidth to frequencies even lower than the L band. The key structure geometrical parameters are discussed, and the corresponding effects on the resonances are determined to guide future design. Additionally, because of the large-scale adoption of polymethylacrylimide (PMI) foam (density of 50 kg/m³ and dielectric constant of 1.05+i0.001), the entire meta-structure has another advantage of low surface density, making it promising for many practical applications.

 

Fig. 1. (a) Design flow of the HMMA for broadband EM absorption. (b) Measured EM parameters of the selected magnetic material versus frequency. (c) Simulated normal-reflectivity under different conditions.

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2. Theory and design

To realize a dual-broadband HMMA as desired that can consider the ultra-low frequency of interest, as illustrated in Fig. 1(a), we combine a widely available broadband MMA (left-side image in Fig. 1(a)) with a MAM [middle image in Fig. 1(a)]. The predesigned MMA exhibits high performance of reflection loss than –10 dB both from 4.8 GHz to 22.6 GHz and from 27.5 GHz to 40 GHz [navy line in Fig. 1(c)], giving it a fundamental absorption feature. Given that we can hardly obtain the EM parameters of the MAM exceeding 40 GHz, the corresponding simulated results are not included in Fig. 1(c). To improve the low-reflection performance at ultra-low frequencies, a custom-made MAM with optimized EM parameters, as shown in Fig. 1(b), is selected, which does a favor to an anti-reflection peak at approximately 1.8 GHz [red line in Fig. 1(c)]. Subsequently, by replacing the bottom PMI layer of the MMA [left-side image in Fig. 1(a)] with the selected MAM, the resonances separately induced by these two parts can be superposed, where the overlapping of the two leads to the required absorption detection [olive line in Fig. 1(c)]. In addition, the redshift of all the resonances [Fig. 1(c)] can be evidently observed as a result of the mutual coupling between the multi-layered structure [left-side image in Fig. 1(a)] and the magnetic material [middle image in Fig. 1(a)].

The proposed HMMA [right-side image in Fig. 1(a)] is constructed by a layer-stacked structure comprising graphene films with optimal sheet resistances and deliberately selected MAM. The typical unit cell is modeled and optimized by utilizing the commercial software, namely CST Microwave Studio 2019. When conducting simulations, a frequency-domain solver is used with periodic boundary and Floquet port. The corresponding geometry parameters are determined as follows: P = 15.0 mm, d = 2.0 mm, a₁ = 6.0 mm, a₂ = 9.3 mm, a₃ = 12.6 mm, a₄ = 13.0 mm, a₅ = 8.0 mm, h₁ = h₂ = h₃ = h₄ = 6.0 mm. The sheet resistances of the square-shaped patterns are respectively r₁ = 180 Ω/□ (blue color) and r₂ = 30 Ω/□ (red color), as shown in Fig. 1(a). A low-density PMI is adopted to hold and connect the neighboring layers, and the MAM at the bottom of the entire structure is supported by a metallic plate made of copper (with a conductivity of 5.8×10⁷ S/m) to prevent the EM waves from passing through.

At the beginning of this section, we characterized the proposed HMMA from a macro perspective. To further present the physical insight of the dual-band absorption, particularly the ultra-low feature, the simulated E-field, H-field, and surface currents are first revealed in Figs. 2(a)–2(c) from 0.79 GHz to 20.9 GHz. At the resonance R1, the E-field is tightly localized at the edge of the patterned graphene films [upper left in Fig. 2(a)] when the proposed HMMA interacts with the incident wave, resulting in the vibration of free electrons and generation of a time-varying current [right image in Fig. 2(a)]. Meanwhile, the distribution of the H-field [lower-left image in Fig. 2(a)] is extracted from the simulated near-field results, and it is evident that the H-field is enhanced where the anti-parallel currents are induced, by comparing the lower-left image and the right image in Fig. 2(a). Evidently, the accumulated surface currents are induced through both the E-field and H-field couplings, and considering the ohmic loss, the incoming energy can be partially dissipated at the graphene layers. Additionally, because of the high permeability and magnetic loss of the MAM at low frequencies [Fig. 1(b)], as shown in the lower-left image of Fig. 2(a), the significantly concentrated H-field can be expended through rubbing and rotating the magnetic domains [36], thus consuming the incident EM waves. Accordingly, there is no doubt that the origin of the ultra-low-frequency absorbing performance is the synergistic effect between the MMA [left-side image in Fig. 1(a)] and MAM [middle image in Fig. 1(a)] as initially predicted. Similar phenomena can be observed at R2 and R3 despite the different distributions of the surface currents [Figs. 2(b)–2(c)].

 

Fig. 2. (a(–(c) Simulated distribution of the E-field, H-field, and surface currents at resonances R1−R3. (d) Cross-section view of the simulated power flow at resonances R4−R6. Inset: circular arrows represent the directions of the anti-parallel currents. [Max. Min.] in the color bar is equal to [21624 0] (V/m, E field), [16.7 0] (A/m, H field), [10.3 0] (A/m, surface current), and [47802 0] (V.A/m², power flow).

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Next, the source of the absorption in the second operation band from 25.1 GHz to 40.0 GHz is also explored. Because the high-frequency performance of the HMMA is mainly determined by the multi-layered MMA [Fig. 1(b)], the simulated power flows among the inter graphene layers are presented to clarify the resonant behaviors at R4–R6. Once the energy flux flows across the graphene films highlighted with bold orange lines, a significant decline in the EM energy can be successfully captured from Fig. 2(d), uncovering the origin of the ohmic loss. Note that due to the relatively high sheet resistance (180 Ω/□ and 30 Ω/□), the Q-factor of the induced resonances can be relieved, thus helping broaden the effective bandwidth where the reflectivity is no more than –10 dB.

Until now, we performed an in-depth investigation on the physical origin of the dual broadband absorption shown in Fig. 2. Subsequently, the key factors determining the absorption properties of the proposed HMMA were also discussed, as shown in Fig. 3, to conclude their changing laws and thus simplifying the design process. Based on the previous study, the total feature of our design is mainly determined by the graphene films and the MAM. Therefore, the influences of the corresponding parameters, including r₁, r₂, and d, on the reflection spectra are considered. Figure 3(a) shows that with the increase in r₁ (from 120 Ω/□ to 180 Ω/□), the reflectivity at high-frequency resonances (R4–R6) gradually decreases, while the low-frequency performance is maintained. When r₁ reaches 200 Ω/□, the resonant peak (R4) dramatically shifts to a higher frequency. In contrast, there is little difference among the resonances R4–R6 as r₂ or d varies. However, the absorption peak R1 moves to a higher frequency with the increase in d. Considering the increase in r₂, from the zoom-in spectra shown in Fig. 3(b), the intensities of R1 and R2 attenuate as well as their effective bandwidths shrink. Therefore, based on the conclusion drawn above, the HMMA with a custom-made working band can be flexibly implemented with our strategy.

 

Fig. 3. Effects of the critical parameters r₁ (a), r₂ (b), and d (c) on the reflection properties of the proposed HMMA. Insets of (b)−(c): partially enlarged images.

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Finally, the angular dependence of the absorption performance is investigated, as shown in Fig. 4. The absorption efficiency can be expressed as $A(\omega ) = 1 - T(\omega ) - R(\omega )$, where $R(\omega ) = {|{{S_{11}}} |^2}$ and $T(\omega ) = {|{{S_{21}}} |^2}$ are the reflectance and transmittance obtained from the frequency-dependent complex S-parameters, respectively. Since the backside is grounded by a metallic plane, the transmittance $T(\omega )$ is zero. Thus, the absorptivity shown in Fig. 4 can be calculated as $A(\omega ) = 1 - R(\omega )$. With the increase in the incident angle from 0° to 60°, both for TE and TM waves, the operating bandwidth at low frequencies is dramatically extended despite some deterioration in the sideband performance due to the mismatched impedance at oblique incidence. Meanwhile, the passband (strong reflection parts in Fig. 4) gradually moves toward a higher frequency without shrinking. Note that because of the lack of simulated results exceeding 40 GHz, the influence on the high-frequency working bandwidth cannot be demonstrated as the incident angle increases.

 

Fig. 4. Simulated absorption performance of the proposed HMMA under various incident angles for both TE (a) and TM (b) modes.

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3. Experimental section

3.1 Sample fabrication

To verify the reliability of the simulated results, we fabricated a sample with dimensions of 300 × 300 mm², as shown in Fig. 5. The home-made magnetic absorbent was prepared through a press forming method, with the raw material being a mixture of rubber and carbonyl iron nanocrystalline flakes added in a weight ratio of 1:9. The ball milling approach was adopted to obtain the corresponding magnetic power; the details are described in Ref. [37]. The EM parameters in the 1–40 GHz range of the prepared MAM were measured, as shown in Fig. 1(b), using a vector network analyzer (VNA, Agilent Technology N5247A). The relatively high permeability facilitates impedance matching at the ultra-low frequency as well as attenuating the incoming EM power as predicted in Fig. 1(c).

 

Fig. 5. Simulated and measured absorption performance of the fabricated HMMA illuminated with the normal incident wave. Inset: Photograph of the sample.

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The graphene films with different conductivities were also synthesized in our own laboratory by reducing graphene oxide (GO), with a thickness of approximately 15 µm. The details of the process have been described elsewhere [38,39]. Before fine processing, the fabricated graphene films were first adhered to the thin polyimide (PI) films (dielectric constant of 3.0+i0.003) with a thickness of 10 µm rather than directly covering the PMI foam and MAM to facilitate the manufacturing, with little discrepancy in terms of the total absorption performance compared with the initial design (Fig. 5). Subsequently, the patterned graphene films were obtained with the help of a laser machine. We shaped the PMI foams and MAM following the optimal structural parameters using a computer numerical control (CNC) machine with a precision of 0.01 mm. Finally, the predesigned HMMA was built by assembling the above components based on the design flow shown in Fig. 1(a).

3.2 Experimental measurement

The arch method was carried out in a microwave anechoic chamber to measure the reflection properties of the sample. Three sets of broadband horn antennas (1–8 GHz; 8–18 GHz; 26.5–40 GHz) were utilized to transmit and receive EM signals. During the experiments, the antennas were connected to the VNA through low-loss cables. The same-sized metallic plate should be firstly obtained for calibrating the directly measured results of the sample. Then, the reflectivity of the sample versus frequency except for the K band can be acquired through the abovementioned comparison test. Due to the limitation of the test environment and setup, the performance below 1.0 GHz cannot be reached.

As shown in Fig. 5, the absorptivity spectrum of the optimized HMMA was measured with the two-port method. In the first frequency band from 1.0 GHz to 18.0 GHz, the measured absorptivity was largely consistent with the simulated one despite the slight deterioration in the anti-reflection performance at the first valley (Fig. 5). Meanwhile, the as-fabricated sample could achieve wideband absorption with an efficiency of more than 90% in the frequency range of 26.5–40 GHz. Although some discrepancy can be observed in Fig. 5, attributed to manufacturing errors and lack of consideration of PI films when conducting the simulations, the measured experimental result agrees well with the simulated one, thus validating our scheme.

4. Conclusion

In summary, we demonstrated a multi-layered HMMA composed of a MAM operating in the low-frequency region and a dual-wideband MMA. Owing to the superposition of their resonances, our design exhibits excellent wideband absorption features through spectrum overlapping. Additionally, the reflection loss at ultra-low frequencies (less than 1 GHz) was dramatically improved due to the mutual coupling between them. The experiments prove that the manufactured HMMA enables high absorption efficiency (more than 90%) in the dual-frequency ranges of 1–18 GHz and 26.5–40 GHz, which fits well with the simulated results. Consequently, our strategy can provide some valuable guidelines for the future design of EM absorbers considering the low frequency and wideband simultaneously. The proposed HMMA has a surface density of 9.8 kg/m² with the usage of PMI foam and graphene films, enabling numerous potential applications in both military and civil fields.