Enhanced Electromagnetic Wave Absorption Properties of FeCo-C Alloy by Exploiting Metamaterial Structure

1. Introduction

The microwave metamaterial absorbers (MAs) became to be an emerging class of materials which have shown great potential in applications such as electromagnetic (EM)-wave absorption, stealth technology, and energy harvesting [1]. These artificial materials consisted of sub-wavelength unit cells which was designed to interact with incident EM waves, leading to an efficient absorption [2,3]. The absorption mechanism depends on the specific design and constituent materials of metamaterial structure [4]. A significant challenge in the microwave MA is the extension of absorption bandwidth, particularly, towards higher frequencies. Researchers have developed several strategies to overcome this challenge [5,6,7]. One approach includes the design of MA structures with multiple resonant modes, which might expand the absorption spectrum. Another way is to use multilayer structures with varying materials and thicknesses, leading to a gradient of the effective permittivity and permeability, which results in a broad absorption bandwidth.

The recent research has focused on the employment of FeCo and nano-carbon materials for the microwave absorption applications. The FeCo-based materials have shown high magnetic permeability and can be magnetized easily, making them well-suited for the microwave absorbers based on the magnetic loss [8,9,10]. Conversely, the nano-carbon materials, such as carbon nanotubes or graphene, have a high electrical conductivity and can be used for the absorbers in terms of resistive loss [11,12,13,14,15]. Therefore, the incorporation of FeCo nanoparticles into the carbon-based materials, has been shown to improve the magnetic loss significantly, while the kind of materials can enhance the electrical conductivity [16,17,18,19]. Overall, the use of alloys might lead to the development of more efficient and effective microwave absorbers.

In our work, by exploiting both usual MA and alloy, a novel FeCo/carbon-based metamaterial structure is presented to enhance the microwave absorption. The simulated results demonstrate a remarkable improvement in the absorption bandwidth of proposed MA, compared with that of FeCoC plate backed by the bare copper. We clarify the absorption mechanism by investigating the electric- and magnetic-field distribution and study the contribution of losses in the MA. Moreover, the effects of polarization and incident angle on the absorption are examined to evaluate the operational performance of proposed MA.

2. Structural Design and Methods

Figure 1 shows the schematic of proposed MA, featuring the optimized design for the unit cell. The structure comprises three layers: FeCo/graphite nanosheets (FeCo-C) whose shape looks like a flat sheet with two punched-in rings at the top, a middle layer of FR-4, and a continuous copper plate at the bottom. In our simulation, we used a relative permittivity of FR-4 of 4.3, with a loss tangent of 0.025, and employed the copper layer with a conductivity of 5.8 × 10⁷ S/m. We utilized the polyhedral FeCo/graphite nanosheet material, whose frequency-dependent complex permittivity and permeability were determined experimentally by Xiaogang Su et al. [20], as indicated in Figure 2.

We used the CST Microwave Studio software [21] to conduct the simulation, employing the frequency domain solver in a frequency range from 1 to 15 GHz. To impose the periodic boundary conditions, we utilized the x- and y-direction. The absorption was calculated by using formula $A\left(\omega \right)=1-R\left(\omega \right)-T\left(\omega \right)$, where $R\left(\omega \right)=\left|S_{11}\right(\omega ){|}^2$ and $T(\omega )=|S_{21}\left(\omega \right){|}^2$ were the reflection and transmission, respectively. In our design, the bottom layer was composed of a continuous copper plate, resulting in zero transmission in the microwave region, and thus the absorption becomes simply to be $A\left(\omega \right)=1-R\left(\omega \right)$.

3. Results and Discussion

As the initial step, we examined the reflection-loss properties of FeCo-C material, which was utilized on a copper plate [Figure 3(a)]. The thickness of FeCo-C layer was changed gradually from 1.6 to 5.3 mm in Figs. 3(b) and 3(c). That of the copper plate was t_m = 0.036 mm. Figures 3(b) and 3(c) display the simulated reflection loss and absorption spectrum, respectively, of FeCo-C according to the layer thickness, which was backed by the copper plate. Our simulated results are in accordance with the reported results in Ref. 20.

Figure 4(a) shows the absorption spectrum of MA, based on FeCo-C. The proposed structure exhibits a broadband absorption, with an absorption over 90% in a frequency range of 7.9 to 14.6 GHz, featuring two peaks with the near-unity absorption at 9.4 and 12.5 GHz, respectively. The absorption spectrum of the FeCo-C-based MA was found to be significantly broader than that of the copper-backed FeCo-C, indicating an improvement in the absorption upon integrating the FeCo-C material into the metamaterial structure. To clarify the role of different layers in the metamaterial structure, the fractions of energy dissipated in the FeCo-C and FR-4 layer are presented in Figure 4(b). It is shown that more than 98% of the energy loss occurred in the FeCo-C layer, while the loss in the FR-4 one was limited to be only 2%. The energy-dissipation results prove that the FeCo-C layer in MA is the main factor contributing to the broadband absorption.

As shown in Figure 4, the strongest absorption peaks are located at 9.4 and 12.5 GHz. Therefore, the distributions of electric and magnetic field at these frequencies are presented in Figs. 5 and 6 to clarify the nature of absorption. Figure 5(a) and 5(b) show that of the magnetic field in the (E, H) and (H, k) planes, respectively, at the lower absorption frequency of 9.4 GHz. The corresponding one of electric field in the (E, k) plane is in Figure 5(c). It can be observed that the magnetic field is strongly excited at the corners of MA structure. Specifically, the magnetic dipoles are seen along the direction of incident H-field with electric half vortices at the same positions. The observed phenomena suggest that the absorption mode at 9.4 GHz is due to a magnetic-dipole Mie-resonance, caused by the dielectric resonator [22,23,24,25,26,27]. Figure 6 presents the distributions of electric and magnetic field in different planes at 12.5 GHz. The MA also exhibits the magnetic-dipole Mie-resonance, as indicated by the strong magnetic dipoles along the H-direction and the electric half vortices in the (E, k) plane. However, the locations of magnetic dipoles at 12.5 GHz differ from those at 9.4 GHz. As shown in Figure 6, the induced magnetic dipoles are distributed in both center and outer edges of the MA structure, which are, of course, parallel to the H-direction.

To investigate the role of the real and imaginary parts of the complex permittivity (ε’ and ε”) in the absorption mechanism, we analyzed the absorption characteristics of MA structure by reducing the ε’ and ε” value to be 1/2, 1/4 and 1/6 of the original value, as illustrated in Figure 7. Initially, for the original ε’ and ε” values in Figure 2, the absorption spectrum showed a wide bandwidth of 7.9-14.6 GHz with an absorption exceeding 90%. As the ε’ value is decreased, the absorption of structure also decreases and the absorption peak shifts to a higher-frequency region [Figure 7(a)]. In addition, the reduction of ε” value results in the change of absorption spectrum to be from the wideband to multi-band absorption [Figure 7(b)]. These results suggest that the real part of FeCo-C permittivity defines mainly the frequency range of absorption spectrum, while the imaginary part is responsible for the bandwidth of absorption.

We also investigated the role of the real and imaginary parts of the complex permeability (μ’ and μ’’) on the absorption mechanism. The absorption characteristics of MA structure according to the values of μ’ and μ’’ were simulated, as shown in Figure 8. Similarly, to the reduction of the real part of permittivity, lowering the μ’ value causes a shift of the absorption spectrum towards a higher-frequency range. However, the results in Figure 7(b) indicate that reducing the imaginary-part μ’’ value does not change significantly the absorption spectrum of MA.

To evaluate the performance of proposed MA structure, we also investigated the absorption spectra by varying incident angle and polarization of incoming EM wave. We found that the absorption spectrum was largely unaffected by the change in polarization angle owing to the inherent symmetry of structure, as shown in Figure 9(a). However, the absorption of MA is influenced by the incident angle, as indicated by a reduction in both absorption magnitude and bandwidth [see Figs. 9(b) and 9(c)]. Nonetheless, the proposed MA still reveals a good absorption property for both transverse-electric (TE) and transverse-magnetic (TM) polarization even at large incident angles. Specifically, for the TE polarization, the absorption decreases as the incidence angle increases from 0 to 55° but remains higher than 90% in a frequency range of 8 to 11.1 GHz, as shown in Figure 9(b). Similarly, in the TM mode, the absorption is maintained to be higher than 90% in a frequency region of 9.5 to 14.6 GHz for incident angles up to 55°, as demonstrated in Figure 9(c). These results reveal the high performance of proposed MA, which is insensitive to the polarization of incoming EM wave and highly stable under the oblique incidence.

Finally, the absorption properties of proposed MA are compared with those of other absorbers reported previously (shown in Table 1), such as plain FeCo-C composites [20], FeCo/ZnO ones [28], Fe₃C/C nanofibers [29], and snowflake-like MnO₂@NiCo₂O₄ ones [30]. The efficient bandwidth (EBW) of absorption is calculated as follows.

$$EBW=f_{high}-f_{low}$$

(1)

where $f_{high}$ and $f_{low}$ are the highest and lowest frequencies where the absorption is greater than 90%, respectively. The results indicate that our proposed absorber exhibits an enhanced absorption bandwidth, which can be attributed to not only the intrinsic properties of FeCo-C material but also the exploitation of MA structure.

4. Conclusions

We demonstrated that the EM-wave absorption properties of FeCo-C alloy were enhanced by exploiting the metamaterial structure. The ultrabroadband absorption was achieved between 7.9 and 14.6 GHz, with an absorption above 90% in case of the normal incidence of incoming EM wave for all polarization angles. The absorption remains to be above 90% in a frequency range of 8-11.1 GHz at wide angles of incidence from 0 to 55° for the TE polarization, while in the TM mode the absorption was also over 90% in a frequency range of 9.5-14.6 GHz. The physical mechanism of proposed MA was elucidated, revealing that the high and ultrabroadband absorption was controlled by the magnetic-dipole Mie-resonances in the MA structure and the intrinsic EM properties of FeCo-C material. Our work might contribute to the exploitation of various materials for the development of future MAs, which are used potentially for the microwave applications in radar and telecommunication technology, as well as for EM shielding for health safety.