Ultra-wide-angle and broadband metamaterial absorber based on monopole top loading antenna and its reciprocity Open Access

In order to meet the needs in the field of radar stealthy, the metamaterial absorbers should have both broadband absorption^1–6 and wide-angle absorption^7–13 properties. Loading resistive films¹ and lumped elements^2–4 can control the dispersion and make the permittivity and permeability equal in a wideband,² and then, a broadband absorption effect will be realized. Building three-dimensional (3D) structures has by far been the most effective way to achieve large angle absorption because the 3D structures can provide anisotropic electromagnetic parameters¹⁴ and flexible design freedom. In Ref. 8, a 3D MA consisting of periodic graphite resistive films organized in a honeycomb-like lattice was put forward. This 3D MA provided multiple resonances, resulting in a broadband absorption of 50–460 GHz, and the angular range for TE and TM polarizations is 0°–56°(>90%) and 0°–70°(>80%), respectively. In Ref. 10, a 3D MA composed of six split square-ring shaped resistive films with different sizes standing on a metal plate was designed. Owing to the upright resistive films of different sizes, the angular range for TE and TM polarizations in the frequency range of 39–144 GHz is 0°–45°(>80%) and 0°–60°(>90%), respectively. Shen et al.¹¹ proposed a 3D absorber inspired by the origami, and it achieves a larger-incident angle absorption until 75° in the frequency band of 3.6–11.4 GHz for TM polarization.

In 2005, Andersen pointed out that the absorption of the receiving antenna is between 0% and 100%,¹⁵ and the absorption efficiency depends on the directivity of the antenna and the scattering pattern.²³ In 2009, Pozar theoretically proved that the ground plate dipole array has the ability to absorb 100% of the energy of the reflected wave, that is, it is possible for the receiving antenna to achieve perfect absorption, and the ground plate dipole array is one of these types of antenna.¹⁶ In 2016, Lin et al. designed an ultra-wideband material absorber with dipole loaded resistance based on the principle of antenna reciprocity.¹⁷ 

Inspired by the above idea of antenna and the reciprocity principle, here, we designed an ultra-wide-angle and broadband metamaterial absorber by using a monopole top loading antenna with a 3D structure. The absorption of the MA-MTLS under oblique incidence was investigated. The wide-angle absorption performance of this structure is especially good for TM polarized waves. The results of simulation well matched the experimental results.

It is an important means for antenna miniaturization of loading a disk or radial blade on the top of a grounded monopole antenna. Through the top loading technology, the current distribution on the antenna can be improved and the effective height of the antenna can be increased. The disk or radial blade has distributed capacitance to the ground, which changes the overall current distribution of the loaded monopole antenna, and its top is no longer the wave node of the current. Therefore, the omnidirectional radiation capability will also be greatly improved.^18,19 According to the reciprocity principle, when a monopole top loading antenna is used as an absorber, it will also have a better omnidirectional absorption performance.

First, we obtain a monopole-like antenna absorber (MLAA) by placing a square cylindrical shell with a resistive film on the outer surface on a copper plate, as shown in Fig. 1. The period of the absorber is p; the outer side length and the thickness of the cylindrical shell are a and t, respectively; and the height is h₂. The dielectric constant of the square cylindrical shell is ε = 3.65(1 − i0.025). The thickness of the copper plate is 0.017 mm, and its conductivity is σ = 5.96 × 10⁷ S/m.

Second, a square ring or an open square ring shaped resistive film attached to the horizontal dielectric plate is put on the top layer, as shown in Fig. 2. The inner length of the square ring is a, and the ring width is b. The side length and the thickness of the dielectric plate are p and h₁, respectively. The width of the oblique 45° opening is t. The composites in Figs. 2(b) and 2(d) are typical metamaterial absorbers with monopole top loading structures (named MA-MTLS1 and MA-MTLS2, respectively).

To illustrate the absorption performance, the reflection of MLAA and MA-MTLS were calculated using the CST Microwave Studio software. The periodic boundary conditions were used in the x and y directions, and the open boundary condition was used in the z direction. Because the thickness of the copper plate is small enough compared with the penetration depth, the transmission (T) is negligible and, thus, its absorption is A = 1 − R, where A is the absorption and R = |S₁₁|² is the reflection. After optimization, the parameters were chosen as p = 40.0 mm, a = 15 mm, b = 5.5 mm, t = 0.6 mm, h₁ = 0.6 mm, and h₂ = 5.8 mm and the sheet resistances of the top and middle layers were 50 and 550 Ω/sq, respectively.

Figure 3(a) shows the absorption spectra of MLAA with different heights. It is clear that the absorption becomes better as height h₂ increases. The absorption of MA-MTLS-1 in which the monopole is top loaded will increase greatly with the minimum height h₂ = 5.8 mm, as shown in Fig. 3(b). This means that the top loading technology is a useful way to increase the effective height of the MLAA; thus, an excellent absorption effect with a low profile is achieved.

Let us still focus on the absorption effect of MA-MTLS-1. The absorption curve of MA-MTLS-1 whose ring width is b = 5.5 mm is shown in black in Fig. 3(b). It is clear from the black curve that the absorber has a relatively poor absorption in the frequency band of 6–8 GHz. In order to improve the absorbing performance in this frequency band, we analyzed the input impedance using Smith chart, as shown in Fig. 4(a). It is inductive as a whole in the frequency band of 6–8 GHz, and the equivalent resistance is 0.53Z₀–0.73Z₀, where Z₀ is the free space impedance. What we need to do next is to reduce the inductance and increase the equivalent resistance. For this purpose, we analyzed the current distribution at 7 GHz and then drew the equivalent circuit;²¹ see Figs. 5(a) and 5(b).

Formulas (1) and (2) indicate that the inductance L and resistance R both decrease as the ring width b increases; here, the inner length of the square ring a is a constant. This is consistent with Fig. 4(b), where L and R both become smaller compared to Fig. 4(a), which shows that our equivalent circuit is reasonable. However, due to the decrease in resistance R as b increases, the absorption deteriorates in the frequency band of 6–8 GHz; see the red curve in Fig. 3(b). In order to reduce the inductance L without reducing the resistance R, four oblique 45° openings were made at the four corners of the square ring on the top layer, known as MA-MTLS-2 with an open square ring. The surface current density and its equivalent circuit are shown in Figs. 5(c) and 5(d). The introduction of corner capacitance reduces the equivalent inductance of the whole circuit, as shown in Fig. 4(c), and the absorption of MA-MTLS-2 in the frequency band of 6–8 GHz increases to more than 90%; see the blue curve in Fig. 3(b).

To further broaden the absorbing bandwidth of MA-MTLS-2, the input impedance at 13 GHz was analyzed using Smith chart, and it is capacitive as a whole, as shown in Fig. 6(a). Therefore, in order to improve the impedance matching effect, we need to reduce the capacitance. In other words, the inductance of MA-MTLS-2 should be increased to offset the negative capacitance. From formula (1), increasing the inner length a of the square ring and reducing the ring width b seems to work. For this purpose, the open square ring of MA-MTLS-2 is split into two rings, and then, a new absorber named MA-MTLS-3 is obtained, as shown in Fig. 7(a). The distance between the two rings is e = 2 mm, and the width of the two rings is c = 3.5 mm and d = 2 mm, respectively. The capacitance of MA-MTLS-3 decreases a bit, as shown in Fig. 6(b). In order to continue decreasing the capacitance of MA-MTLS-3, an open square ring with a width of g = 1 mm is added on the periphery of the two rings of MA-MTLS-3, and then MA-MTLS-4 is obtained, as shown in Fig. 7(b). The distance between the two outer rings of MA-MTLS-4 is f = 1 mm. From Fig. 6(c), it can be seen that the capacitance of MA-MTLS-4 is much lower compared to MA-MTLS-3.

The absorption performance of the above three absorbers is shown in Fig. 8 when the electromagnetic wave is incident normally. It can be seen that with an increase in the number of open square rings, the absorption band becomes wider. The absorption of MA-MTLS-4 with three open square rings loaded on the top is greater than 90% in the frequency range of 3.3–13.8 GHz, and its relative absorption bandwidth can achieve 123%. See the black curve in Fig. 8.

Here, the effects of dielectric parameters on the absorption performance of MA-MTLS-4 are discussed. From Fig. 9(a), it can be seen that the dielectric thickness h₁ of the top layer has a greater impact on absorption, especially in the high frequency band. The smaller the thickness, the greater the relative bandwidth. The thickness of the cylindrical shell t has a little influence on absorption, as shown in Fig. 9(b). In Figs. 9(a) and 9(b), the dielectric constant ε = 3.65(1 − i0.025) is a constant. Keeping the dielectric thickness of the top layer h₁ = 0.6 mm and the thickness of the cylindrical shell t = 0.6 mm constant, the curve with an absorption greater than 90% moves to the low frequency with an increase in the real part of the dielectric constant, as shown in Fig. 9(c). However, the amplitude change is small, especially in the low frequency band. Figure 9(d) shows that the effect of loss tangent on absorption is so little that we do not need to consider its influence in subsequent experiments.

Finally, the absorption performance at oblique incidence of electromagnetic waves of MA-MTLS-4 with a dielectric constant ε = 3.65(1 − i0.025) and dielectric thickness h₁ = 0.6 mm was investigated. For a TE polarized wave, the incident angle range of MA-MTLS-4 with an absorption greater than 87% in the frequency band of 3.7–13.8 GHz is 0°–40°. When the incident angle increases to 60°, the absorption of the absorber is higher than 70% in the frequency band of 3.5–14.8 GHz, as shown in Fig. 10(a). For a TM polarized wave, the absorption of MA-MTLS-4 is higher than 90% in the frequency band of 3.6–13.8 GHz and the incident angle range is 0°–80°. When the incident angle increases to 83°, the absorption is higher than 80% in the frequency band of 3.7–14.5 GHz, as shown in Fig. 10(b). It can be seen that MA-MTLS-4 has a better ability to absorb TM polarized waves at a broader range of angles.

Table I shows the comparison with other published studies of 3D metamaterial absorbers. Compared with our previous work in Ref. 7 and others’ work in Refs. 11 and 12, the proposed absorber has a smaller thickness and better absorption performance under oblique incident waves of C-band and X-band for both TE and TM polarization modes, especially for TM polarization mode.

In the experiment, the square cylindrical shells and the top dielectric as a whole was printed using 3D printing technology, as shown in Fig. 11(a). The dielectric used here is a resin, and its relative dielectric constant is about 3.65. The entire size of the 3D printing structure is 400 × 400 × 7.2 mm³. For the sake of the robustness of the 3D printing structure, the dielectric thickness of both the top layer and the square cylindrical shell is 1.4 mm, which is higher than the thickness shown in the simulation. The resistive films in Fig. 11(b) were pasted on the outside of the square cylindrical shells. The resistive films on the top layer with patterns shown in Fig. 11(c) were fabricated by the screen printing technology. The average square resistance values of the top and the middle are 50 and 550 Ω/sq, respectively. Finally, the 3D printing structure and the copper plate were stuck together with epoxy resin, and the final sample was obtained, as shown in Fig. 11(d).

Before the test, we connected a pair of standard horn antennas working in the 2–18 GHz frequency band to the arch-shape bracket—one for transmitting electromagnetic waves and the other for receiving the reflected signal from the sample, as shown in Fig. 11(e). The measured and simulated results are compared in Fig. 12. There is a good agreement between them in higher frequency bands. In lower frequency bands, the test results are not as good as the simulation results. This is because the sample size in the experiment is not very large compared to the low frequency wavelengths, and it is significantly different from the infinite size in the simulation.

Inspired by the omnidirectional radiation performance of a top loading monopole antenna and the reciprocity principle, MA-MTLS-4 with a monopole top loading-like structure was designed. The absorption of MA-MTLS-4 under oblique incidence was investigated. It shows that the simulated and test absorption results of MA-MTLS-4 with a dielectric constant ε = 3.65(1 − i0.025) and dielectric thickness h₁ = 1.4 mm are basically consistent. This work may provide an effective way for designing wide-angle metamaterial absorbers that can effectively absorb microwaves in the C-band and X-band,²² especially for TM polarized waves.

The authors acknowledge the support from the National Natural Science Foundation of China under Grant No. 62001504 and the National Key Research and Development Program of China under Grant No. 2022YFB3806200.

The authors have no conflicts to disclose.

Aixia Wang: Funding acquisition (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Lei Li: Methodology (equal); Software (equal); Writing – review & editing (equal). Gaiping Zhang: Formal analysis (equal); Software (equal). Wenjie Wang: Formal analysis (equal); Resources (equal); Validation (equal), Xinmin Fu: Resources (equal); Validation (equal). Jiafu Wang: Conceptualization (lead); Supervision (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.