1 Introduction

Microwave absorbers have long been a hot research topic due to their wide application in both civil and military fields, such as sensors [1], electromagnetic stealth [2], energy harvesting [3, 4], and radar cross section reduction [2, 5]. The unique properties of metamaterials (MMs), such as negative refractive indices [6] and subwavelength diffraction [7], which are naturally unavailable, render them important in the field of wave absorption research. To extend the bandwidth of metamaterial absorbers, researchers have proposed a variety of methods, including high impedance surfaces [8, 9], multi-layer structures [10], and multi-resonant unit cells [11, 12]. While these methods have increased absorption bandwidth, concomitant increasing costs have arisen due to increasing MM design and manufacturing complexity.

In recent years, all dielectric MMAs have been proposed because of their medium dispersion characteristics [13]. Due to its fluidity, and that it is one of the most abundant and cheapest resources in nature, water is obviously highly attractive in manufacturing complex structures. The high permittivity of water [14, 15], which is close to 80 under normal conditions, is suitable for multi-scattering resonances. Simultaneously, the dielectric losses [14] of water are particularly high, making it an ideal material for perfect absorption. For example, Yoo proposed an MMA [16] comprising periodic water droplets, which achieved a broadband absorption rate of 90% in the range 8–18 GHz. Shen synthesized a transparent MMA [17] loaded with a water substrate using the transparency of water, which not only achieved broadband absorption, but also tunable infrared radiation. Because the permittivity of water varies greatly with temperature, Pang designed a thermal water-based broadband MMA [18]. Taking advantage of the fluidity of water, Odit demonstrated a water-based tunable metasurface [19], providing a novel way to study water-based absorbers.

In this paper, we present a water-based MMA with ultra-broadband absorption at microwave frequencies. Both simulation and experiment show that the absorption efficiency of the absorber in the 5.5–27.5 GHz band is over 90%. The angular tolerance of the absorber indicates that it works well at wide angles of incidence. The absorption characteristics of a curved absorber (curving introduces novel properties) are also discussed. Due to the above properties, future applications of the absorber, such as electromagnetic stealth and energy harvesting, are envisaged.

2 Design, simulation, and experiment

The unit structure consists of three parts, as shown in Fig. 1a: a water layer; a specially designed resin shell, which serves as a water-filled container; and a metal backplane. The geometric parameters are shown in Fig. 2. The optimized parameters are as follows: A = 4 mm, B = 3 mm, C = 3 mm, D = 1 mm, E = 0.5 mm, H1 = 5.3 mm, H2 = 0.5 mm, P = 10 mm, P1 = 4 mm.

Fig. 1
figure 1

a The unit structure of the designed absorber (the light blue structure is resin shell; the red structure is water layer which is embedded in the resin shell); b the fabricated sample; c the structure of water layer

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Fig. 2
figure 2

Geometric parameters of the corresponding structure

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The simulation is carried out using CST Microwave Studio. The x- and y-axes are set as a unit cell, and the z-axis is set as open (which means that the z-axis is the propagation direction of the incident electromagnetic wave). The permittivity and loss tangent of the resin are 3.0 and 0.001, respectively. The metal backplane is made of copper with a thickness of 0.035 mm and the electric conductivity of copper is \(5.8\, \times \,10^{7} {\text{s/m}}\). To demostrate the permittivity and loss tangent of water at microwave frequencies, the Debye formula [20] is used in the simulation:

$$\varepsilon \left( {\omega , T_{{{\text{water}}}} } \right) = \varepsilon_{\infty } \left( {T_{{{\text{water}}}} } \right) + \frac{{\varepsilon_{0} \left( {T_{{{\text{water}}}} } \right) - \varepsilon_{\infty } \left( {T_{{{\text{water}}}} } \right)}}{{1 - i\omega \tau \left( {T_{{{\text{water}}}} } \right)}},$$

where \({ }\varepsilon_{\infty }\) and \(\varepsilon_{0}\) are the optical and static permittivity, respectively; and \(\tau\) is the rotational relaxation time. The absorption of the absorber can be calculated as \({\text{ A}}\left( {\upomega } \right) = 1 - |S_{11} \left( \omega \right)|^{2}\), where S11 (ω) is the reflection.

For measurement, the proposed absorber, consisting of 20 × 20 unit cells and constructed by 3D printing, was tested at room temperature (20 ℃). The schematic of the experiment is presented in Fig. 3. During the test, the distance between the absorber and the antennas was 0.6 m, and the normal angle of incidence was 0°.

Fig. 3
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A schematic of the experiment

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3 Results and discussion

Figure 4 shows the reflection found in the simulation and in the experiment. The simulation shows that the absorption of the absorber is over 90% in the frequency range 5.5–27.5 GHz with a relative bandwidth of 133.3%. Due to limitations in the experimental equipment, tests were carried out within 4–18 GHz, which showed that the experimental results and the simulation results were basically consistent in this range. The main reason for the difference between the experimental and simulation results is that the manufacturing precision of the absorber cannot meet the requirements of the design. In addition, the water used in the experiment does not perfectly confirm to the Debye formula, because the water in nature contains impurities, leading to experimental error. As the trend of the experimental curve is consistent with the simulation curve, it is predicted that experimental absorptivity can also exceed 90% in the range 18–27.5 GHz.

Fig. 4
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The reflection of the simulation (4–30 GHz) and experiment (4–18 GHz)

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To demonstrate the advantages of the designed absorber, the absorption band and thickness of different water-based absorbers are listed in Table 1. The designed absorber has the widest bandwidth and the thinnest structural thickness.

Table 1 Comparison between the presented absorber and previous water-based MMAs
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It is important to understand the absorption principles of the absorber by analyzing the electric field distributions at the four peak frequencies, shown in Fig. 5a. At the low-frequency resonance peaks, f1 and f2, the electric field strength is mainly focused on the edge of the water. As frequency increases, greater electric field strength is focused on the resin shell. It is also evident that strong electric resonance is mainly concentrated on the boundary of the water layer. Meanwhile, the electric field energy strength in the resin shell is greater than in the water layer. According to formula of the boundary conditions [27] for the electromagnetic field, \({\varvec{N}} \cdot \left( {{\varvec{D}}^{\left( 1 \right)} - {\varvec{D}}^{\left( 2 \right)} } \right) = 0\), where \({\varvec{N}}\) is the vector to the surface. Thus, the normal component of the electric displacement vector, \({\varvec{D}}\), is continuous in the perpendicular direction of the boundary. In addition, \({\varvec{D}} = \varepsilon \,{\text{E}}\), where \(\varepsilon\) is the relative permittivity and \({\varvec{E}}\) is the electric field component. The high permittivity of water causes the electric field strength within the water to be lower than in the resin shell. Figure 6b shows the power loss densities at the four frequencies. The energy loss is mainly concentrated in the water layer, where the electric field distribution is strong, which is caused by the high dielectric loss of water.

Fig. 5
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The electric field distribution (a) and power loss densities (b) at the four frequencies

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Fig. 6
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The relative effective impedance of the absorber

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To further understand different absorption properties of the proposed absorbers, the impedance matching method was used. The impedance (Z) [28] can be reflected as \(Z = \sqrt {\frac{{(1 + s_{11} \left( {\omega )^{2} } \right)}}{{(1 - s_{11} \left( {\omega )^{2} } \right)}}}\). Figure 6 represents the real and imaginary parts of the relative effective impedance of the proposed absorber. Ideal impedance matching occurs when the real part of Z is 1, while the imaginary part is 0. As shown in Fig. 6, the real and imaginary parts of Z are close to 1 and 0 in the frequency range 5.5–27.5 GHz. Through observation of the equivalent impedance and corresponding absorption, the important relationship between absorption and ideal impedance matching is elucidated.

The absorption of the absorber at different angles of incidence, from 0° to 45°, is considered. Figure 7a and b show the absorption under the transverse electric (TE) mode in simulation and experiment. The absorption efficiency of the absorber decreases gradually with increasing incidence angle. When the angle of incidence increases from 0° to 30°, the absorption rate in the band 5.5–27.5 GHz exceeds 90%. At an angle of incidence of 45°, the absorption curve decreases significantly, but the absorption rate at the lowest point in the range 5.5–27.5 GHz still exceeds 70%. The experimental results and simulation results are obviously quite different under 8 GHz because far-field conditions were not well enough accounted for in the experiment, and the size of the absorber which we made was not large enough. When the angle of incidence increases in the transverse magnetic (TM) mode, the absorption intensity and bandwidth of the absorber increase gradually, as in Fig. 8. When the angle of incidence increases to 30°, the maximum frequency point of the perfect absorption band is over 30 GHz. The absorber shows an affinity for TM waves with wide angles of incidence.

Fig. 7
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The absorption of TE mode at different incidence angles: (a) simulation results; (b) experimental results

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Fig. 8
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The absorption of TM mode at different incidence angles: (a) simulation results; (b) experiment results

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When the MMA is applied to a surface structure, the absorption performance under curved surface conditions is particularly important. We bent the absorber into a cylindrical shape in the -z direction, as shown in Fig. 9a. The absorption of the curved MMAs (the size of the absorbers is 90 × 90 mm2, the curvature, R, is 40–70 mm with a step of 10 mm) is characterized in Fig. 9a. The curved MMA shows omnidirectional absorption in the frequency range 5–40 GHz under different curvatures. To evaluate the performance at different polarization angles of the curved absorber, the absorption of the absorber (R = 70) at a 0–45° polarization angle is studied, as shown in Fig. 9b. Clearly, absorption barely changes at different polarization angles.

Fig. 9
figure 9

The absorption of the absorber (a) on curved surface at different curvature, the illustration: the curved absorber; (b) at different polarization angles (R = 70)

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4 Conclusion

In conclusion, we have demonstrated a water-based MMA with ultra-wideband perfect absorption in the microwave band. The absorption rate of the absorber is over 90% in the frequency range 5.5–27.5 GHz, and the relative bandwidth is 133.3%. The distribution of electric field and power loss at different resonant frequencies are examined to elucidate the mechanism of ultra-wideband absorption; this confirms that the energy of the incident wave is mainly consumed by the water layer. The results also show that the absorber can work well under wide-angle incident waves, especially TM waves. More importantly, an omnidirectional ultra-wideband polarization insensitive absorber is realized when the designed absorber is bent. The absorber has broad application prospects in many fields, such as anti-radar and stealth technology.