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Abstract
Traditional absorbers are mostly limited by their large size and high profile, which renders them unfavorable for practical devices. To solve this problem, we design and test an ultra-thin metamaterial absorber (UTMA). The top layer of the metamaterial absorber is designed as a patterned combination of split ring and metal strips, so that its resonant frequency point is in the target low frequency. Meanwhile, ohmic loss is enhanced by loading lumped resistance in the gap of the meta-surface to improve the absorb efficiency (> 90%) and to expand the working bandwidth (1.24–3.14 GHz). Moreover, the total thickness of the absorber is 9 mm (0.037λwith respect to the lowest operating frequency). The working mechanism of UTMA is analyzed based on the equivalent media theory, surface current and electric field energy distribution. The experimental results are in good agreement with the simulation, which verifies the feasibility of the design. In this work, the metamaterial absorber is designed to meet the target requirements from three performance indexes: low frequency, ultra-thin, and wideband, leading to the prospect of broad applications in the military and civil fields.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the development of the times and the progress of science and technology, the demand for absorber in military and social fields is increasing. Traditional natural material absorbers suffer from inherent limitations, such as narrow bandwidth, low efficiency, complex processing and high cost [1–3]. In particularly, the military fighter is difficult to achieve stealth when facing the search and detection of the enemy's multi-station radar, thus exposing the target and reducing the survival rate. It is urgent to solve these practical problems in the current absorber field.
Recently, metamaterials [4–29] have been widely researched in sensors [10–13], invisibility cloaks [14,15], super lenses [16–21] and surface plasmons [22,23] due to their special electromagnetic properties, which do not exist in natural materials. Since Landy put forward the concept of perfect absorption [24], many broadband and efficient absorbers have been proposed, and the research of frequency ranges have been expanded to microwave [25–27], visible [28,29] and terahertz [30,31]. Traditional low-frequency absorber is mostly affected by the structure of large size and high thickness, and has limitations in specific engineering applications, such as stealth of fighter aircraft, electromagnetic shielding of communication and high-precision medical system, which reflects the practicability and urgency of researching ultra-thin low-frequency absorber. However, the absorber operating in the low frequency band below 3.5 GHz still faces the challenges of huge size and high thickness due to its large working wavelength, which limits its practical application [32–34]. Nowadays, significant progress has been made to solve these defects, such as the loading of lumped elements [35,36] and the application of magnetic materials [37,38]. Shi at el proposed the absorber that consist of a planar array with resistance-loaded metallic cross patterns and a vertical periodic crossed mesh array with resistance-loaded metallic ring patterns, which leads to excellent performance with low profile in 2.11–3.89 GHz [35]. They explored the effect of lumped elements on reducing thickness of the absorber. Meanwhile, Zhang at el realized broadband (2.2–9.5 GHz) performance by combining multi-layer conventional medium and magnetic coatings, and investigated the impact of magnetic materials on expanding working bandwidth [37]. Although many previous studies have been done in this area, it is still a challenging task to reduce the thickness of the absorber operating in the L - S band, expand the bandwidth and improve the absorption.
In this paper, an ultra-thin metamaterial absorber consisting of a magnetic material bonded to FR-4 substrate and loaded with lumped resistance in split metal ring is proposed, shown in Fig. 1. We have theoretically and experimentally proved that the absorption performance is higher than 90% at 1.24–3.14 GHz, and the structure thickness is only 9 mm ($0.037\lambda $). The working mechanism of the UTMA is analyzed based on equivalent media theory, surface current and electric field energy distribution. Meanwhile, the experimental results are in good agreement with that of the simulation. Our research provides a new exploration method for the development of ultra-thin, high-efficiency broadband absorber working in low frequency range.
Fig. 1. Structure and absorbing properties of the UTMA. The absorber we proposed consists of a metal surface loaded lumped resistors, an intermediate dielectric layer (FR-4 and magnetic material) and a metal sheet with a total thickness of 9 mm (), which could realize the absorption of more than 90% in 1.24 - 3.14 GHz.
2. Design, principle and characterization of the absorber
The UTMA we designed is composed of four layers, as shown in Fig. 2(a). The first layer is the surface structure of two parallel copper ($\sigma = 5.8 \times {10^7}S/m$) strips and the split ring loaded with lumped resistance. The specific structural parameters are as follows: the inner and outer radius of the metal ring is r1 and r2, the width of the gap on both sides and in the middle is g1 and g2, the width of the metal strip is w1 and w2, and the period is p, as shown in Fig. 2(b). The second layer is FR-4 medium with dielectric constant of 4.3, tangent loss angel of 0.025 and the thickness of h2. The third layer is a commercial magnetic material with a thickness of h1, which is composed of resonant magnetic insulated silicon wafers. In the material library of CST commercial simulation software, it is ECCOSORB SF 11.0-18.0 with complex permittivity of ${\varepsilon _\textrm{r}}\textrm{ = }{\varepsilon _\textrm{r}}^{\prime} + {\varepsilon _\textrm{r}}^{\prime\prime}$ and complex permeability of ${\mu _\textrm{r}}\textrm{ = }{\mu _\textrm{r}}^{\prime} + {\mu _\textrm{r}}^{\prime\prime}$, as shown in Figs. 2(c)-(d). Intense magnetic resonance can be generated to improve absorption efficiency due to the large imaginary part of the permeability. The bottom of the UTMA is a copper back plate with a thickness of 0.036 mm that prevents electromagnetic waves from passing through the absorber and ensures a transmission rate of zero. After optimization, the parameters are selected as: r1 = 5 mm, r2 = 4.5 mm, g1 = 2 mm, g2 = 5 mm, w1 = 3 mm, w2 = 1 mm, h1 = 5 mm, h2 = 4 mm, p = 25 mm.
Fig. 2. Structure and material parameters of UTMA. (a) Complete stereo view of the absorber. (b) Vertical view. Electromagnetic parameters of magnetic materials: (c) complex permittivity, (d) complex permeability.
Initially, the low-frequency ultra-thin absorber (without the resistance) we designed only had a point frequency resonance at f = 2.2 GHz, with narrow working bandwidth and absorbing efficiency lower than 90%, which was far from the expected design target, as shown in Fig. 3(a). In order to address these deficiencies, lumped resistance is loaded in the surface structure of the absorber. Due to the ohm loss of lumped resistance, low frequency incident electromagnetic waves completely bound by the absorber can be converted into electrical and heat energy and thus lost, so as to improve the absorption rate. Through this method, narrowband point frequency resonance of the absorber is successfully extended to 1.9 GHz (1.24–3.14 GHz), and the absorbing efficiency is higher than 90%, as shown in Fig. 3(b). We further analyze the working principle of the UTMA. The absorption of metamaterial absorber can be calculated by the formula [24]:
where $R(\omega )$ is the reflectivity of the absorber irradiated by electromagnetic wave and $T(\omega )$ is the transmittivity. Due to the bottom of the ultra-thin absorber designed by us is a copper backboard, whose thickness is far greater than the skin depth, the electromagnetic wave that is not exhausted by the absorber can be completely reflected, so that the $T(\omega )$= 0. Then, the calculation formula of the absorption rate can be simplified as $A(\omega ) = 1 - |{S_{11}}{|^2}$. The relative impedance is:Fig. 3. The impact of lumped resistance. Reflectivity and absorption curves of the absorber (a) without lumped resistance, (b) with lumped resistance. The$0.037\lambda $ normalized impedance of the absorber (c) without lumped resistance and (d) with lumped resistance.
${\mu _r}$ and ${\varepsilon _r}$ are relative permeability and permittivity respectively. It can be seen from Eq. (2) that the equivalent impedance of metamaterial absorber is equal to the free space impedance Z0 when the real and imaginary parts are equal to 1 and 0, respectively.
According to formula (4), we can calculate the equivalent impedance of the absorber by deriving the simulated S parameters. Perfect absorption over the corresponding frequency can be theoretically achieved once Zeff matches Z0. In order to explain the principle of impedance matching and the specific function of the lumped resistance loaded on the UTMA, the Zeff(f) of the absorber loaded and unloaded resistance is calculated. In Fig. 3(c), the real part of the equivalent impedance of the absorber without resistance fluctuates and does not remain near 1, and the imaginary part is also unstable and deviates greatly from 0, resulting in a poor absorbing performance, which is consistent with CST simulation results as shown in Fig. 3(a). The equivalent impedance of the UTMA loaded with resistance matches well with that of the free-space in 1.24 - 3.14 GHz, with the real part is stable at 1 and the imaginary part is almost 0, causing an efficiency absorption greater than 90%, as shown in Fig. 3(d).
The equivalent medium theory is used to analyze the working mechanism. It is well-known that metamaterial absorbers with subwavelength units can modify dispersion by introducing multiple resonances with controllable dissipation [36]. Through the design of the unit to dominate the electromagnetic parameters of metamaterial to make it possess the unique electromagnetic characteristics that the natural materials do not have, so as to achieve excellent performance. One of the most widely utilized techniques for extracting electromagnetic parameters of metamaterials is to retrieve the S-parameters acquired by simulation or experiment. The refractive index(n), equivalent impedance(z) and complex constitutive parameters (${\varepsilon _r}$, ${\mu _r}$) can be calculated as follows [39]:
As shown in Fig. 4(a), three magnetic resonances around 1.0, 2.2 and 3.4 GHz and two electrical resonances at 1.4 and 2.8 GHz are excited, which has a quite narrow bandwidth. The real and imaginary parts of the complex permittivity and permeability are equal respectively at 1.3 and 3.1 GHz, and the imaginary part is a large positive value, which meets the requirement of perfect absorbing (>99%) mentioned above, and corresponds to the reflectivity of the red solid line sho in Fig. 4(d) with a value less than −20 dB at these two points. After increasing the value of the resistor to 200$\mathrm{\Omega }$., shown in Fig. 4(b), the frequency with similar complex constitutive parameters appears around 2.1 GHz, realizing perfect absorption with enhanced bandwidth of reflectivity less than −20 dB as shown in the solid blue line in Fig. 4(d). From the analysis mentioned above, it can be concluded that by adjusting the value of the lumped resistance, the constitutive parameters of the metamaterial absorber can be changed to modify its absorption and bandwidth. Based on this, we optimize the resistance value of 64 ohm through CST simulation to realize a better performance. Meanwhile, its constitutive parameters are extracted as shown in Fig. 4(c). In the range of 1.24–3.14 GHz, the real and imaginy parts of the equivalent permittivity and permeability are flatter and approximately equal due to the increased dissipation, making the reflectivity lower than −10 dB, as shown by the black line in Fig. 4(d), which accords with the theoretical derivation.
Fig. 4. Complex constitutive parameters and reflectivity. Equivalent permittivity and permeability for different lumped resistance values (a) 10$\mathrm{\Omega }$, (b) 200$\mathrm{\Omega }$. and (c) 64$\mathrm{\Omega }$. (d) Reflectivity curves.
For further study on the high-performance of the UTMA in low-frequency range, the surface current and electric field energy distributions are presented in Fig. 5. At the resonant frequency f = 1.48 GHz, the current is mainly concentrated at the junction of the split ring and two parallel bands, there is also a strong current distribution at the lumped resistance, shown in Fig. 5(a). However, at the other resonant frequency f = 2.7 GHz, the surface current is mainly distributed along the direction of the electric field in the upper and lower metal strips, which causes a strong electrical resonance to consume the incident electromagnetic wave. Meanwhile, the electric field energy distribution is shown in Figs. 5(c)-(d). At 1.48 GHz, the electric field energy mainly concentrates on the four ends of the split ring and the middle resistance, while it mainly focuses on the two metal strips at 2.7 GHz, which is also a good proof of the loss mechanism. In summary, the lumped resistance can not only change the equivalent resistance of the UTMA to achieve impedance matching, but also conduct the current in the split resonant ring to enhance the loss.
Fig. 5. Analysis of working mechanism of the UTMA. (a) surface current and (c) electric field energy distributions at f = 1.48 GHz, (b) surface current and (d) electric field energy distributions at f = 2.7 GHz.
The UTMA is a multilayer absorber composed of a variety of materials, whose structural parameters have specific effects on its absorbing performance. Therefore, we adjust and optimize the parameters in CST to achieve our design objectives. As the radius of the split copper ring increases, the resonant frequency moves to the low frequency. Based on this, the absorber can be designed to work in the lower frequency range. But the value of S11 will increase, even more than −10 dB, as shown in Fig. 6(a). Lumped element plays a key role in affecting the performance of the UTMA. With the increase of R, the reflectivity is decreased, while the operating bandwidth will be relatively reduced. Therefore, both of the bandwidth and absorptivity should be taken into account during the simulation, as shown in Fig. 6(b). It can be seen from Figs. 6(c)-(d) that the increase of g1 improves the absorption efficiency at 2.7 GHz slightly, but has the opposite effect at 1.5 GHz. The increase of g2 will enhance the reflectivity of the two resonant points and reduce the absorptivity, but almost has no effect on the bandwidth. Thus, it can conclude that the gaps have little influence on the UTMA, which brings convenience for the following physical processing. Shown in Figs. 6(e)-(f), as the width of the parallel metal strips increases, the working bandwidth will move to a lower frequency and can even achieve the efficient absorption of 1–2.5 GHz. However, the absorption efficiency is inversely proportional to the size of w1, blindly increasing the width cannot achieve the best performance. The width of the internal strips mainly affects the absorption efficiency at the two resonant frequency points. For example, the increase of w2 will improve the reflectivity and decrease the absorption rate at 2.7 GHz, while at the low resonant frequency, the effect is opposite. The thickness of the absorber has a crucial influence on the properties, in order to achieve ultra-thin requirements, the thickness should be as low as possible first, and then the research should be carried out in the direction of increasing bandwidth and improving absorption efficiency. The variation of magnetic medium and FR-4 thickness has similar effect on reflectivity. As shown in Figs. 6(g)-(h), with the decrease of h1, the resonant frequency will shift from low to higher frequency, result in the deterioration of reflectivity, so that only the high range maintains perfect absorption performance. Similarly, with the decrease of h2, the low-frequency absorbing performance deteriorates, and perfect absorption performance only appears in the high frequency band. Therefore, in order to achieve low-frequency broadband microwave absorption, it is necessary to comprehensively consider the performance indexes of working bandwidth and absorption efficiency, and reasonably adjust the thickness of h1 and h2.
Fig. 6. Parameter optimization of the UTMA. (a)Radius of metal ring. (b) Lumped resistance. (c-d) The inner and outer gaps of the split ring. (e) Outer and (f) inner width of metal strips. The thickness of (g) magnetic medium and (h) FR-4.
To experimentally validate the performance of the UTMA, a $500mm \times 500mm \times 9mm$ sample has been fabricated. For the magnetic material (MM), firstly the rubber additives are added to the raw rubber, the magnetic material and rubber are mixed, then the unvulcanized rubber is calendered to the desired thickness and put into the pressure mold for high temperature vulcanization, finally the vulcanized magnetic rubber sheet is removed from the mold for trimming treatment. The reflectivity performance comparison of MM and ECCOSORB SF 11.0–18.0 under the set size is shown in the Figs. 7(c)-(d). It can be seen that they have similar reflectivity curves, especially in the low frequency band we need. Therefore, we used MM instead of ECCOSORB SF 11.0–18.0 due to the difficulty of processing. For the surface structure (SS), for the convenience of manufacturing, we choose the chip resistance of 62$\mathrm{\Omega }$. instead of 64. in the simulation. The bottom layer is a metal sheet of copper, which is designed to block the transmission of electromagnetic waves as shown in Fig. 7(b). We connected two linear polarization standard gain broadband horn antennas to an AV3672B Vector Network Analyzer (VNA) as the transmitter and receiver, shown in Fig. 7(a). For the purpose of eliminating the influence of environmental interference, we used the time domain gate function in the (VNA). In Fig. 7(e), the absorption curve of experimental test is in good agreement with the results of simulation calculation, which proves the feasibility of the UTMA proposed by us. The deviation of test result is mainly due to resistance welding material processing. For different incident angles and polarization problems, the simulation results are shown in the Fig. 7. As can be seen from Fig. 7(f), under TE polarization mode, with the increase of incident angle, the reflectivity of UTMA increases, resulting in the decrease of absorption efficiency. In the range of $0^\circ{-} 30^\circ $, the absorption efficiency of the absorber is still higher than 90%, but the bandwidth is slightly reduced. While the incident angle is higher than $30^\circ $, the reflectivity of the absorber is greater than −10 dB, and the absorption efficiency is less than 90%, resulting in serious performance deterioration. It can be seen from Fig. 7(g) that the absorber of this structure does not have absorption performance under TM mode. This is because the structure of UTMA does not have geometric centrosymmetric structure, which eventually leads to its sensitivity to the polarization mode of incident wave.
Fig. 7. Experimental tests and performance. (a) Experimental test setup. (b) Sample structure for processing. Reflectivity contrast at set size between (c) ECCOSORB SF 11.0–18.0 and (d) magnetic material. (e) The absorption curve of experimental test and simulation. The reflectivity of UTMA varies with incident angle under (f)TE and (g)TM polarization modes.
Table 1 shows the comparison of working band and structural thickness between relevant work and the proposed low-frequency ultra-thin absorber. It can be seen that under the joint action of surface structure and lumped resistance of UTMA, the absorber works in the range of 1.24 - 3.14 GHz, and the absorption rate is higher than 90%. At the same time, the structure thickness is only 9 mm. Other work will sacrifice the thickness of the structure at the cost of reducing the operating band. In the field of low-frequency absorption, UTMA has great advantages in electromagnetic performance and physical size.
Table 1. Comparison with other absorbers.
The performance comparison between UTMA and commercial absorbers is shown in Table 2. It is obvious that UTMA still has great room for improvement in performance and thickness, but it can provide a method reference in the structural design and thickness reduction of metamaterial absorber, and the commercial absorber needs to be improved in terms of strength enhancement and damage resistance, which limits its application scenarios.
Table 2. Comparison with commercial microwave absorbing plate
3. Conclusion
In summary, we proposed an ultra-thin low-frequency metamaterial absorber, which consists of a top metal patterned structure lumped resistance, a middle FR-4 and magnetic material medium, and a bottom metal sheet. The surface metal strips and split ring determine the low resonance frequency, while the lumped resistance broadens the bandwidth and increases the absorption efficiency. The complex constitutive parameters of the UTMA are extracted to analyze its working principle with equivalent media theory. Meanwhile, the distribution of surface current and electric field energy also confirms its working mechanism. We manufactured a sample for testing, and the experimental results are in good agreement with that of the simulation, which proves the feasibility of the design. Finally, the UTMA proposed in this paper can realize more than 90% absorption efficiency in 1.24–3.14 GHz, and the thickness is 9 mm ($0.037\lambda $), break through the limitation of high profile of traditional low-frequency absorbers and provide a method guidance for the design of ultra-thin absorbers.
Funding
China Postdoctoral Science Foundation (2020M671720); President's Fund of Air Force Engineering University (XZJ2020068); Key Projects of Aviation Foundation (201918037002); Natural Science Foundation of Shaanxi Province (2019JQ-013); National Natural Science Foundation of China (61701572, 61871394, 61901512).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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