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Abstract
Wideband microwave absorbers, especially those with high optical transparency, are significantly used in civil and military fields. This paper proposes an ultra-wideband optically transparent metamaterial absorber (MMA) with causal optimal thickness and high angular stability. Based on the equivalent circuits model of the MMA, a genetic algorithm is adopted to identify the best circuit parameters that can realize broadband microwave absorption. High transparent indium tin oxide and poly-methyl methacrylate are utilized to realize the absorber. Optimization and simulation results show that the designed MMA presents a high microwave absorption above 90%, covering a wide frequency of 2.05–15.5 GHz with an impressive FBW of 153.3%. The proposed MMA exhibits extraordinary angular stability. For TM polarization, it can still maintain a fractional bandwidth (FBW) over 114.5% at an incidence angle of 70° and over 142% at an incidence angle of 60°, while the FBW of both TE polarization and TM polarization exceeds 150% when the incidence angle is below 45°. Furthermore, the proposed absorber has the advantages of high transparency and polarization insensitiveness. A prototype of the proposed MMA is fabricated and experimentally tested. The measured results are in excellent agreement with the optimized design and the full-wave simulation results, demonstrating its excellent performance. Most significantly, the overall thickness of the absorber is 0.102 λ at the lowest working frequency and only 1.08 times the causality-dictated minimum sample thickness. The MMA proposed herein provides methods to achieve high compatibility with wideband microwave absorption, optical transparency, and wide-angle incidence, thus enabling a wide range of applications in stealth, electromagnetic pollution reduction, and electromagnetic compatible facilities.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of wireless communications, 5 G, and other technologies, the electromagnetic (EM) environment is becoming increasingly complex, and EM safety and compatibility are consequently facing more challenges. The electromagnetic interference (EMI) and EM radiation caused by communication equipment are increasingly serious, directly affecting human health and the normal operation of electronic equipment [1,2]. Ultra-wideband microwave absorption materials provide an excellent solution to this challenge and have been a hot research field for decades. Among the existing materials, carbon-based materials are promising owing to their tunable properties, environmental stability, and low-density properties [3]. Graphene, a hot material, has shown potential in microwave absorption because of its tunable conductivity, good processability, and low density [4]. Magnetic loss strategy materials such as ferrite and metal compounds are widely used in microwave absorption. However, high filler ratio, high density, and low corrosion resistance limit their further applications [5–7]. In recent years, metamaterials have been developed rapidly, making it possible to optimize the absorption spectra of specific targets in different application scenarios due to their excellent electromagnetic modulation properties [8]. Compared to conventional microwave absorbers composed of carbon-based materials and metal-organic frameworks derived materials [3–7], metamaterial absorbers (MMAs) exhibit advantages such as ultra-wideband microwave absorption, small weight and thickness, and high design flexibility and tunability [8–20]. Moreover, it is difficult for traditional absorbers to reach the causality-dictated minimum thickness for broadband absorption since it may involve changing the material properties. However, MMA could potentially achieve this [8]. In 2008, Landy et al. proposed a perfect MMA by placing periodic metal resonant rings on an FR4 dielectric layer to form a cell structure with rectangular metal as the base plate. The MMA achieves nearly perfect absorption at the working frequency of 11.48 GHz [9]. Since then, MMA has attracted substantial attention in numerous applications such as sensors [11,21], ultra-wideband absorption [12,13,19], terahertz absorbers [14,15], energy harvesters [17], multi-band absorption [15,18], and radar cross section reduction [22–24].
However, since most of the abovementioned absorbers use opaque metals and substrate materials, these designs are hardly suitable for applications requiring high microwave absorption and high optical transparency. Consequently, light-transmissive MMAs are demanded to address these challenges. Owing to the prospects offered by transparent resistive films for microwave absorption, optically transparent MMAs have developed rapidly in recent years. For example, Jang et al. obtained higher absorption performance in the frequency band spanning 5.8-12.2 GHz by employing aluminum wire grids to construct transparent MMAs [25]. Wu et al. realized a transparent W-band absorber using a concise metal mesh structure fabricated by the electro hydrodynamics printing technology [26]. Meanwhile, conductive indium tin oxide (ITO) film with high optical transparency also facilitated the development of optically transparent MMAs. Hu et al. explored ITO as a standing-up closed-ring resonator, achieving over 85% absorption over a broad frequency range of 5.5-19.7 and 22.5-27.5 GHz, while only for one specific polarization [27]. Water as substrates enables optically transparent MMAs to perform better in radar-infrared bi-stealth or tunable characteristics [28–30]. Air spacing was also directly used to design optically transparent MMAs [31–33]. Nevertheless, most design schemes are based on transparent glasses or plastic substrates and ITO films [22,34–45]. The absorber can be highly optically transparent by using highly conductive ITO films to form the functional layer and glasses as the dielectric substrates [34–38]. Xu et al. demonstrated a multilayer structured MMA using glass as substrates. The proposed MMA achieved more than 90% absorption in the 8-20 GHz frequency range, with absorption performance insensitive to incident polarization [38]. Compared to glasses, MMA with poly-methyl methacrylate (PMMA), polyethylene terephthalate (PET), polyvinyl chloride (PVC), and other polymers as dielectric substrates also exhibit high optical transparency. These materials have smaller permittivity and can provide higher bandwidth [39–44]. Jiang et al. demonstrated a sandwich structure consisting mainly of transparent PVC layers with some flexibility while having a fractional bandwidth (FBW) of 85.7% [40]. Using two resonant layers, Li et al. achieved an ultra-wide absorption in the frequency range from 2 to 11.37 GHz with an impressive FBW of 140.2% [42]. Despite the growing evolution of transparent MMA, it is still challenging to simultaneously realize the combination of ultra-wideband and strong absorption at wide angular incidence while being optically transparent and polarization-independent. And high absorption performance at a large incidence angle is even more significant in practical scenarios. Unfortunately, optically transparent MMAs that can maintain high absorption performance and FBW over 150% even at large angular incidence are rarely reported. Besides, achieving better performance with simple, easy-to-mass fabricate structures is also quite significant. Moreover, for a passive absorber, there is a standard and universal causality-dictated minimum sample thickness for an arbitrarily given absorption spectrum [46]. This theoretical limit also plays a critical role in the design of acoustic absorbers [47] and microwave transmission systems [48]. Recently, Qu et al. [49] reported a composite absorber that can approach the causality-dictated minimum sample thickness, few other reported absorbers can achieve such results. However, their absorber combines hierarchical metal ring structures with foam patches to achieve absorption, which is not optically transparent and cannot be easily encapsulated and integrated. Meanwhile, it is difficult to achieve engineering applications. To the best of our knowledge, the causal optimal optically transparent metamaterial absorber has not yet been designed and experimentally realized, which therefore is one of the challenges we were trying to overcome.
In this paper, a causal optimal and optically transparent ultra-wideband MMA with high angle stability based on a simple patterned metasurface has been designed, fabricated, and experimentally tested, consisting of three-layers ITO and three-layers PMMA substrate as shown in Fig. 1. The bandwidth (BW) with an absorptivity higher than 90% in simulation and experimental results ranges from 2.05 to 15.5 GHz, and the FBW is 153.3%. The total thickness of the whole structure is 15 mm (only 0.102 λ at the lowest working frequency), which is quite close to the minimum thickness (13.85 mm) as dictated by the causality constraint. High angle stability for both TM polarization and TE polarization is demonstrated. For TM polarization, FBW over 114.5% was maintained at a maximum incidence angle of 70°. Moreover, more than 150% FBW can be achieved until the incidence angle reaches 45° for both TM polarization and TE polarization. Besides, the proposed MMA has the advantage of polarization insensitiveness.
Fig. 1. The proposed MMA and its performance. A Schematics of optically transparent ultra-wideband MMA. B Schematics of a unit cell and its equivalent circuits model of the MMA. C S11 parameters, S21 parameters, and absorption comparison of the GA optimization results and full-wave simulation.
2. ECM optimization and full-wave simulations
The schematic diagram of a unit cell and its equivalent circuits model (ECM) of the MMA is shown in Fig. 1. The Cover, Substrate 1, and Substrate 2 are PMMA (ɛr = 2.8, tanσ=0.001). Layer 1, Layer 2, and Back Layer are transparent ITO resistive layers with different sheet resistances. A two-step design process was adopted to obtain high and ultra-wideband microwave absorption. First, a genetic algorithm (GA) is used to search for the best circuit parameters (Ri, Li, and Ci, i = 1, 2) that can realize broadband absorption according to the ECM of the MMA. Then, a retrieval process is executed to match the geometric parameters (P, gi, and li, i = 1, 2) and sheet resistance of Layer 1 and Layer 2 with the corresponding optimized equivalent parameters, and the complete structure is then constructed.
As shown in Fig. 1, the MMA can be regarded as a two-port network based on the transmission line theory. In this two-port network, PMMA slabs are modeled as transmission lines with characteristic Zi (Zi = Z0/(ɛr, i)0.5, Z0 = 120π Ω is the impedance of free space), and ITO resistive layers are modeled as series inductance Li, capacitance Ci, and resistance Ri. After establishing the ECM of the MMA, the ABCD matrix is adopted to calculate the absorption through equivalent parameters under normal incident waves.
Combining Eqs. (1)–(5), the microwave absorption of MMA can be easily calculated through fundamental parameters Ri, Li, Ci, and di, i = 1, 2, 3. However, it is challenging to manually find a sound combination of parameters to achieve wideband absorption due to their complicated numerical relationships. Consequently, GA is introduced to automatically obtain the appropriate equivalent circuit parameters to maximize the average absorption in the desired band. Considering that the working band of the MMA and the conventional thickness of PMMA can be easily acquired, in the optimization process, di is set as 5 mm. The absorption performance of the MMA will be better if di is also a parameter that can be arbitrarily optimized. This issue will be discussed in the causal limit on sample thickness section. The remaining optimal circuit parameters are listed in Table 1. S11 parameter and absorption calculated by using the circuit model are presented in Fig. 1(C). It is evident that the optimized circuit parameters can offer excellent absorption over 0.9, covering an ultrawide frequency range of 2.05–15.5 GHz, and the FBW is 153.3%. Moreover, two absorption peaks can be observed at 2.72 GHz and 14.47 GHz.
Table 1. Optimal Circuit Parameters and The Geometry Parameters of The Final Structure
The second step is to find the geometric parameters of Layer 1 and Layer 2 corresponding to the optimized equivalent parameters. As shown in Fig. 1(B), simple resonance ring arrays are selected as the basic unit to realize optimized equivalent parameters. It is worth noting that rings with large perimeters and narrow line widths can provide large inductances, and small distances between adjacent rings always produce large capacitances. Meanwhile, to release the influence of PMMA slabs, a PMMA-resonance ring layer-PMMA sandwich structure is adopted in the retrieval process. By adjusting the period P, geometric parameters li, gi, and sheet resistance until the real part and imaginary part of actual impendence are close to the impedance ZMMA, i formed by the optimal parameter Ri, Li, and Ci, resonance layers matching the optimal circuit parameters can be obtained. The obtained geometric parameters dimensions are P = 6 mm, g1 = 20 µm, g2 = 150 µm, l1 = 950 µm, and l2 = 320 µm, and the sheet resistances of Layer 1 and Layer 2 are 40 Ohm/sq and 35 Ohm/sq, respectively. ITO-PET film with 6 Ohm/sq sheet resistances is utilized as the Back layer. The S11 parameter, S21 parameter, and absorption of the constructed MMA simulated by full wave simulation are presented in Fig. 1(C). As shown in Fig. 1(C), the S21 parameter of the constructed MMA is less than −30 dB in the range of 2–18 GHz, which means that the MMA has almost no transmission and the Back layer has a perfect reflection effect similar to metal plates.
Simulated absorption and FBW under different incident angles of the constructed MMA for both TM-polarized and TE-polarized waves are shown in Fig. 2. Figures 2(A) and (B) depict that TM polarization is more advantageous than TE polarization in absorptivity at different incidence angles, especially at large incident angles. For TM polarization, the absorptivity is still above 0.9 at incident angles larger than 70°. Moreover, for both TM polarization and TE polarization, the absorptivity is above 0.9 at incident angles from 0° to 45°. And as can be seen from the FBW data provided in Figs. 2(C) and (D), under both TE polarization and TM polarization, with the increase of incident angles, the lowest frequencies have little change (2.05-2.43 GHz), and the highest frequencies shift from 15.5 GHz to 17.0 GHz, while the bandwidth is increased. Meanwhile, the FBW exceeds 150% for both TM-polarized and TE-polarized incident waves at incident angles from 0° to 45°. Figures 2(E) and (F) show the S11 parameter and absorption of different polarizations at incidence angles of 0°, 30°, 45°, 60°, and 70°, respectively, from which a more intuitive result can be obtained that the absorption bandwidth under TM polarization is 4.53-16.74 GHz at an incidence angle of 70°, and the FBW is 114.5%. While for the incidence angle of 60° under TM polarization, the FBW will be increased to 141.9%. These previous results indicate convincingly that the designed MMA exhibits high angular stability in terms of absorptivity and absorption bandwidth.
Fig. 2. Absorption, FBW, and S11 parameters under different incident angles. A C E TM polarization, B D F TE polarization. A B Absorption, the contour line is 0.9, C D FBW, E F S11 parameter under 0°, 30°, 45°, 60°, and 70°.
Figure 3 shows the absorption of the MMA under different polarization angles and incident angles for both TE polarization and TM polarization. It is clear that the absorptivity and bandwidth are almost identical at various polarization angles from 0 to 90° under normal and oblique incidence, which demonstrates that the design has the advantage of being polarization insensitive.
Fig. 3. Absorption under different incident and polarization angles, the contour line is 0.9. A C TE polarization, B D TM polarization. A B Normal incidence, C D oblique incidence (θ=30 degrees).
3. Experiment verification
For verifying the ultra-wideband absorption performance of the designed MMA, a 300 × 300 mm2 sample with 50 × 50-unit cells is fabricated, as shown in Fig. 4. ITO-PET films with 0.1 mm thickness are used to replace resistive layers. The Back Layer is 6 Ohm/sq ITO-PET films with high optical transparency. A high-precision laser etching process is utilized during the sample fabrication process to realize the periodic cell structure of Layer 1 and Layer 2. Figures 4(D) and (E) show microscope photographs of Layer 1 and Layer 2 after etching, and it is apparent that a high precision of the sample processing is accomplished. Even though the minimum spacing between the periodic cells is 40 µm, the processing technology can still achieve excellent results. The experiment environment is presented in Fig. 4(A), and the arch test method is selected to measure the microwave absorption of the sample.
Fig. 4. Fabricated MMA sample and test results. (A) test environment. B C fabricated MMA sample and its optical transparency, (B) covered with the sample, (C) non-covered. (D, E) micro photo of the ITO film. (F) Optical transmittance experiment results. (G) Comparison of the simulation and experiment results.
A logo covered with and without fabricated MMA is shown in Figs. 4(B) and (C), respectively. As shown in Figs. 4(B) and (C), covering the logo with the fabricated absorber would not affect its visibility, and the logo in Fig. 4(B), including the text therein, is still clearly visible compared to the uncovered case in Fig. 4(C), which illustrates its high optical transparency. The optical transmittance of the PMMA, ITO films, and the MMA sample are shown in Fig. 4(F). In the visible light band (400-780 nm), the average optical transmittance of the MMA sample is 56.0%.
The tested absorption performance under normal incidence and the corresponding results for full-wave simulation and the GA-optimized equivalent circuit are shown in Fig. 4(G). The absorption is better than 0.9 from 2.06 to 15.52 GHz, which agrees well with the simulation and calculated results. Meanwhile, the tested results show strong absorption near 2.7 GHz and 14.5 GHz, which agrees with the two absorption peaks obtained by full-wave simulation and equivalent circuit calculation.
4. Discussion
4.1 Impedance and electromagnetic field analysis
The equivalent impedance Zeff(ω) is obtained to analyze the proposed MMA's absorption mechanism. It can be calculated from the simulated S-parameters according to the effective medium theory [49].
For further understanding of the proposed MMA's absorption mechanism, the electromagnetic responses of Layer 2 and Layer 1 under normally incident TE plane waves at 2.72 GHz and 14.47 GHz are shown in Figs. 6 and 7. Figures 6(A) and (C) show the electromagnetic field distribution of Layer 2 at 2.72 GHz, and Figs. 6(B) and (D) show the electromagnetic field distribution of Layer 2 at 14.47 GHz. Similarly, Figs. 7(A) and (C) and Figs. 7(B) and (D) show the electromagnetic field distribution of Layer 1 at 2.72 GHz and 14.47 GHz, respectively.
Fig. 6. Electromagnetic responses of Layer 2 under normally incident TE plane wave. (A, C) @2.72 GHz, (B, D) @14.47 GHz. (A, B) distributions of the surface electric field, (C, D) distributions of the surface magnetic field.
Fig. 7. Electromagnetic responses of Layer 1 under normally incident TE plane wave. (A, C) @2.72 GHz, (B, D) @14.47 GHz. (A, B) distributions of the surface electric field, (C, D) distributions of the surface magnetic field.
At 2.72 GHz and 14.47 GHz, the electric field exists only at the gap between the two ring structures and there is almost no electric field exists in the interior of the rings, which indicates that the movement of electrons in the conductive ITO film under the action of incident electric field causes the accumulation of charge and the charge is stored in the gap between the two ring structures. For both Layer 2 and Layer 1, the electric field exhibits different characteristics at 2.72 GHz and 14.47 GHz because the location of accumulated charge is related to the incident wavelength. On the contrary, the magnetic field is existed only around the rings, while almost no magnetic field exists inside the rings or at the gap between the two rings, which indicates that the directional movement of charge generates a surface current that is parallel to the direction of the incident electric field and the surface current is stored in the form of a magnetic field on the rings. For both Layer 2 and Layer 1, the magnetic fields exhibit similar characteristics at 2.72 GHz and 14.47 GHz, and the induced magnetic fields are generated in the same way. The electric field between the gaps generates a strong capacitive effect, while the magnetic field around the rings generates a strong inductive effect, which can correspond precisely to C and L in the previous equivalent circuit model. Although the electromagnetic field distribution of Layer 2 and Layer 1 are different at two resonance frequencies, they always work together to form broadband absorptions.
4.2 Influence of material parameters variations on absorption performance
Since the permittivity and thickness of the existing PMMA substrate differ slightly from the ideal values, the influences of the relative permittivity and thickness of three PMMA substrates on the absorptivity were investigated. Figures 8 and 9 display the absorptivity and FBW of the proposed MMA simulated by changing the relative permittivity and thickness of PMMA slabs, respectively. As can be seen from Figs. 8(A) and (B), either TE polarization or TM polarization, the change in relative permittivity does not affect fmin. Instead, fmax tends to shift to lower frequencies as the relative permittivity increases. As shown in Figs. 8(C) and (D), the FBW decreases as the relative permittivity increases, maintaining above 150.5% in all cases. Similarly, the results in Figs. 9(A) and (B) show that an increase in substrate thickness has no significant change on fmin, while fmax tends to lower frequency. Moreover, the FBW is around 153% at all thicknesses. The consistency of the above results for TE polarization and TM polarization further verifies that the designed MAA is polarization insensitive.
Fig. 8. Absorption and FBW under different relative permittivity. (A, C) TE polarization, (B, D) TM polarization.
Fig. 9. Absorption and FBW under different substrate thickness (A, C) TE polarization, (B, D) TM polarization.
4.3 Causal limit on sample thickness
Figure 10 illustrates the S11 parameter variation by only changing the thickness of the Cover layer. There is a wide variation in the absorption effect when the thickness of the Cover layer can be changed arbitrarily. The MMA operates in 2.08 GHz-16 GHz with a relative bandwidth of 154.0% when the thickness of the Cover layer is 4.2 mm. Meanwhile, the maximum absorptivity exceeds 99.9%, and the relative thickness is decreased to 0.0985. This means that better results would be obtained if the thickness of the Cover layer is also used as one of the optimization parameters during the design process. Similarly, the proposed MMA has certain tunable features by changing the thickness of the Cover layer. Unfortunately, it is not easy to obtain unconventional thicknesses of PMMA slab during the actual manufacturing process of the sample. Therefore, other Cover layer thickness cases were not tested.
Fig. 10. S11 parameter under different Cover thicknesses. A Full-wave simulation, B comparison of full-wave simulation and ECM.
For a given absorption response to the incident wave, there is a minimum sample thickness because of the fundamental causal nature of the absorber [46], and it is defined as
4.4 Comparison with other absorbers
For evaluating the performance of an absorber, two significant indicators, figure-of-merit (FoM) and Rc, were introduced. FoM is the ratio of FBW to the relative thickness and Rc is the causality ratio. The first indicator FoM emphasizes the trade-off between the effective bandwidth and unit thickness, and Rc characterizes whether the actual sample thickness is causally optimal. Based on FoM and Rc, the overall performance of an absorber can be comprehensively evaluated. Comparisons between the proposed MMA and its competitive counterparts are listed in Table 2. By comparing our work with other metamaterial absorbers, our design scheme is more effective and straightforward. The MMA proposed therein has a thickness extremely close to the causal limit, impressive broadband absorption capability, small relative thickness, and small relative unit size. For example, while the absorber of Ref. [50] has a very close thickness and Rc, its FoM is quite small and our absorber works at a more challenging lower frequency band. Due to its combination of hierarchical metal ring structures and foam patches, it is not optically transparent and not easily encapsulated, resulting in its limited practical application. Also, despite a slightly advantageous FoM of 15.58 for the absorber in Ref. [42], its Rc is quite large and not as competitive as others.
Table 2. Comparison of The Proposed Ultra-wideband MMA and its Counterpartsa
5. Conclusion
In summary, an MAA with ultra-wideband absorption, high angular stability, polarization insensitiveness, and high optical transparency based on ECM and GA optimization was proposed in this paper. Both simulation results and experimental tests proved these characteristics. The overall thickness of the designed MMA is only 0.102 λ0 at the lowest working frequency, and the total thickness is also quite close to the causality-dictated minimum thickness. Simple rings are utilized as basic unit structures, which are easier to fabricate than other complex unit structures, and the relative unit cell size is only 0.040 λ0. Due to the small coverage of the ITO part, the optical transparency of the designed MMA has been substantially improved. Measurements show that over 90% microwave absorption was obtained in the frequency range of 2.06 GHz to 15.52 GHz. This absorber operates at lower frequencies (lowest 2.06 GHz) and shows better wideband absorption performance with over 153% FBW than other designs. High absorption performance can be maintained even at large incident angles. For TM polarization, an over 114% FBW was maintained at a maximum incidence angle of 70°. More advantageously, over 150% FBW can be achieved until the incidence angle reaches 45° for both TM polarization and TE polarization. High angular stability is applicable in practical situations, especially since electromagnetic waves may be incident at large angles, which means that the MMA we designed might be a preferable alternative for practical application. The proposed transparent MMA has potential applications in optical windows for aeronautics and medical facilities, transparent EM stealth defense systems, EM pollution reduction, and EM-compatible buildings and facilities.
Funding
National Natural Science Foundation of China (51977219, 52177013); National Key Laboratory Foundation of China (61422062109, 61422062111); National Defense Basic Scientific Research Program of China (JCKYS2021LD1).
Acknowledgments
The authors acknowledge Y.G. Feng for assistance in the sample fabrication. The authors gratefully acknowledge Miss Xiao from CangXi School for helping and guiding us in the beautification of figures. Jie Li wishes to appreciate Jie Xiao for her companionship and support.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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