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Multispectral transparent electromagnetic-wave-absorbing optical window technology based on a random grid

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Abstract

A multimode detection system has stringent requirements in terms of electromagnetic characteristic control and electromagnetic compatibility. To meet these requirements, we designed and manufactured a type of transparent electromagnetic-wave-absorbing optical window based on a random grid (EAOWRG) in this study. Owing to the design and regulation of the materials of the random grid and the structures of the metasurface, the optical window has excellent multispectral transparency, electromagnetic wave absorption, and electromagnetic shielding performance. The experimental results showed that the transmissivity of the EAOWRG in the optical spectral ranges of 460–800 nm and 8–12 µm is above 89.77%, the electromagnetic reflectivity in the frequency ranges of 3.6–7.2 GHz and 14.3–17.7 GHz is not more than – 5 dB, the bandwidth at which the electromagnetic reflectivity is not more than −10 dB is 4.4 GHz, the electromagnetic shielding effectiveness in the frequency range of 2–18 GHz is above 31 dB. The average radar cross section of the detection system using the EAOWRG in the ± 60° angle domain at 6 GHz is 8.79 dB lower than that before processing. The detection system has a good imaging effect in the visible and infrared bands, meeting the requirements of the electromagnetic characteristic control and electromagnetic compatibility, and has good application prospects.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Optical windows, such as aircraft cabins and vehicle cockpits, are strong scattering sources of target electromagnetic waves because of the effect of cavity scattering [1]. When precision instruments in an aircraft cabin are exposed to a microwave environment for a long duration, they exhibit a gradual deterioration in the performance or may even fail [24]. Therefore, the electromagnetic characteristic control of an optical window requires reducing the radar cross section (RCS) and improving the electromagnetic shielding performance, while they must be able to penetrate visible light, infrared, and other detection bands without affecting the normal operation of the optical sensor; this is challenging for the target electromagnetic characteristic control technology. Indium tin oxide (ITO) films and ultra-thin Au films have good visible light transmittance and electromagnetic shielding performance and have been applied to the control of the electromagnetic characteristics of aircraft cockpits and vehicle windows; however, their high reflectivity in the infrared band limits their application.

A metal grid exhibits multispectral transparency and electromagnetic shielding; the development of such grids is currently an important research direction for controlling the electromagnetic characteristics of optical windows. Zhengang of Harbin University of Technology proposed a metal grid with a periodic circular ring structure. The grid was prepared by an orthogonal arrangement of circular ring elements in the horizontal and vertical directions. When the transmittance was 94%, the shielding efficiency at 18 GHz was better than 35 dB; however, there was a certain amount of stray light, which reduced the imaging quality of the optical window [5]. To solve the above problems, Halman et al. designed and prepared metal grids with a wheel–spoke structure, a hexagonal structure, and an overlapping ring structure; they confirmed that the introduction of random structural elements can help smoothen the intensity distribution of higher-order diffraction stray light [6]. Ziyang et al. designed a metal network conductive film with a random six-ring surface structure, which has a higher optical transmittance than the conventional two-dimension lattice structure metal grid, achieving a transmission loss of 10.5% in the long-wave infrared band and an average electromagnetic shielding efficiency of 37.9 dB in the 0.2–20 GHz electromagnetic spectrum band. Owing to the introduction of random variables in the structure, it can also suppress higher-order diffraction stray light [7]. Venkatarayalu of Singapore Polytechnic University prepared a glass substrate into a checkerboard surface and used an ITO film as a transparent conductive layer. By adjusting the conductivity of the conductive film, which is a key parameter, a transparent checkerboard pattern surface with an RCS shrinkage reduction capability was obtained [8]. Tiejun et al. from the Southeast University proposed a method to design an optically transparent coded metasurface using a conductive ITO film. The abnormal reflection-coded metasurface designed using a periodic phase gradient sequence can reflect normally incident electromagnetic waves at a certain abnormal angle. The designed random diffusion-coded metasurface could achieve a backward RCS reduction of at least 7.8 dB in the frequency range of 11.5–12.5 GHz. However, due to the use of the ITO matrix material, the transmittance is good in the visible light band [911]. Ruichao Zhu et al. resorted to the machine learning to solve the multispectral compatibility problem of metamaterials and demonstrated the design of a new metafilm with multiple mechanisms that can realize small microwave scattering, low infrared emissivity, and visible transparency simultaneously using a multilayer back-propagation neural network [12,13]. Yi Luo et al. proposed a novel design method of multispectral compatible integration based on a lossy capacitive multispectral meta-film (MMF). The flexible structure finally obtained a low infrared emissivity of 0.534, wideband microwave absorption from 8.9 to 16.4 GHz covering X, Ku, and high visible transmission of 70.18% and ultra-thin thickness of 2.3 mm [14,15]. Currently, these studies are mainly based on the low-scattering profile of optical windows. By improving the shielding effectiveness of optical windows, their electromagnetic characteristics can be adjusted and controlled, and the RCS of the target can be reduced. For optical windows that are not low-scattering profiles, the effect is poor. Moreover, due to the low transmittance of ITO in the infrared band, it is difficult to achieve multispectral optical transparency and control of the electromagnetic characteristics of the multimode detection system.

In this study, a multispectral transparent electromagnetic-wave-absorbing optical window based on a random grid (EAOWRG) was developed. Random grid materials with impedance characteristics were innovatively prepared and applied. Through the structural design of the random grid and the control of the electromagnetic parameters of the matrix material, the EAOWRG exhibits a high transmittance in the visible light, near infrared, and mid-far infrared bands; good electromagnetic shielding performance in the microwave band; and good electromagnetic absorption performance in a specific microwave band. Because the grid adopts random structural elements, it can well suppress high-order diffraction stray light [16]. The experimental results showed that the average transmittance of the EAOWRG in the visible and infrared bands is above 89.77%, the electromagnetic reflectivity in the frequency ranges of 3.6–7.2 GHz and 14.3–17.7 GHz is not more than −5 dB, the bandwidth at which the electromagnetic reflectivity is not more than −10 dB is 4.4 GHz, and the electromagnetic shielding effectiveness in the frequency range of 2–18 GHz is not less than 31 dB. These results meet the requirements for realizing electromagnetic characteristic control and electromagnetic compatibility performance of aircraft detection systems without affecting the normal operation of the optical sensor. Moreover, the RCS control ability of the target is irrespective of the low-scattering shape of the optical window, enabling more versatile and broader application prospects.

2. Structural design and simulation

Figure 1 shows the structure of the EAOWRG. Considering the adjustability of material impedance and the low cost of the material, the top random grid is made of a single layer Cu–Ni–Ti composite material with impedance characteristics. The grid line width is 1.85 µm, the average period is 78 µm, and the thickness (d1) is 127 nm. It uses ohmic and resonance losses to achieve the absorption performance and further improves the absorption bandwidth and spectral transmittance through the design of the metasurface. The metasurface adopts hexagonal periodic structural elements to enhance the polarization insensitivity of the optical window to electromagnetic waves; the side length of the outer hexagon L1, side length of the inner hexagon L2, line width W, and period P are 5.5, 4.7, 0.066, and 10.39 mm, respectively. The intermediate medium layer is made of multispectral zinc sulfide with a thickness (d2) of 4.5 mm; Multispectral zinc sulfide is a type of zinc sulfide with superior visible and infrared dual band transmittance. The bottom random grid is made of Cu as the substrate material, which has the same structural size as the top grid, with a thickness of 127 nm(d3), but no metasurface design has been carried out. On the one hand, it is used as the reflection layer of the absorbing structure, and on the other hand, it can ensure the effectiveness of electromagnetic shielding.

 figure: Fig. 1.

Fig. 1. Overall structure of an electromagnetic-wave-absorbing optical window based on a random grid (EAOWRG).

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According to the metamaterial surface theory, the metamaterial with smaller element size than the wavelength of the incident electromagnetic wave can be equivalent to a resistance- inductance-capacitance (RLC) circuit. The capacitance C and inductance L are mainly determined by the geometry, size and periodic arrangement of the metamaterial structure. The resistance R comes from the resistance loss and radiation loss of metamaterials, and it’s determined by the surface resistance of the material. When the metamaterial is coated on the dielectric substrate, the dielectric substrate can be equivalent to a transmission line with length d [18]. The equivalent circuit of a composite material based on a metamaterial is shown in Fig. 2 when the dielectric substrate is lined with a metal backing plate.

 figure: Fig. 2.

Fig. 2. Equivalent circuit of a composite material based on a metamaterial.

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For hexagonal metasurfaces, their equivalent inductance L and capacitance C can be calculated by Formulas (1) and (2).

$$L = \sqrt 3 \ast L1\ast \textrm{f}(P/2,2\ast W,\lambda )/P$$
$$C = 8\ast L1\ast \textrm{f}(P,P - \sqrt 3 \ast L1,\lambda )/P$$

According to transmission line theory, the reflection coefficient F of the structure can be calculated by Formula (3).

$$F = \frac{{{Z_S} - {Z_0}}}{{{Z_S} + {Z_0}}}$$

In the above formula,

$${Z_S} = \frac{{{Z_M} \bullet {Z_\textrm{N}}}}{{{Z_M} + {Z_\textrm{N}}}}$$
$${Z_M} = \frac{{1 - LC + jRC}}{{jC}}$$
$${Z_N} = j\sqrt {{\mu _r}{\mu _o}/{\varepsilon _r}{\varepsilon _o}} \tan (\beta d2)$$

ZS is the input impedance of the entire structure and Z0 is the wave impedance of free space. ZM is the impedance of the metamaterial, ZN is the impedance of the dielectric substrate, εr is the dielectric constant of the dielectric substrate, and μr is the permeability constant of the dielectric substrate. ε0 and μ0 are the dielectric constant and the permeability constant of free space, respectively, and β is the transmission constant of the electromagnetic wave in the dielectric substrate. R is the equivalent resistance of metamaterial. We can reasonably adjust the parameters R, L, and C to get the reflection characteristics of the composite material.

The wave absorption performance simulation of the EAOWRG was completed in the electromagnetic simulation software computer-simulation-technology (CST) [17,18]. Figure 3(a) shows the simulation model. The period of a random grid is on the micrometer scale, much smaller than the wavelength of electromagnetic waves, so it can be equivalent to a uniform surface for electromagnetic waves. At the same time, due to the existence of certain periodic pores in the random grid and the fact that the grid material does not completely shield electromagnetic waves, it is equivalent to a uniform plane with a certain surface resistance. The equivalent resistance is determined by the conductivity of the grid material, as well as the period and line width of the grid. In the fabrication process, the conductivity of the grid matrix material can be controlled by adjusting the proportion of composite materials Cu, Ni, and Ti. By adjusting the process parameters of grid preparation, such as coating speed and drying time, the period and line width of the grid can be controlled. Then, we can control the equivalent surface resistance of the grid. The approximate relationship between grid parameters and equivalent surface resistance R can be expressed by Formula (7).

$$\frac{{4{\textrm{g}^2}}}{{{\lambda ^2}}}{[\ln (\sin \frac{{\pi a}}{{2g}})]^2} = \frac{{377 - R}}{{377 + R}}$$

 figure: Fig. 3.

Fig. 3. a) Model diagram of the EAOWRG simulated in CST. b) Surface current of the EAOWRG.

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In the Formula (7), a and g are the line width and period of the grid respectively, and λ is the wavelength of the electromagnetic wave.

Figure 3(b) shows the surface current of the EAOWRG by adding monitors in CST. The electromagnetic wave mainly excites current inside the metasurface structure along the direction of electromagnetic waves. The absorption of electromagnetic waves by EAOWRG originates from Ohmic loss and resonance effect of metasurface. At the same time, the presence of metasurface increases the number of reflections of electromagnetic wave in the multispectral zinc sulfide. First, the reflectivity of the EAOWRG under different equivalent surface resistances of the top random grid and 50mΩ equivalent surface resistance of the bottom random grid was simulated. Figure 4(a) shows the simulation results. The reflectivity of the EAOWRG under different thicknesses of the multispectral zinc sulfide was further simulated. Figure 4(b) shows the simulation results [1924].

 figure: Fig. 4.

Fig. 4. a) Reflectivity curve of the EAOWRG under different equivalent surface resistances of the top random grid (thickness of the multispectral ZNS is 4.5 mm). b) Reflectivity curve of the EAOWRG under different thicknesses of the multispectral zinc sulfide (equivalent surface resistance of the top random grid is 85 Ω).

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Figure 4 shows that with the increase in the equivalent surface resistance of the top random grid, the peak positions in the reflectivity curve of the EAOWRG in the frequency ranges of 4–8 GHz and 14–18 GHz gradually shift to the low frequency range, and the absorption peak shows a trend of deepening and narrowing. However, once the equivalent surface resistance of the top random grid exceeds 85 Ω, the wave absorption performance of the EAOWRG begins to deteriorate gradually. When the equivalent surface resistance of the top layer random grid is fixed at 85 Ω, with the increase in the thickness of multispectral zinc sulfide, the peak positions in the reflectivity curve of the EAOWRG in the frequency ranges of 4–8 GHz and 14–18 GHz gradually shift to low frequencies. Given the manufacturing process of the random grid and the requirements of the detection system for the optical imaging and intensity of the multispectral zinc sulfide, it is considered that the EAOWRG has a good electromagnetic absorption performance when the equivalent resistance of the top random grid surface is 85 Ω and the thickness of the multispectral zinc sulfide is 4.5 mm.

3. Materials and methods

3.1 Impedance-type top random grid preparation

The surface of the multispectral zinc sulfide optical glass was cleaned with ethanol to remove dust and oil on the surface. A water-based acrylic lotion was coated on the glass surface by spin coating, at a coating speed of 500 r/min and a spin coating time of 30 s. The surface was dried for 12 h at a temperature of 25 °C and humidity of 45% to generate a random grid pattern mask layer. A Cu–Ni–Ti composite material was evaporated on the random grid mask film of upper surface of window by magnetron sputtering at a sputtering power of 1500 W and a sputtering time of 15 min. The random grid mask layer was dissolved in the stripping process using propylene glycol methyl ether acetate, and a random grid pattern with surface impedance characteristic was obtained [2527].

Figure 5 reveals a scanning electron microscope (SEM) image of grid. The grid is random and relatively evenly distributed, with a line width of 1.75-1.96 µ m and a period of 50-106 µ m. The height of the grid is126-128 nm.

 figure: Fig. 5.

Fig. 5. SEM image of the grid produced. a) Overall structure of the grid. b) Distribution of the grid. c) Line width of the grid. d) Height of the grid.

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3.2 Bottom random grid preparation

The top random grid interface is well protected. Cu was evaporated on the random grid mask film of lower surface of window by magnetron sputtering at a sputtering power of 1500 W and a sputtering time of 15 min. The random grid mask layer was dissolved in the stripping process using propylene glycol methyl ether acetate, and a random grid pattern with surface impedance characteristic was obtained.

3.3 Metasurface structure formation of top grid

An infrared laser etching instrument (FM-SD50; Shanghai Fermi Technology Co., Ltd.) was used to complete the etching and shaping of the optical window with a metasurface structure. The specific process steps were as follows: First, the drawn metasurface structure was imported into the control software, and the following working parameters were set: laser wavelength λ = 1064 nm, laser power P = 50 W, and laser frequency F = 50 kHz. The optical window was then installed on the etching platform, an airborne camera was used to locate and process the optical window, and finally, the etching effect and size were observed under an optical microscope [2731].

3.4 Measurement

A spectrophotometer (Lambda950; PerkinElmer Company) was used to measure the optical transmittance of the EAOWRG. The Agilent vector network analyzer was used to test the electromagnetic reflectivity, electromagnetic shielding effectiveness and RCS of the EAOWRG in a microwave anechoic chamber [32].

4. Results and discussion

4.1 EAOWRG

Figure 6(a) shows the actual EAOWRG produced. The figure shows that the EAOWRG has good visible light transmittance. The random grid and metamaterial structure can be seen in the optical image, as shown in Fig. 6(b). The grid line width is consistent, presents a random shape distribution, and the metamaterial structure is clear. The multispectral zinc sulfide substrate surface is in good condition.

 figure: Fig. 6.

Fig. 6. a) Actual physical image of the EAOWRG produced. b) Random grid and metamaterial structure.

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4.2 Reflectivity of EAOWRG

The electromagnetic reflectivity and absorptivity tests of EAOWRG were completed in a microwave anechoic chamber. Figure 7 shows the electromagnetic reflectivity and absorptivity test status and test results of the EAOWRG. The electromagnetic shielding effectiveness reflects how much electromagnetic wave energy can penetrate EAOWRG, which is an important basis to measure the electromagnetic compatibility of materials. The higher the value, the better the shielding performance, and the better the electromagnetic compatibility of the material. Electromagnetic shielding effectiveness is measured by emissivity antenna and receiving antenna. The EAOWRG was illuminated by a focused Gaussian plane wave formed by a focusing lens. Firstly, the received power response during direct transmission in free space was measured as Po. Secondly, the received power response when placing the EAOWRG was measured as Pa. Then, the electromagnetic shielding effectiveness of the EAOWRG can be calculated according to Formula (8):

$$E = 1 - \frac{{P\textrm{a}}}{{Po}}$$

 figure: Fig. 7.

Fig. 7. a) Electromagnetic reflectivity test status of EAOWRG. b) Electromagnetic reflectivity test results. c) Electromagnetic absorptivity test results.

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In the Formula (8),

E: electromagnetic shielding effectiveness

Po: the received power response during direct transmission in free space

Pa: the received power response when placing the EAOWRG

If expressed in dB, the calculation of shielding effectiveness is shown in Formula (9).

$$E = 10\lg (1 - \frac{{P\textrm{a}}}{{Po}})$$

Figure 8 shows the electromagnetic shielding effectiveness test status and test results. Table 1 shows the test data for electromagnetic reflectivity and shielding effectiveness. The figure and table show that the electromagnetic reflectivity of the EAOWRG is not more than −5 dB (78%) in the frequency ranges of 3.6–7.2 GHz and 14.3–17.7 GHz. The bandwidth at which the electromagnetic reflectivity is not more than −10 dB (90%) is 4.4 GHz, which is consistent with the simulation results. The reason for the narrow band width is due to the high dielectric properties of multispectral zinc sulfide, reaching 8.9, which is very unfavorable for impedance matching. Due to the high difficulty of the manufacturing process of multispectral zinc sulfide and the high requirements of optical windows, it is difficult to design multi-layer absorbing structures, resulting in a narrow absorption bandwidth of the EAOWRG. With the improvement of multispectral zinc sulfide manufacturing technology, broadband absorption is promising. The electromagnetic shielding effectiveness of the EAOWRG in the frequency range of 2–18 GHz is not less than 31 dB.

 figure: Fig. 8.

Fig. 8. a) Shielding effectiveness test status of EAOWRG. b) Shielding effectiveness test results.

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Tables Icon

Table 1. The test data for electromagnetic reflectivity and shielding effectiveness

The spherical multispectral Zinc sulfide was first prepared by hot pressing, then the grid was prepared by the same process as the planar EAOWRG. Finally, the grid metamaterial was processed with a five-axis laser etching system to form a spherical EAOWRG. The point-frequency RCS of the detection system loaded with the spherical EAOWRG at 6 GHz was further tested. Figure 9 shows the test status and results. Clearly, the RCS of the detection system without processing the optical window is relatively high. In comparison, the RCS of the detection system with the conventional metal grid for the optical window is reduced to a certain extent. The RCS of the detection system with EAOWRG has been further reduced, and the RCS is less than –17 dBsm in the angle range of ± 60°.

 figure: Fig. 9.

Fig. 9. a) Spot frequency RCS test status of the detection system equipped with a spherical EAOWRG. b) Spot frequency RCS test results.

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4.3 Spectral transmittance of EAOWRG

Figure 10 shows the spectral transmittance test status of the EAOWRG. Figure 11 shows the test curves. Table 2 shows the test data. The figure and table show that the transmissivity of the EAOWRG in the optical spectral ranges of 460–800 nm and 8–12 µm was above 89.77%. EAOWRG has good transmittance mainly due to its small random grid linewidth and minimal spectral loss.

 figure: Fig. 10.

Fig. 10. Spectral transmittance test status of EAOWRG.

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 figure: Fig. 11.

Fig. 11. a) Spectral transmittance test curve of EAOWRG at 460-800 nm. b) Spectral transmittance test curve of EAOWRG at 8–12 µm.

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Tables Icon

Table 2. The test data for spectral transmittance

The visible and infrared imaging of the detection system equipped with the EAOWRG in the 460-800 nm and 8–12 µm band was further tested, as shown in Fig. 12. The figure shows that the visible and infrared imaging effect of the detection system is good, and there is no diffraction stray light phenomenon.

 figure: Fig. 12.

Fig. 12. a) Visible imaging test results of the detection system equipped with a spherical EAOWRG. b) Infrared imaging test results of the detection system equipped with a spherical EAOWRG.

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5. Conclusions

In this study, a type of transparent electromagnetic-wave-absorbing optical window based on a random grid was designed and manufactured. The experimental results showed that the transmissivity of the EAOWRG in the optical spectral ranges of 460–800nm and 8–12 µm was above 89.77%, the electromagnetic reflectivity in the frequency ranges of 3.6–7.2GHz and 14.3–17.7GHz was not more than −5dB, the bandwidth at which the electromagnetic reflectivity was not more than −10dB was 4.4GHz, and the electromagnetic shielding effectiveness in the frequency range of 2–18GHz was not less than 31dB. The average radar cross section of the detection system with the EAOWRG in the ± 60° angle domain at 6GHz was 8.79dB lower than that before processing, and the visible and infrared imaging effects were good. Compared to conventional electromagnetic optical windows, EAOWRG has the advantages of multi-spectral transmission and independent of window shape. Further, EAOWRG can be expanded to transmit electromagnetic waves at specific wavelengths by changing the size or shape of the metamaterial structure. The detection system with the proposed EAOWRG meets the requirements of electromagnetic characteristic control and electromagnetic compatibility and has good application prospects.

Funding

National Basic Strengthening Project of China (No. 2022-JCJQ-040-00).

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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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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Figures (12)

Fig. 1.
Fig. 1. Overall structure of an electromagnetic-wave-absorbing optical window based on a random grid (EAOWRG).
Fig. 2.
Fig. 2. Equivalent circuit of a composite material based on a metamaterial.
Fig. 3.
Fig. 3. a) Model diagram of the EAOWRG simulated in CST. b) Surface current of the EAOWRG.
Fig. 4.
Fig. 4. a) Reflectivity curve of the EAOWRG under different equivalent surface resistances of the top random grid (thickness of the multispectral ZNS is 4.5 mm). b) Reflectivity curve of the EAOWRG under different thicknesses of the multispectral zinc sulfide (equivalent surface resistance of the top random grid is 85 Ω).
Fig. 5.
Fig. 5. SEM image of the grid produced. a) Overall structure of the grid. b) Distribution of the grid. c) Line width of the grid. d) Height of the grid.
Fig. 6.
Fig. 6. a) Actual physical image of the EAOWRG produced. b) Random grid and metamaterial structure.
Fig. 7.
Fig. 7. a) Electromagnetic reflectivity test status of EAOWRG. b) Electromagnetic reflectivity test results. c) Electromagnetic absorptivity test results.
Fig. 8.
Fig. 8. a) Shielding effectiveness test status of EAOWRG. b) Shielding effectiveness test results.
Fig. 9.
Fig. 9. a) Spot frequency RCS test status of the detection system equipped with a spherical EAOWRG. b) Spot frequency RCS test results.
Fig. 10.
Fig. 10. Spectral transmittance test status of EAOWRG.
Fig. 11.
Fig. 11. a) Spectral transmittance test curve of EAOWRG at 460-800 nm. b) Spectral transmittance test curve of EAOWRG at 8–12 µm.
Fig. 12.
Fig. 12. a) Visible imaging test results of the detection system equipped with a spherical EAOWRG. b) Infrared imaging test results of the detection system equipped with a spherical EAOWRG.

Tables (2)

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Table 1. The test data for electromagnetic reflectivity and shielding effectiveness

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Table 2. The test data for spectral transmittance

Equations (9)

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L = 3 L 1 f ( P / 2 , 2 W , λ ) / P
C = 8 L 1 f ( P , P 3 L 1 , λ ) / P
F = Z S Z 0 Z S + Z 0
Z S = Z M Z N Z M + Z N
Z M = 1 L C + j R C j C
Z N = j μ r μ o / ε r ε o tan ( β d 2 )
4 g 2 λ 2 [ ln ( sin π a 2 g ) ] 2 = 377 R 377 + R
E = 1 P a P o
E = 10 lg ( 1 P a P o )
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