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Abstract
Here, we proposed an ingenious grid pattern design method called pattern randomization to obtain metallic meshes with uniform stray light. The periodicity of a grid is weakened by the pattern randomization. By comparing the diffraction patterns of one-dimensional periodic grid, one-dimensional aperiodic grid and concentric rings structure, we found that the “radial homogenization” and “angular homogenization” can uniform the high-order diffracted energy. The pattern randomization is proposed to achieve the “radial homogenization” and “angular homogenization” two-dimensional grid while ensuring connectivity. For collimated incident beam, the metal grid with a randomness (90%, 90%) obtained by pattern randomization method generates uniform stray light, while it maintains high visible light transmittance and high electromagnetic shielding efficiency (SE). The simulated results are experimentally verified that the high-order diffraction spots can be effectively suppressed. The coefficient Cv is reduced from 1078.14% to 164.65%. Meanwhile, the randomness of the designed grid structure hardly affects the visible light transmittance and shielding efficiency. The metallic mesh with a shielding efficiency about 17.3 dB in the Ku-band, a relative transmittance higher than 94% in the visible light band and an ultra-uniform diffraction pattern is obtained.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the rapid development of electronic technology, the electromagnetic environment of space is becoming more and more complex, which results in electromagnetic pollution [1,2]. Therefore, shielding electromagnetic interference (EMI) are vital in many fields [3–5], especially for the most extensive and strongest microwaves and radio waves in space. The optical window of an instrument is expected to have a high transmittance in the visible band to the middle-IR band, a strong EMI shielding efficacy in the microwave range, and a small impact on imaging quality in the high-performance optical detection systems [6,7]. Therefore, many shielding strategies were proposed to achieve transparent EMI shielding [6–31], such as transparent conductive oxides (TCOs) [18,19], carbon nanotubes (CNTs) [20,21], metallic meshes [6,13–17], metallic nanowires [22–26], and graphene [27–31]. Among them, metallic meshes or grids with submillimeter periodicity and micrometer linewidth are the most prominent candidates. Metallic meshes have been widely investigated for transparent EMI shielding because of their high transmission in visible-IR bands and strong reflection in wide-band low-frequency microwave bands [32].
However, the drawback of the periodic metallic meshes is the highly concentrated diffractive stray light caused by periodic metallic wires [6,33]. This would generate ghost image, which degrades the imaging quality of optical windows [34]. Meanwhile, the visual effects of the optical windows under strong light should be more comfortable and without glitzy interference [35].
To solve this problem, researchers have developed the metallic grids with different ring units to homogenize the high-order diffractive stray light [6,13,15,17]. For continuous curves, the small line width metallic rings are difficult to fabricate in large scale. Recently, the aperiodic metallic meshes with randomly position distribution grids or rings were proposed to eliminate Moiré effect in display screen [7,34,36,37]. However, these works only studied the influence of a few structural parameters on the diffraction pattern. The fundamental principle of achieving diffraction homogenization does not be thoroughly explored. The general design schematic of random structures also does not been investigated.
In this paper, we found that one can achieve the radial and angular homogenization of the high-order diffracted energy by increasing the distribution range of the lengths and the inclination angles of the grid lines, respectively. The diffraction patterns of one-dimensional periodic grid lines, one-dimensional aperiodic grid lines and concentric rings were analyzed. Quantitative randomization of the two-dimensional metal grid is realized by giving the position of the two-dimensional metal grid node a certain offset. The diffraction characteristics of the designed random grids are experimentally tested. To quantitatively evaluate the diffraction pattern, the coefficient of variation Cv is used as an evaluation index. Meanwhile, the effect of grid randomness on visible light transmittance and shielding efficiency was studied.
2. Basic principles and methods to achieve diffraction homogenization
As shown in Figs. 1(a)–1(c), three different line grid structures are considered as the example, which are one-dimensional periodic grid lines, one-dimensional aperiodic grid lines and concentric rings. Their diffraction patterns, which are obtained by numerical calculation of Fraunhofer diffraction, are displayed as Figs. 1(d)–1(f). For the one-dimensional periodic grid line with period px, the diffractive field is concentrated on the zero-order and two vertical directions. Giving each grid line a moving range of size Δx (Δx < px) in the x-direction to generate one-dimensional aperiodic grating, the higher-order diffraction spots are suppressed, as shown in Figs. 1(d) and 1(e). The structure in Fig. 1(b) has randomness r=90%. The process of Figs. 1(d) to 1(e) is the “radial homogenization” of the grating diffraction. Meanwhile, the concentric rings of Fig. 1(c) are also examined. The diffracted energy is dispersed in the circumferential direction. Compared with that of Figs. 1(a) and 1(b), the angle between the circular grid line micro-element and the y-axis is evenly distributed from 0 to 360 degrees instead of only 90 degrees. Therefore, by homogenizing the angular distribution of the grid lines, that is, “angular homogenization”, the higher order diffracted energy can be dispersed in all angular directions.
Fig. 1. (a) one-dimensional periodic grid line, (b) one-dimensional aperiodic grid line, (c) concentric rings. (d)–(f) Corresponding diffraction pattern of (a)–(c), respectively.
However, for EMI, the metal grid should be high degree of connectivity. Based on a highly connected square grid, the distribution of the line lengths and the inclination angles of a two-dimensional grid are controlled by an offset to the grid node. The schematic of the proposed pattern randomization method is shown as Fig. 2. The period of the original grid in the lateral direction (x-direction) and the vertical direction (y-direction) are px and py, respectively. Obviously, the grid line lengths have two values of px and py. The grid line inclination angles have two values of 0 and 90 degrees. However, as shown in the pink square in Fig. 2(b), if each node has the moving range of size Δx (Δx < px) in the x-direction and that of size Δy (Δy < py) in the y-direction, the pattern randomization is achieved. The randomness in the x- and y-directions are defined as rx=Δx/px and ry=Δy/py, where Δx and Δy are uniformly distributed random numbers generated by the computer.
Fig. 2. Schematic of the grid design process of the proposed pattern randomization. (a) Original mesh grid. (b) Randomized mesh grid.
To validate the validity of the proposed grid randomization process in “radial homogenization” and “angular homogenization”, three grids with randomness (0, 25%), (0, 90%) and (90%, 90%) were generated as Fig. 3. The distributions of the lengths and the inclination angles of the grid lines are shown as Figs. 4(a)–4(c) and Figs. 4(d)–4(f), respectively. The abscissa is the number of the grid lines. The period of the initial grid is 250 µm and the line width is 4 µm, respectively. For the metal grid with a randomness of (0, 25%), the lengths of the grid lines in the x- and y-direction are from 250.00 µm to 257.69 µm, and 187.50 µm to 312.50 µm in the extreme case, respectively. The lengths of the grids in Fig. 3(a) in the x- and y-directions are distributed from 250.00 µm to 257.4 µm, and 190.4 µm to 308.3 µm respectively, which are close to the extreme case. In Fig. 3(a), the inclination angles of the grid lines in x-direction is −13.81 degrees to 13.77 degrees. As shown in Fig. 4(d), it is close to the extreme case of −14.04 degrees to 14.04 degrees. The angles between the grid lines in the y-direction and the x-axis are 90 degree, as the randomness in the x-direction is 0. When the randomness in the y-direction increases to 90%, the range of the grid lines lengths in both directions and the range of the inclination angles of the grid lines in the x-direction are increasing, as shown in Figs. 4(b) and 4(e). For the grid with the large randomness of (90%, 90%) in Fig. 3(c), the lengths of the grids in the x- and y-directions are from 56.41 µm to 477.90 µm, and 50.17 µm to 478.7 µm [Fig. 4(c)]. The angles are from −72.46 degrees to 60.30 degrees, and 26.49 degrees to 159.60 degrees [Fig. 4(f)]. Obviously, the higher the randomness, the larger the distribution range of the grid lines lengths and the grid lines inclination angles are achieved. Therefore, by applying the pattern randomization method, one can achieve the “radial homogenization” and “angular homogenization” to the two-dimensional grid. Therefore, the grid generated by the pattern randomization method will exhibit uniformly high order diffraction spots.
Fig. 3. Grid structures with the different degrees of randomness. (a) (0, 25%), (b) (0, 90%), and (c) (90%, 90%).
Fig. 4. Grid lengths distribution (a)–(c) and grid inclination angles distribution (d)–(f) of grids with randomness of (0, 25%), (0, 90%) and (90%, 90%).
3. Optical performance and experimental results
To analyze the effect of the pattern randomization method on the optical performance of a metal grid, the optical diffraction patterns of four designed grids are analyzed. The original structure of the four random grids is a square grid with a period of 250 µm and a line width of 4 µm. The randomness of the four grids are (0, 0), (0, 25%), (0, 90%), and (90%, 90%). Because the optical system is usually constrained by a circular aperture, a circular aperture is added to the grid structure in simulation. For the simulation, the laser spot diameter is 6 mm, the laser wavelength is 632.8 nm, and the focal length of the lens is 300 mm, respectively. To analyze the distribution of high-order diffraction more clearly, the intensity of the region with radius R1=0.380 mm at the zero-order is set to zero. R1 is the half distance between the +1st-order spot and the zero-order spot. The diffraction pattern of the (0, 0) mesh is the orthogonally distributed spots array [ Fig. 5(a)], which will disturb the image sensors behind the mesh. When the randomness in the y-direction is increasing from 0 to 90%, the high-order diffractive spots on the line x=0 are blurred. The intensity of these spots decreases, as shown in Figs. 5(b) and 5(c). When the randomness of the x- and y-directions are up to 90%, the light intensity distribution in both directions is greatly suppressed. The high-order diffraction spots almost disappeared. Obviously, the image quality and the reliability of optical sensors will be improved by the proposed pattern randomization method.
Fig. 5. Simulated diffraction patterns of four grids by subtracting zero-order. (a) (0, 0), (b) (0, 25%), (c) (0, 90%), and (d) (90%, 90%).
To quantitatively evaluate the distribution of the high-order diffractions, an evaluation method was proposed. In the proposed evaluation method, the standard deviation Isd and the mean value Imn of the light intensity of the diffraction pattern are applied to calculate the ratio Cv=Isd/Imn×100%, which is defined as the high-order diffraction evaluation index. Obviously, for the smaller Cv, the more uniform the intensity distribution of the high-order diffraction spots and the smaller the influence of the grid on the imaging system are achieved. For the grid with (90%, 90%) Cv is about 397.95%. However, Cv is as large as 1588.60% for the grid with randomness (0, 0).
The evaluation of the distribution of grids with different randomness was shown in the Fig. 6. The abscissa indicates the number of the grid. No. 0-9 represents the grid with randomness of (0, 0), (0, 10%), (0, 20%) - (0, 90%), No. 11-99 represent grids with randomness of (10%, 10%), (20%, 20%), (30%, 30%) - (90%, 90%). Figures 6(a) and 6(c) show the normalized total light intensity and zero-order intensity of different grids. The difference between the total light intensity and zero-order intensity of these 19 kinds of grid is less than 0.65% and 0.61%, respectively. Changing in randomness will not cause significant fluctuation of total light intensity and zero-order intensity. Figures 6(b) and 6(d) show Cv for different grids. When the randomness rx remains at 0 and the randomness ry increases, Cv first decreases significantly [from 1588.60% (0, 0) to 1268.53% (0, 20%)] and then remains almost unchanged (about 1228.46%), because of the Isd cannot keeping decreasing with the increase of the ry, which is in dominant in Cv with an almost constant Imn, due to the high-order diffractions along x-axis cannot be suppressed with increasing ry. When the randomness in both directions of the grid is equal and increases, Cv decreases significantly with increasing randomness (from 1588.60% (0,0) to 476.31% (90%, 90%)) as shown in Fig. 6(d), because of the high-order diffractions in both directions are suppressed by increasing randomness, and Cv shows a downward trend with increasing randomness. Obviously, the increasing range of the grid lengths and the inclination angles is excellent to homogenize the intensity of the high-order diffracted light by increasing the randomness.
Fig. 6. (a) and (c) Normalized total light intensity and zero-order light intensity of different grids. (b) and (d) Cv of different grids.
The four designed metallic grids in Fig. 5 were fabricated by the photolithography and lift-off technology with an adhesion layer of 30 nm chromium and a silver layer of 220 nm. A set-up was established to verify the fundamental that the increasing randomness would homogenize the diffraction pattern by evaluating the optical properties of the fabricated metallic meshes. The four metal grid samples were illuminated by a collimated He-Ne laser beam with the wavelength of 632.8 nm. The diffraction patterns of the metal grid were collected by a CMOS camera (LUSTER LightTech Co., Ltd., China). A focusing lens is placed between the sample and the CMOS camera. The length of focus of the employed lens is 300 mm. As shown in Fig. 7, the measured diffraction pattern (the greyscale value of the part with radius R1=0.380 mm at the zero-order is set to zero) is consistent with the numerical results. When the randomness is as large as (90%, 90%), the high-order diffracted light is greatly suppressed, which is extremely beneficial for the imaging of the optical window. The Isd, Imn, and Cv of the four grids obtained in the experiment are listed in Table 1. The Cv of the grid with the randomness (90%, 90%) is about 164.65%, which is 913.49% smaller than the Cv of the grid with the randomness (0, 0). Both the simulated and the experimental results indicate that the high-order diffractions can be significantly homogenized by the increasing randomness.
Fig. 7. Diffraction patterns of metal grids with the randomness of (a) (0, 0), (b) (0, 25%), (c) (0, 90%) and (d) (90%, 90%) illuminated by He-Ne laser beam.
The optical transmission of the fabricated grids was examined, which can be estimated by analyzing the lengths of the lines since the metal lines in the samples are opaque to the visible light. When the randomness of the metal grid is (0, 0), the theoretical optical transmission is about 96.83%. As shown in Figs. 4(a) and 4(b), when only increasing ry, the average line length in the x-direction is greater than the period px, and the average line length in the y-direction is equal to the period py. Therefore, the optical transmittance is reduced. When the randomness of the grid is (90%, 90%), the length of the grid lines in both directions is between 25.00 µm to 525.59 µm, and the optical transmittance is about 96.66%. Obviously, when the randomness increases, the optical transmittance of the grid will decrease slightly. The optical transmittance of the sample with metal grids relative to a glass substrate without metal grids was measured by using the UVmini-1240 spectrophotometer (Shimadzu, Japan) at wavelength of 380 nm to 800 nm with the scanning step of 1 nm, as shown in Fig. 8. The measured average relative transmittances of the four samples are 95.25%, 95.29%, 95.84% and 94.64%, respectively. The experimental results show that the transmittance of the metal grid samples with different randomness is close. The measured results are slightly lower than the predicted because the widths of the processed metal lines are greater than 4 µm. Moreover, the four metal grids have flatly relative transmittance, which indicate that the visible light transmittance of the metal grid is independent of the wavelength. Therefore, the randomization of the structural parameters of the metal grid does not worse the optical transmittance.
Fig. 8. Experimentally measured visible band relative transmittance spectrum of the metal grids with the randomness of (0, 0), (0, 25%), (0, 90%) and (90%, 90%)
Table 1. Evaluation index of experimental results.
4. Electromagnetic shielding performance analysis and experiments
When a metal grid is working for electromagnetic shielding, the shielding efficiency (SE) should be investigated. SE is defined as SE (dB)=-10log (Et/Ei), where Ei and Et are the received energy before and after the shielding material, which is placed between the transmitter and the receiver.
The 20 different randomness metal grids were calculated by CST Microwave Studio software package. The SE of the grid with randomness of (0, 0), (0, 25%), (0, 90%) and (90%, 90%) as a function of frequency is shown in the Fig. 9. In Fig. 9(a), the electric field of the incident electromagnetic wave is along the y-direction (TE polarized), while in Fig. 9(b) along the x-direction (TM polarized). The difference in SE between the grids with randomness of (0, 0), (0, 25%), (0, 90%) and (90%, 90%) is less than 1.29 dB for the TE polarized electromagnetic waves and 1.85 dB for the TM polarized electromagnetic waves. Meanwhile, the SE decreases monotonically with frequency due to the effective mesh becomes relatively large.
Fig. 9. Simulated results of SE of the metal grid with different randomness as a function of frequency. Electric field of the incident electromagnetic wave along (a) the y-direction and (b) the x-direction.
The SE of 19 kinds of grids at a single frequency of 15 GHz is shown in the Fig. 10. When rx is kept at 0 and ry is increased, the SE of the grid to TE polarized electromagnetic waves is almost unchanged with a variety less than 0.6 dB, as shown by the solid black line in Fig. 10(a), because of the grid lines in the y-direction are the same. For the TE polarized electromagnetic waves, the effective metal line length of the unit structure is $\textrm{|}{p_y} \cdot \textrm{cos(9}{\textrm{0}^ \circ }\textrm{ - }\angle \textrm{1)|= }{p_y}$, where $\angle \textrm{1 = 9}{\textrm{0}^ \circ }$ is the angle between the longitudinal metal line and the x-axis. When the incident electromagnetic wave is TM polarized, the SE decreases with increasing randomness ry, as shown by the red dotted line in Fig. 10(a). The randomness of the 10 grids in the y-direction is different, which means the angles between the horizontal lines and the x-axis are not ${0^ \circ }$, and they are in a certain range. As shown in Fig. 4, the range of the angles is increasing for the increasing randomness. For TM electromagnetic waves, the effective metal line length is $\textrm{|}{p_x} \cdot \textrm{cos(}\angle \textrm{2)|} \le {p_x}$, where $\angle \textrm{2}$ is the angle between the horizontal metal line and the x-axis. The larger the $\angle \textrm{2}$, the lower the SE is. The randomness of the grid examined in Fig. 10(b) is equal in both directions, i.e., rx=ry. The SE is polarization-insensitive, and they all decrease with increasing randomness. Change trend between SE and randomness in the Fig. 10 at 15 GHz is consistent with the entire Ku-band.
The shielding performances of the metal grids with the randomness of (0, 0), (0, 25%), (0, 90%) and (90%, 90%) in Ku-band (12-18GHz) were measured as shown in Fig. 11. The incident electric fields in Figs. 11(a) and 11(b) is polarized along the y-direction and the x-direction, respectively. The shielding efficiency of the four random metal grids is about 17.3 dB at 12-18 GHz, which means only about 1.86% of the electromagnetic wave energy passes through the sample. The simulated results are higher than the measured results because the material used for the simulation is the perfect electrical conductor. While the coating material is silver with a finite conductivity. Meanwhile, silver layer is oxidized by air. The metal line width is uneven and there is a small amount of broken line. Moreover, the actual test system exists measurement error. The measured results indicate that the randomness of the metal grid has no significant effect on SE.
Fig. 11. SE of four randomness metal grids with frequency. Electric field of the incident electromagnetic wave along (a) the y-direction and (b) the x-direction.
5. Conclusion
In this paper, to suppress the high-order diffraction of a metallic grid, the pattern randomization method was explored theoretically and experimentally. We discussed the increasing distribution range of the grid line lengths and the grid line inclination angles, which inspired us to propose a grid multi-parameter uniform design method to suppressing high-order diffraction interference of a two-dimensional grid. The parameter Cv are proposed to evaluate the high-order diffraction of complex metal grids. Simulated and experimental results show that the increasing randomness of the grid can reduce the interference under the condition of little influence on shielding efficiency and optical transmittance. When the randomness is increased from (0, 0) to (90%, 90%), Cv decreased from 1078.14% to 164.65%. The average relative optical transmittance of the metal grid with a randomness of (90%, 90%) is as high as 94.64%. The shielding efficiency of the four random metal grids is about 17.3 dB at 12-18 GHz. Obviously, the high-order diffracted stray light can be further suppressed by increasing the randomness. Moreover, the pattern randomization method builds the link between the periodic structure and the aperiodic structure, which makes the analysis of aperiodic structures more convenient and reliable.
Funding
National Natural Science Foundation of China (61675056, 61875048); Natural Science Foundation of Heilongjiang Province (2017010).
Disclosures
The authors declare no conflicts of interest.
References
1. G. Abdel-Rassoul, O. A. El-Fateh, M. A. Salem, A. Michael, F. Farahat, M. El-Batanouny, and E. Salem, “Neurobehavioral effects among inhabitants around mobile phone base stations,” NeuroToxicology 28(2), 434–440 (2007). [CrossRef]
2. A. Balmori, “Electromagnetic pollution from phone masts. Effects on wildlife,” Pathophysiology 16(2-3), 191–199 (2009). [CrossRef]
3. B. Wen, X. Wang, W. Cao, H. Shi, M. Lu, G. Wang, H. Jin, W. Wang, J. Yuan, and M. Cao, “Reduced graphene oxides: the thinnest and most lightweight materials with highly efficient microwave attenuation performances of the carbon world,” Nanoscale 6(11), 5754–5761 (2014). [CrossRef]
4. D. Polley, B. Anjan, and R. Mitra, “EMI shielding and conductivity of carbon nanotube-polymer composites at terahertz frequency,” Opt. Lett. 39(6), 1541–1544 (2014). [CrossRef]
5. H. Lv, Z. Yang, S. Ong, C. Wei, H. Liao, S. Xi, Y. Du, G. Ji, and Z. Xu, “A Flexible Microwave Shield with Tunable Frequency-Transmission and Electromagnetic Compatibility,” Adv. Funct. Mater. 29(14), 1900163 (2019). [CrossRef]
6. Z. Lu, H. Wang, J. Tan, L. Ma, and S. Lin, “Achieving an ultra-uniform diffraction pattern of stray light with metallic meshes by using ring and sub-ring arrays,” Opt. Lett. 41(9), 1941–1944 (2016). [CrossRef]
7. Y. Han, Y. Liu, L. Han, J. Lin, and P. Jin, “High-performance hierarchical graphene/metal-mesh film for optically transparent electromagnetic interference shielding,” Carbon 115, 34–42 (2017). [CrossRef]
8. W. Jeong, J. Min, H. Kwak, Y. Jeon, H. Lee, K. Kim, J. Lee, S. Kang, D. Kim, and D. Lee, “A highly conductive and flexible metal mesh/ultrathin ITO hybrid transparent electrode fabricated using low-temperature crystallization,” J. Alloys Compd. 794, 114–119 (2019). [CrossRef]
9. R. Maniyara, V. Mkhitaryan, T. Chen, D. Ghosh, and V. Pruneri, “An Antireflection Transparent Conductor with Ultralow Optical Loss (<2%) and Electrical Resistance (<6 Ω sq-1),” Nat. Commun. 7, 13771 (2016). [CrossRef]
10. H. Wang, C. Ji, C. Zhang, Y. Zhang, Z. Zhang, Z. Lu, J. Tan, and L. Guo, “Highly Transparent and Broadband Electromagnetic Interference Shielding Based on Ultrathin Doped Ag and Conducting Oxides Hybrid Film Structures,” ACS Appl. Mater. Interfaces 11(12), 11782–11791 (2019). [CrossRef]
11. Y. Bi, J. Feng, J. Ji, Y. Chen, Y. Liu, Y. Li, Y. Liu, X. Zhang, and H. Sun, “Ultrathin and Ultrasmooth Au Films as Transparent Electrodes in ITO-Free Organic Light-Emitting Devices,” Nanoscale 8(19), 10010–10015 (2016). [CrossRef]
12. W. Kim, D. Ku, I. Lee, Y. Seo, B. Cheong, T. Lee, I. Kim, and K. Lee, “The Electromagnetic Interference Shielding Effect of Indium–Zinc Oxide/Silver Alloy Multilayered Thin Films,” Thin Solid Films 473(2), 315–320 (2005). [CrossRef]
13. H. Wang, Z. Lu, Y. Liu, J. Tan, L. Ma, and S. Lin, “Double-layer interlaced nested multi-ring array metallic mesh for high-performance transparent electromagnetic interference shielding,” Opt. Lett. 42(8), 1620–1623 (2017). [CrossRef]
14. H. Wang, Z. Lu, J. Tan, Y. Zhang, J. Cao, X. Lu, Y. Liu, R. Kong, and S. Lin, “Transparent conductor based on metal ring clusters interface with uniform light transmission for excellent microwave shielding,” Thin Solid Films 662, 76–82 (2018). [CrossRef]
15. H. Wang, Z. Lu, and J. Tan, “Generation of uniform diffraction pattern and high EMI shielding performance by metallic mesh composed of ring and rotated sub-ring arrays,” Opt. Lett. 24(20), 22989–23000 (2016). [CrossRef]
16. Z. Lu, H. Wang, J. Tan, and S. Lin, “Microwave shielding enhancement of high-transparency, double-layer, submillimeter-period metallic mesh,” Appl. Phys. Lett. 105(24), 241904 (2014). [CrossRef]
17. Y. Han, J. Lin, Y. Liu, H. Fu, Y. Ma, P. Jin, and J. Tan, “Crackle template based metallic mesh with highly homogeneous light transmission for high-performance transparent EMI shielding,” Sci. Rep. 6(1), 25601 (2016). [CrossRef]
18. B. Koo, D. Oh, D. Riu, and H. Ahn, “Improvement of transparent conducting performance on oxygen-activated fluorine-doped tin oxide electrodes formed by horizontal ultrasonic spray pyrolysis deposition,” ACS Appl. Mater. Interfaces 9(51), 44584–44592 (2017). [CrossRef]
19. G. Fernandes, D. Lee, J. Kim, K. Kim, and J. Xu, “Infrared and Microwave Shielding of Transparent Al-Doped ZnO Superlattice Grown Via Atomic Layer Deposition,” J. Mater. Sci. 48(6), 2536–2542 (2013). [CrossRef]
20. K. Zhang, M. Sun, W. Jiang, Y. Wang, D. Wang, F. Wu, A. Xie, and W. Dong, “A core-shell polypyrrole@silicon carbide nanowire (PPy@SiC) nanocomposite for the broadband elimination of electromagnetic pollution,” RSC Adv. 6(49), 43056–43059 (2016). [CrossRef]
21. H. Xu, S. Anlage, L. Hu, and G. Gruner, “Microwave Shielding of Transparent and Conducting Single-Walled Carbon Nanotube Films,” Appl. Phys. Lett. 90(18), 183119 (2007). [CrossRef]
22. L. Jia, D. Yan, X. Liu, R. Ma, H. Wu, and Z. Li, “Highly efficient and reliable transparent electromagnetic interference shielding film,” ACS Appl. Mater. Interfaces 10(14), 11941–11949 (2018). [CrossRef]
23. F. Ren, H. Guo, Z. Guo, Y. Jin, H. Duan, P. Ren, and D. Yan, “Highly Bendable and Durable Waterproof Paper for Ultra-High Electromagnetic Interference Shielding,” Polymers 11(9), 1486 (2019). [CrossRef]
24. M. Hu, J. Gao, Y. Dong, K. Li, G. Shan, S. Yang, and R. Li, “Flexible Transparent PES/Silver Nanowires/PET Sandwich-Structured Film for High-Efficiency Electromagnetic Interference Shielding,” Langmuir 28(18), 7101–7106 (2012). [CrossRef]
25. L. Jia, D. Yan, X. Liu, R. Ma, H. Wu, and Z. Li, “Highly Efficient and Reliable Transparent Electromagnetic Interference Shielding Film,” ACS Appl. Mater. Interfaces 10(14), 11941–11949 (2018). [CrossRef]
26. D. Kim, Y. Kim, and J. Kim, “Transparent and Flexible Film for Shielding Electromagnetic Interference,” Mater. Des. 89, 703–707 (2016). [CrossRef]
27. Z. Lu, L. Ma, J. Tan, H. Wang, and X. Ding, “Transparent multi-layer graphene/polyethylene terephthalate structures with excellent microwave absorption and electromagnetic interference shielding performance,” Nanoscale 8(37), 16684–16693 (2016). [CrossRef]
28. H. Zhang, Y. Xia, and J. Gai, “Ultrathin Active Layer for Transparent Electromagnetic Shielding Window,” ACS Omega 3(3), 2765–2772 (2018). [CrossRef]
29. J. Kang, D. Kim, Y. Kim, J. Choi, B. Hong, and S. Kim, “High-performance near-field electromagnetic wave attenuation in ultra-thin and transparent graphene films,” 2D Mater. 4(2), 025003 (2017). [CrossRef]
30. S. Hong, K. Kim, T. Kim, J. Kim, S. Park, J. Kim, and B. Cho, “Electromagnetic Interference Shielding Effectiveness of Monolayer Graphene,” Nanotechnology 23(45), 455704 (2012). [CrossRef]
31. K. Batrakov, P. Kuzhir, S. Maksimenko, A. Paddubskaya, S. Voronovich, P. Lambin, T. Kaplas, and Y. Svirko, “Flexible Transparent Graphene/Polymer Multilayers for Efficient Electromagnetic Field Absorption,” Sci. Rep. 4(1), 7191 (2015). [CrossRef]
32. H. Lee, W. Jin, M. Ovhal, N. Kumar, and J. Kang, “Flexible transparent conducting electrodes based on metal meshes for organic optoelectronic device applications: a review,” J. Mater. Chem. C 7(5), 1087–1110 (2019). [CrossRef]
33. M. Kohin, S. Wein, J. Traylor, R. Chase, and J. Chapman, “Analysis and design of transparent conductive coatings and filters,” Opt. Eng. 32(5), 911–925 (1993). [CrossRef]
34. J. Halman, K. Ramsey, M. Thomas, and A. Griffin, “Predicted and measured transmission and diffraction by a metallic mesh coating,” Proc. SPIE 7302, 73020Y (2009). [CrossRef]
35. Y. Han, H. Zhong, N. Liu, Y. Liu, J. Lin, and P. Jin, “In Situ Surface Oxidized Copper Mesh Electrodes for High-Performance Transparent Electrical Heating and Electromagnetic Interference Shielding,” Adv. Electron. Mater. 4(11), 1800156 (2018). [CrossRef]
36. D. Shin and J. Park, “Design of moiré-free metal meshes using ray tracing for touch screen panels,” Displays 38, 9–19 (2015). [CrossRef]
37. I. Murray, V. Densmore, V. Bora, M. Pieratt, D. Hibbard, and T. Milster, “Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software,” Proc. SPIE 8016, 80160U (2011). [CrossRef]
