This paper reports a high-performance transparent electromagnetic shielding material based on an ultrathin and large-area metallic nanomesh, which was fabricated by a facile and rational process utilizing ultraviolet lithography and the ion beam etching technique. Measurements reveal that a single-layer metallic nanomesh can harvest excellent shielding effectiveness exceeding 40 dB in the wide frequency range from 500 MHz to 40 GHz. Besides, efficient light transmittance (85% at 550 nm) is achieved in both visible and near-infrared regions. Furthermore, the proposed structure remains excellent performance at wide incident angles even up to 50°. Hence, it is believed that this metallic nanomesh with easy fabrication can be a potential alternative in the transparent electromagnetic shielding domain.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Electromagnetic interference (EMI), which is considered as a new kind of pollution at the information age, has become a serious issue as it affects the utilities of electronic equipment and brings potential threats to human health. Until now, achieving high-performance EMI shielding with excellent optical transmittance remains a challenge in various optoelectronic applications, such as mobile communication devices, electronic displays, and aircraft [1–3]. As to obtain simultaneous high transparency and EMI shielding effectiveness (SE), materials with optically transparent and electrically conductive properties have gained huge expectations. To date, indium tin oxide (ITO) film is still applied as commercial transparent EMI shielding material, yet excluded from the next-generation candidates for its brittle, high processing temperature and infrared absorbing natures [4,5]. Some substitutes including graphene [6–8], metallic nanowires (MNW) [3,9–11] and carbon nanotubes (CNT) [2,12,13], which have been extensively studied for their inexpensive and large-scale solution-based fabrication, remain imperfect as they are difficult to achieve both high SE and optical transmittance. Moreover, for CNT thin film, the intrinsic drawbacks of percolation and large contact resistances between tubes block its further applications. To improve the performance of graphene, some researches adopt the ideas of hierarchical structures like double and multiple layers , and even compositing with metallic electrodes [15–17]. For example, double-layers graphene is verified to gain nearly an extra 3 dB SE than that of a single layer. However, a sharp drop in optical transmittance is inevitable when stacking the materials [14,18]. Meanwhile, complex and inefficient fabricating processes hinder their practicalities. Overall, these materials fall into the contradictions between electrical and optical properties for lacking in degrees of designing freedoms.
Recently, metallic meshes have attracted considerable attention not only for the outstanding optoelectronic performance but also the designing flexibility while transmittance and SE can be adjusted by altering their heights, widths, pitches, and shapes [19–21]. Approaches to fabricate metallic meshes with widths of a few microns, like jet printing  and selective laser sintering , have been demonstrated. However, micro-scale metallic meshes (with the gap of hundreds of microns between adjacent microwires) bring about poor local collection or delivery of carriers. Undoubtedly, nano-scale metallic meshes could provide a solution to this problem. Nevertheless, random networks formed by MNW [24,25] still suffer from large contact resistances as CNT. In contrast, regular metallic nanomeshes can diminish the percolation among nanowires and contact resistances at their junctions, which contributed to a lower sheet resistance and higher SE [26,27]. In this way, electrospinning  is utilized to manufacture nanomeshes with low contact resistances because the nanowires are fused at their junctions after a thermal process, but this point-by-point scanning method is time-consuming and imposes a serious obstacle for high productivity. Nanoimprint lithography  has been verified to fabricate metallic nanomeshes with high yields. However, delicate molds are necessary for this methodology while sticking and wearing issues need further considerations, which bring more complexities in the fabricating process. Therefore, a facile, quick and large-scale manufacturing method is desperately desired. On the other hand, the superiorities in electrical (e.g., SE, bandwidth and angular stability) and optical properties (e.g., transmittance and diffraction uniformity) of metallic nanomeshes still need profound researches.
Herein, we present a metallic nanomesh for achieving high-performance transparent EMI shielding. A simple process employing ultraviolet (UV) lithography and ion beam etching (IBE) technique have been proposed to engineer the designed metallic nanomesh on a round transparent dielectric substrate with a large diameter of 100 mm. Our works reveal the broadband shielding property of nanomeshes in the frequency range from 500 MHz to 40 GHz through two sets of measuring configurations using waveguide-to-coaxial adapters and lens antennas respectively. Besides, diffractive distribution and angular response of the nanomesh are demonstrated. It is believed that our works could pave a path to thrive the applications of metallic nanomeshes in electromagnetics and optoelectronics.
2. Experimental section
Figure 1(a) illustrates the proposed structure composing of a single-layer metallic nanomesh and a transparent dielectric substrate. The unit cell of the nanomesh is a cross with an optimized width of 850 nm, a pitch of 12 µm and a height of 500 nm, as shown in Fig. 1(b). The optimization requires a comprehensive consideration of visible light transmittance and microwave SE through the Eq. (1) and full-wave simulations respectively. The Eq. (1) expresses the optical transmittance as below :1) is valid for the case of normal incidence when p is far greater than the wavelength and w. For the case of arbitrary incident angle, rigorous coupled-wave theory is suitable for calculating optical transmittance because of its fast calculating speed in comparison with finite element simulation.
The flow chart of the fabricating process is depicted in Fig. 2(a). The glass substrate with a height of 1 mm and a dielectric constant of 3.9 was soaked in piranha solution at 120°C for 30 minutes to eliminate the organic impurities on the surface. Then a chromium (Cr) thin film with 10 nm thickness, as an adhesive layer, was thermally evaporated on the cleaned substrate. Subsequently, 500 nm thick copper (Cu) with σ (electrical conductivity) of 5.6 × 107 S/m was thermally evaporated on the Cr film. The reflective properties of electromagnetic (EM) waves originated from these metallic films. In this work, UV lithography, also known as conventional photolithography was selected to manufacture the nanomesh pattern for its simplicity and reliability. After spinning 500-550 nm thick photoresist (AZ 1500 20 cP, AZ Electronic Materials), the sample was baked at 100°C for 1 minute to evaporate the solvent in the photoresist. We exposed the sample to i line UV source with an intensity of 60-65 mJ cm−2 for 20 seconds where a mask with the identical mesh pattern fabricated by laser directing writing technology (DWL 66+, Heidelberg Instrument) was necessary and then soaked it in AZ 300MIF developer for 30-40 seconds. Right after that, another baking process at 120°C for 30 minutes was necessary to harden the nanomesh pattern.
To transfer the pattern to the underlying metallic films precisely, the IBE technique (ATC-2036-IM, AJA International, Inc.) was applied. Under the bombardment of Ar+ (argon ions) with 150 mA ionic currents and 60 V accelerating voltages, the metallic films were etched thoroughly after 480-500 seconds at the ionic incident angle of 30°. It implied that the metallic films and photoresist keep an etched selectivity ratio of nearly 3:1 [examined by a step profiler (Alpha-Step D-500, KLA)], which meant residual photoresist remained. At last, a stripping process was carried out through oxygen reactive ion etching (RIE) for 5 minutes. Our manufacturing method helped avoid wet processes as far as possible while the humid environment promoted corrosion of metallic meshes. At last, a metallic nanomesh with a width of nearly 850 nm, a thickness of 500 nm, a pitch of 12 µm and a large diameter of 100 mm was realized.
Here we used two configurations to measure SE in the separated frequency range of 500 MHz-18 GHz and 18-40 GHz respectively. As depicted in Fig. 3(a), the measurement was carried out with a couple of waveguide-to-coaxial adapters and a vector network analyzer (VNA, E8363B, Agilent Technologies) to obtain the scattering parameter (S21). Then the fabricated sample was cut into a doughnut-shape ring via a laser cutting process with an inner and outer diameter of 3 mm and 7 mm separately [Fig. 2(c)], which was placed on the commissure of the adapters. In the high-frequency region, a pair of antennas and EM wave lens, as shown in Fig. 3(b), were utilized to propagate signals in the free space where the round sample [Fig. 2(b)] stood between the lens.
Moreover, the surface morphology of the metallic nanomesh was characterized by field emission scanning electron microscopy (FESEM, SU 8010, Hitachi, Inc.). Optical transmittance of the nanomesh was measured in the visible (VIS) and near-infrared (NIR) spectra via a spectrometer (Lambda 1050, PerkinElmer Co, Ltd). Also, both the EMI SE and transmittance were calibrated by a bare glass substrate.
3. Results and discussions
The key to gain high electrical performance is ensuring the completeness of the nanomesh structure. Figure 2(d) reveals that the appearance of the nanomesh remains intact. Furthermore, the orthogonal metallic nanowires keep a firm connection to guarantee low contact resistance as demonstrated in Fig. 2(e), which is beneficial to increase the SE by improving the uniformity of conductivity. However, a few nanoparticles were formed on the surface as shown in Fig. 2(e), which probably resulted from the redeposition of etched materials during the IBE process and may cause a slight decline in optical transmittance. The effect of redeposition can be weakened by an optimal incident angle of the bombarding ions .
EMI SE denoted as a judge of ability to attenuate the EM power at a specified point after insertion of the shielding material, can be defined as:4(a), the metallic nanomesh performs a superior EMI shielding capability in the broadband range of 500 MHz-40 GHz. Experimental results show that more than 40 dB is achieved from L (1-2 GHz) to the Ka band (26.5-40 GHz), where the average SE in 500 MHz-18 GHz and 18 GHz-40 GHz is 47.8 and 42.9 dB respectively. Because of the measuring error between two distinct measurement configurations, the experimental curve is disconnected at 18 GHz. On the other hand, the results by full-wave simulations on commercial software (CST Microwave Studio) are compared with the experimental ones, which show a good match at high frequency like the Ka band. However, due to the manufacturing error in the laser cutting process, the doughnut-shape sample does not fit the waveguide precisely, which results in the leakage of EM waves especially when the wavelength is close to or larger than the aperture of the sample. Hence, it leads to a difference between the simulated and experimental results in the relatively low-frequency band.
The prominent advantage of the nanomesh is the flexibility of manipulating its performance by varying w and p. The theoretical transmittance of the proposed nanomesh is calculated as 86.3% through the Eq. (1). We compare the theoretical and experimental results as shown in Fig. 4(b), which shows good fitness. In addition, the measured results are calibrated by the curve of a bare glass substrate, which reveals the actual transmittance of the single-layer metallic nanomesh. In the VIS range (400-800 nm), the average transmittance is 83.2%. And, 85% is achieved at 550 nm, which is close to the theoretical result. However, the average transmittance of 78.5% is measured in the NIR range (800-1800 nm). The slight difference may result from the optical diffraction. A small aperture in the measurement setup to receive the transmissive light may miss some diffraction energies especially when the energies distribution is more dispersive at a longer wavelength. Yet, this result show superiority compared to ITO material which has poor transparency in the NIR regions. To further illustrate the broadband performance of our metallic nanomesh, comparisons of several works are listed in Fig. 5. Besides the popular materials like silver nanowires , carbon nanotubes films  and graphene [14,16,17], metallic meshes [22,31–33] with similar geometries but different manufacturing processes are within our scope. Our work presents a superior SE, wider bandwidth and an efficient optical transmittance.
Next, we investigate the essential influences of pitches and widths on the performance of metallic nanomeshes by CST as shown in Figs. 6(a) and (b). Evidently, in the millimeter scale where pitch and width are 12 and 1 mm separately, the metallic mesh acts as a frequency selective surface with a resonance at 24.5 GHz. While the metallic mesh is narrowed down to the micro scale, it behaves as a wideband reflector. Moreover, it reveals a trend that a smaller scale gains higher SE. In this case, we fix w/p as a constant value of 1/12 for the identical theoretical transmittance of all metallic meshes. Furthermore, as depicted in Fig. 6(b), while ensuring that the minimum SE in the frequency range of 0.5-40 GHz is nearly higher than 40 dB, the calculated transmittance through Eq. (1) dramatically ascends from 69.4 to 98.3% as the width shrinks from 2 µm to 100 nm when fixing the pitch at 12 µm. These simulated results suggest an effective approach to enhance SE by scaling down the meshes patterns, while the transmittance is unchanged for fixing the porosity ratio defined as the ratio of the area of the square apertures over the surface area. Especially when the width is narrowed down to hundreds of nanometers, an outstanding transparent EMI shielding performance over the broadband (500 MHz-40 GHz) is achieved.
Optical diffraction distribution is another essential consideration while designing the metallic mesh because the high-order diffractive energies (considered as the stray light) may damage the imaging qualities . The nanomesh can be regarded as an optical grating, therefore, a smaller pitch will help to avoid high-order diffractions and concentrate the energy into the desired order. We also investigate the influence of width on the diffraction distribution. To guarantee the accuracy of results when lights may interact with metallic meshes once the widths approach the optical wavelengths, full-wave simulations are performed to extract the E-field distributions with an incident plane wave, which simulates the process of illuminating the nanomesh with monochromatic light of 632 nm. Then calculation based on Huygens-Fresnel diffraction theory  is carried out to derive the energies distributions. Figure 6(c) shows the diffraction pattern of the metallic mesh with p of 12 µm and w of 2 µm. Apparently, energies are mostly accumulated on the central spot where a few weaker spots distribute along the mesh lines. When the width is narrowed down, some similar patterns are witnessed, hence we switch to focusing on the variation of high-order diffraction energies. Figures 6(d)–(f) present that when w decreases from 2 µm to 100 nm while p is fixed to 12 µm, the maximal normalized high-order energies are tremendously suppressed where −6 dB is realized with w of 100 nm. Obviously, low high-order energies are significant for homogenizing stray lights. It can also be explained by Huygens-Fresnel diffraction theory. As we adapt the nanomesh to the multi-slits diffraction model, a greater slit (where its w decreases and p remains unchanged) leads to stronger centralization of light for minimizing the high-order energies. Above all, simulations suggest that nanomesh is superior to micromesh considering the SE and transmittance, where the nanomesh and the micromesh refer to the width w less than 1 µm and larger than 1 µm, respectively. Moreover, a smaller width is beneficial to restrain the stray light. It is noted that some special mesh patterns can be used to homogenize the high-order diffraction energies employing the interlaced or interconnected arrangement of the ring/circle [36–39], the proposed fabrication method also can fabricate the ring/circle micromesh pattern by a prepared mask, which is important for the field of transparent EMI shielding materials.
It should be noted that only the cases of normal incidence are concerned above. However, the robustness of angular response should be emphasized for versatile applications [40,41]. We have studied the stability of SE by full-wave simulations in the case of oblique incidence. With the incident angles increasing from 0° to 60°, SE tends to rise for TE polarization while shows an opposite trend for TM polarization, as depicted in Figs. 7(a) and (b). This phenomenon has been explained by Kohin et al. , who proposed an equivalent film method by characterizing the metallic mesh with an equivalent refractive index. According to thin film theory, the admittances of TE and TM polarizations have a contrary tendency when incident angles vary. Therefore, the responses of the equivalent films have opposite trends. Despite the reduction at a large incident angle by TM polarization, the SE still exceeds 40.9 dB at 50°. Moreover, the SEs of two polarizations show fluctuations less than ± 10% from 0° to 50° compared to the case of normal incidence. On the other hand, the SE is far more dependent on frequency than incident angles. To represent the transmittance response of sweeping angular and wavelength spectra, we have calculated the transmittance of nanomeshes with the incident angle of 0-60° and the wavelength of 400-1800nm by applying rigorous coupled-wave analysis (RCWA) . Both TE and TM modes are considered to investigate the transmittance degradation at oblique angles as seen from Figs. 7(c) and (d), where the transmittances tend to decline slightly from 0 to 50° but drop sharply at larger angles. The proposed nanomesh exhibits moderate angular stability even up to 50°, which enriches its practicality in the complex electromagnetic environments.
In conclusion, we have proposed and experimentally demonstrated the high performance of metallic nanomeshes for transparent EMI shielding. Our metallic nanomesh was fabricated by an easy and reliable process, exhibiting not only an excellent EMI SE beyond 40 dB across the broadband of 500 MHz-40 GHz but also a pretty high transmittance of 85% at 550 nm. Furthermore, full-wave simulations on EMI SE, transmittance and diffraction distribution are performed to investigate the significance of reducing the geometric scale of metallic meshes and verify the wide-angle stabilization. Thus, our works prove the metallic nanomesh to be a tough competitor to other transparent EMI shielding materials and reveal a promising way to broaden its applications in optoelectronic devices. In principle, its performance can be further improved using more advanced techniques such as surface plasmon lithography [44, 45].
National Natural Science Foundation of China (61575202, 61575203).
1. H.-C. Lee, J.-Y. Kim, C.-H. Noh, K. Y. Song, and S.-H. Cho, “Selective metal pattern formation and its EMI shielding efficiency,” Appl. Surf. Sci. 252(8), 2665–2672 (2006). [CrossRef]
2. N. Li, Y. Huang, F. Du, X. He, X. Lin, H. Gao, Y. Ma, F. Li, Y. Chen, and P. C. Eklund, “Electromagnetic interference (EMI) shielding of single-walled carbon nanotube epoxy composites,” Nano Lett. 6(6), 1141–1145 (2006). [CrossRef]
3. M. Hu, J. Gao, Y. Dong, K. Li, G. Shan, S. Yang, and R. K.-Y. Li, “Flexible transparent PES/silver nanowires/PET sandwich-structured film for high-efficiency electromagnetic interference shielding,” Langmuir 28(18), 7101–7106 (2012). [CrossRef]
4. S. I. Na, S. S. Kim, J. Jo, and D. Y. Kim, “Efficient and flexible ITO-free organic solar cells using highly conductive polymer anodes,” Adv. Mater. 20(21), 4061–4067 (2008). [CrossRef]
5. S. Jang, W.-B. Jung, C. Kim, P. Won, S.-G. Lee, K. M. Cho, M. L. Jin, C. J. An, H.-J. Jeon, and S. H. Ko, “A three-dimensional metal grid mesh as a practical alternative to ITO,” Nanoscale 8(29), 14257–14263 (2016). [CrossRef]
6. S. Kim, J.-S. Oh, M.-G. Kim, W. Jang, M. Wang, Y. Kim, H. W. Seo, Y. C. Kim, J.-H. Lee, and Y. Lee, “Electromagnetic interference (EMI) transparent shielding of reduced graphene oxide (RGO) interleaved structure fabricated by electrophoretic deposition,” ACS Appl. Mater. Interfaces 6(20), 17647–17653 (2014). [CrossRef]
7. B. Shen, W. Zhai, and W. Zheng, “Ultrathin flexible graphene film: an excellent thermal conducting material with efficient EMI shielding,” Adv. Funct. Mater. 24(28), 4542–4548 (2014). [CrossRef]
8. J. Han, X. Wang, Y. Qiu, J. Zhu, and P. Hu, “Infrared-transparent films based on conductive graphene network fabrics for electromagnetic shielding,” Carbon 87, 206–214 (2015). [CrossRef]
9. D.-H. Kim, Y. Kim, and J.-W. Kim, “Transparent and flexible film for shielding electromagnetic interference,” Mater. Des. 89, 703–707 (2016). [CrossRef]
10. J. Jung, H. Lee, I. Ha, H. Cho, K. K. Kim, J. Kwon, P. Won, S. Hong, and S. H. Ko, “Highly stretchable and transparent electromagnetic interference shielding film based on silver nanowire percolation network for wearable electronics applications,” ACS Appl. Mater. Interfaces 9(51), 44609–44616 (2017). [CrossRef]
11. L.-C. Jia, D.-X. Yan, X. Liu, R. Ma, H.-Y. Wu, and Z.-M. Li, “Highly efficient and reliable transparent electromagnetic interference shielding film,” ACS Appl. Mater. Interfaces 10(14), 11941–11949 (2018). [CrossRef]
12. H. Xu, S. M. 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]
13. M. H. Al-Saleh and U. Sundararaj, “Electromagnetic interference shielding mechanisms of CNT/polymer composites,” Carbon 47(7), 1738–1746 (2009). [CrossRef]
14. 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]
15. T. Gao, Z. Li, P.-S. Huang, G. J. Shenoy, D. Parobek, S. Tan, J.-K. Lee, H. Liu, and P. W. Leu, “Hierarchical graphene/metal grid structures for stable, flexible transparent conductors,” ACS Nano 9(5), 5440–5446 (2015). [CrossRef]
16. 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]
17. Z. Lu, L. Ma, J. Tan, H. Wang, and X. Ding, “Graphene, microscale metallic mesh, and transparent dielectric hybrid structure for excellent transparent electromagnetic interference shielding and absorbing,” 2D Mater. 4(2), 025021 (2017). [CrossRef]
18. S. De and J. N. Coleman, “Are there fundamental limitations on the sheet resistance and transmittance of thin graphene films?” ACS Nano 4(5), 2713–2720 (2010). [CrossRef]
19. H. Wu, D. Kong, Z. Ruan, P.-C. Hsu, S. Wang, Z. Yu, T. J. Carney, L. Hu, S. Fan, and Y. Cui, “A transparent electrode based on a metal nanotrough network,” Nat. Nanotechnol. 8(6), 421–425 (2013). [CrossRef]
20. S. Shen, S.-Y. Chen, D.-Y. Zhang, and Y.-H. Liu, “High-performance composite Ag-Ni mesh based flexible transparent conductive film as multifunctional devices,” Opt. Express 26(21), 27545–27554 (2018). [CrossRef]
21. Z.-Y. Jiang, W. Huang, L.-S. Chen, and Y.-H. Liu, “Ultrathin, lightweight, and freestanding metallic mesh for transparent electromagnetic interference shielding,” Opt. Express 27(17), 24194–24206 (2019). [CrossRef]
22. S. K. Vishwanath, D.-G. Kim, and J. Kim, “Electromagnetic interference shielding effectiveness of invisible metal-mesh prepared by electrohydrodynamic jet printing,” Jpn. J. Appl. Phys. 53(5S3), 05HB11 (2014). [CrossRef]
23. S. Hong, J. Yeo, G. Kim, D. Kim, H. Lee, J. Kwon, H. Lee, P. Lee, and S. H. Ko, “Nonvacuum, maskless fabrication of a flexible metal grid transparent conductor by low-temperature selective laser sintering of nanoparticle ink,” ACS Nano 7(6), 5024–5031 (2013). [CrossRef]
24. P.-C. Hsu, S. Wang, H. Wu, V. K. Narasimhan, D. Kong, H. R. Lee, and Y. Cui, “Performance enhancement of metal nanowire transparent conducting electrodes by mesoscale metal wires,” Nat. Commun. 4(1), 2522 (2013). [CrossRef]
25. S. Ye, A. R. Rathmell, Z. Chen, I. E. Stewart, and B. J. Wiley, “Metal nanowire networks: the next generation of transparent conductors,” Adv. Mater. 26(39), 6670–6687 (2014). [CrossRef]
26. C. A. Klein, “Microwave shielding effectiveness of EC-coated dielectric slabs,” IEEE Trans. Microwave Theory Tech. 38(3), 321–324 (1990). [CrossRef]
27. Y. Liu and J. Tan, “Frequency dependent model of sheet resistance and effect analysis on shielding effectiveness of transparent conductive mesh coatings,” Prog. Electromagn. Res. 140, 353–368 (2013). [CrossRef]
28. H. Wu, L. Hu, M. W. Rowell, D. Kong, J. J. Cha, J. R. McDonough, J. Zhu, Y. Yang, M. D. McGehee, and Y. Cui, “Electrospun metal nanofiber webs as high-performance transparent electrode,” Nano Lett. 10(10), 4242–4248 (2010). [CrossRef]
29. M. Song, H.-J. Kim, C. S. Kim, J.-H. Jeong, C. Cho, J.-Y. Lee, S.-H. Jin, D.-G. Choi, and D.-H. Kim, “ITO-free highly bendable and efficient organic solar cells with Ag nanomesh/ZnO hybrid electrodes,” J. Mater. Chem. A 3(1), 65–70 (2015). [CrossRef]
30. P. G. Glöersen, “Ion− beam etching,” J. Vac. Sci. Technol. 12(1), 28–35 (1975). [CrossRef]
31. 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]
32. 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]
33. S.-I. Chung, P. K. Kim, T.-G. Ha, and J. T. Han, “High-performance flexible transparent nanomesh electrodes,” Nanotechnology 30(12), 125301 (2019). [CrossRef]
34. X. Xie, K. Liu, M. Pu, X. Ma, X. Li, Y. Guo, F. Zhang, and X. Luo, “All-metallic geometric metasurfaces for broadband and high-efficiency wavefront manipulation,” Nanophotonics (2019), [CrossRef] .
35. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55(4), 373–381 (1965). [CrossRef]
36. 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]
37. I. B. Murray, V. Densmore, V. Bora, M. W. Pieratt, D. L. Hibbard, and T. D. Milster, “Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software,” Proc. SPIE 8016, 80160U (2011). [CrossRef]
38. J. I. Halman, K. A. Ramsey, M. Thomas, and A. Griffin, “Predicted and measured transmission and diffraction by a metallic mesh coating,” Proc. SPIE 7302, 73020Y (2009). [CrossRef]
39. J. Tan and Z. Lu, “Contiguous metallic rings: an inductive mesh with high transmissivity, strong electromagnetic shielding, and uniformly distributed stray light,” Opt. Express 15(3), 790–796 (2007). [CrossRef]
40. X. Ma, M. Pu, X. Li, Y. Guo, and X. Luo, “All-metallic wide-angle metasurfaces for multifunctional polarization manipulation,” Opto-Electro. Advan. 2(3), 18002301–18002306 (2019). [CrossRef]
41. Y. Wang, X. Ma, X. Li, M. Pu, and X. Luo, “Perfect electromagnetic and sound absorption via subwavelength holes array,” Opto-Electro. Advan. 1(8), 18001301–18001306 (2018). [CrossRef]
42. M. Kohin, S. J. Wein, J. D. Traylor, R. C. Chase, and J. E. Chapman, “Analysis and design of transparent conductive coatings and filters,” Opt. Eng. 32(5), 911–926 (1993). [CrossRef]
43. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings,” J. Opt. Soc. Am. A 24(9), 2880–2890 (2007). [CrossRef]
44. X. Luo, “Subwavelength artificial structures: opening a new era for engineering optics,” Adv. Mater. 31(4), 1804680 (2019). [CrossRef]
45. P. Gao, M. Pu, X. Ma, X. Li, Y. Guo, C. Wang, Z. Zhao, and X. Luo, “Plasmonic lithography for the fabrication of surface nanostructures with a feature size down to 9 nm,” Nanoscale 12, 2415–2421 (2020). [CrossRef]