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Optica Publishing Group

Embedded flexible and transparent double-layer nickel-mesh for high shielding efficiency

Open Access Open Access

Abstract

An efficient approach to obtain high shielding effectiveness (SE) in transparent shielding in an optical window field is proposed and demonstrated by fabricating an embedded double-layer metallic mesh (DLMM) comprised of randomly structured Ni meshes on both sides of a flexible substrate, employing a facile and low-cost double-sided nanoimprinting method. The unique nonperiodic random structure contributes to uniform diffraction and eliminates the Moiré fringe generated by double-layer periodic meshes, ensuring high imaging quality for optical applications. The designed DLMM films simultaneously achieve strong shielding in the X-band and high transmittance in the visible spectrum, demonstrating a high transmittance of 88.7% at the 550-nm wavelength and a SE of 46.9 dB at a frequency of 8.2 GHz. An ultra-high SE of 80 dB is achieved at 64.2% transmittance, which reveals the highest reported SE over a metallic mesh for transparent shielding, indicating the high potential for this transparent electromagnetic interference shielding material for practical optical applications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The recent surge in growth of the electronic and wireless market materializes the electromagnetic interference (EMI) generated by electronic devices as a serious global problem, as it provokes the malfunction of electronic equipment, threatens information security, and even presents a hazard to the human body [15]. Thus, EMI shielding is in increasing demand, in particular with regard to the widely concerning electromagnetic microwave range X-band (8.2–12.4 GHz) [68]. Significant efforts have been devoted to the development of high-performance EMI shielding materials [914]. In addition to the EMI shielding effectiveness (SE), high optical transmittance is another imperative requirement for practical transparent EMI shielding materials in optoelectronic equipment, particularly in optical windows, aerospace domes, and electronic displays [1518]. More importantly, transparent EMI shielding materials must exhibit good flexibility, and high image quality is demanded for the fast-growing next-generation flexible electronics [1921]. Materials with high electrical conductivity and good connectivity contribute to improvements in the EMI SE performance [2226]. In general, stacked metallic nanowires have intrinsic drawbacks, such as the large contact resistance between wires and inhomogeneous distribution, which limits the optical transmittance and SE [2729]. Patterned metallic meshes have a controllable design of their regular microscale structure with regard to the continuous and junction-free metal grids, adjustable grid space, line width, and line thickness, whose calibration can alleviate the trade-off between transmittance and the EMI SE [3032]. Furthermore, the SE can be independently adjusted by increasing the metal thickness, while maintaining the transmittance [26]. However, due to restrictions in the current microscale fabrication technology, the aspect ratio of the metallic mesh has an upper limit (∼2 at linewidth 2–6 µm) [3336], at which the shielding effectiveness of transparent shielding film with single-layer metallic mesh attains its maximum and cannot be significantly improved, limiting its application for high efficiency requirements. Thus, double-layer metallic mesh (DLMM) structure was proposed to increase the shielding effectiveness of transparent shielding film [3739]. Moreover, for the metallic mesh with a periodic structure, the stray light caused by high-order diffraction significantly degrades image quality, and further efforts are required to obtain high image quality shielding films [40,41]. Therefore, the development of EMI shielding materials integrated with all desirable features mentioned above remains a considerable challenge.

Herein, we propose a novel type of embedded DLMM with random structured Ni meshes mechanically embedded on each side of a flexible substrate by a facile and low-cost inverted film process. By adopting this DLMM, we achieved extraordinary performance, including high EMI SE and even a higher optical transmission that overcomes the drawback of the single-layer metallic mesh (SLMM). To further reduce stray light interference caused by the diffraction superposition of periodic structures, we introduced random patterns to establish uniform diffraction and eliminate the Moiré fringe generated by double-layer periodic meshes. Consequently, the as-fabricated DLMM that exhibits flexibility, good transmittance, strong EMI SE, high mechanical stability, and excellent optical image quality is a promising transparent EMI shielding material for practical optoelectronic applications.

2. Experiments

2.1 Preparation of Ni-mesh supported on indium tin oxide (ITO) glass

First, the photoresist (AZ-4620 USA) was spin-coated on a pre-cleaned ITO glass (∼ 6 Ω/sq, China) and placed in an oven for solidification. Subsequently, the random structured groove was patterned by a laser direct-writing technique in the photoresist layer. Next, Ni was selectively electrodeposited in the photoresist micro-trench to form a continuous Ni-mesh film. Finally, the sample plate was soaked in sodium hydroxide solution to fully remove the excess photoresist and achieve the hollowed-out Ni-mesh supported on ITO glass with a thickness of 4 µm and line width of 6.5 µm.

2.2 Fabrication of SLMM and DLMM films

The dispersed UV-curable resin (D580, Phichem) was drop-casted onto the ITO supported Ni-mesh, and a poly(ethylene terephthalate) (PET) substrate was fixed onto the UV resin using a roller to purge the air bubbles. Subsequently, the UV resin was exposed to UV light curing for several seconds. Afterwards, the PET was peeled off from the ITO glass with the Ni-mesh inverted in the UV resin, and embedded SLMM film with PET as substrate was achieved. Followingly, another Ni-mesh was transferred onto the other side of the PET to obtain the DLMM film.

2.3 Characterization

The optical transmittance of the films was measured using a Lambda 750UV-VIS spectrometer (Perkin Elmer USA). The sheet resistance was recorded by a four-point probe (ST2263). MATLAB software was used to simulate the diffraction distribution of different pattern arrangements. The CST Microwave Studio software was employed to analyze the SE value of SLMM and DLMM films with a varying period and separation distance. The experimental SE in the X-band was tested by an Agilent N5230C PNA Network Analyzer with a calibration kit WR-90.

3. Results and discussion

The fabrication of the Ni-mesh is shown in Fig. 1(a), illustrating the laser direct-writing technique and Ni electrodeposition process. The randomly structured Ni meshes with supported ITO glass have a unified ultrathin thickness of 4 µm and line width of 6.5 µm, with periods varying from 50 µm to 200 µm. The ultrathin Ni meshes were imprinted onto the flexible PET substrate with dispersed UV-curable resin, thereby mechanically anchoring the Ni meshes in UV resin. We developed both single- and double-layer Ni-mesh films with SLMM embedded on one side, and DLMM on each side of PET, as shown in Fig. 1(b). Owing to the double-sided imprint transfer method, the flexible substrate was fully utilized by arranging the two Ni meshes on both sides, and the thickness of the DLMM film becomes similar to the substrate-supported SLMM with only increasing of the additional neighboring ultrathin Ni-mesh (∼ 4 µm), which provides the DLMM film with good mechanical stability. Figures 1(c) and 1(d) illustrate the mechanism of EMI shielding by DLMM from the top and side view, respectively. The Ni-mesh with excellent electrical conductivity contributes to the interaction between electric and magnetic fields of the incident microwave. Owing to the mutation of wave impedance between the shielding material and air, when the electromagnetic wave is incident on the shielding film, a large portion of the incident microwave is reflected at the first layer of DLMM. The remaining portion of the wave penetrates the first Ni-mesh and enters the interior of the film; the dielectric PET exhibits high transparency to microwaves, such that the wave proceeds directly through to the substrate. When the transmitted wave arrives at the second Ni mesh layer, most of it is reflected to the incident side, and the reflected wave is further reflected and transmitted onto the interface of the first Ni mesh layer. Furthermore, the second reflected wave is reflected and refracted iteratively between the two layers of Ni meshes until the energy is completely consumed and transmitted, thereby significantly attenuating the incident microwave.

 figure: Fig. 1.

Fig. 1. (a) Fabrication of Ni-mesh. (b) Fabrication of SLMM and DLMM film. (c) Diagram of DLMM film. (d) Side view of DLMM film depicting the shielding mechanism.

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3.1 Optical properties

For optical image applications, a uniformly distributed illumination is crucial for high image quality. As the light penetrates through the film, the regular metallic mesh would generally introduce high-order diffractions, giving rise to stray light and engendering false targets that degrade the image quality, for which, only zeroth-order diffraction is conducive to optical devices [39]. Since the diffraction spot distribution of DLMM is a superposition of the diffraction pattern of two SLMM, the two meshes with identical pattern structures would give rise to a similar diffraction pattern for the DLMM film, along with the reduction of the zero-order diffraction intensity and an increase in the higher-order diffraction intensity. The stray light is further enhanced due to the overlay of metallic meshes. Thus, a metallic mesh with a uniform diffraction distribution is an urgent requirement in optical imaging. Moreover, the Moiré fringe generated by DLMM with periodic meshes also contributes with a disadvantageous visual impact. To further reduce light interference caused by the superposition of periodic structures, we introduced a random pattern mesh to gain uniform diffraction and eliminate the Moiré fringe generated by double-layer periodic meshes.

The metallic meshes with a patterned arrangement of the honeycomb structure and random configurations were fabricated and investigated to explore the diffraction characteristics of the SLMM and DLMM with different structures. Figure 2 illustrates the simulated and experimental diffraction results of the two patterned meshes. Figures 2(a-i)–2(a-iv) depict the microstructures of the two types of samples. The corresponding diffraction distribution was obtained by MATLAB software based on the Fourier diffraction theory, as shown in Figs. 2(b-i)–2(b-iv), and the diffraction intensity distribution is shown in Figs. 2(c-i)–2(c-iv). Moreover, the experimental result shown in Figs. 2(d-i)–2(d-iv) indicates good agreement with the simulation obtained by the theoretical model. In contrast to the regular honeycomb mesh diffraction spot in Fig. 2(a-i), where the high-order diffraction evolved along the three crossing lines (Figs. 2(b–i) and 2(d-i)), the random mesh with a nonperiodic structure shows a quite uniform diffraction distribution in Figs. 2(b-iii) and 2(d-iii). The honeycomb structured DLMM with an unaligned layout exhibits an angle θ between the two layers and retains the rotation angle on the diffraction crossing lines. The generated higher-order diffraction crossing lines causing an enhanced high-order diffraction, which contributes to the degradation of imaging quality. Meanwhile, the DLMM with random arrangement weakens the higher-order spot and finally reduces the effect of stray light on the imaging quality.

 figure: Fig. 2.

Fig. 2. Diffraction pattern analysis of SLMM and DLMM films with different pattern structure. (a) Different structures, (b) simulation of diffraction distribution, (c) the three-dimensional intensity profile of the simulated diffraction spots, and (d) the experimental test of the diffraction distribution for SLMM and DLMM with honeycomb and random arrangement.

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Apart from the stray light contributed by the higher-order diffraction, the Moiré fringe generated by periodic DLMM likewise negatively impacts the image quality. The introduction of a random structured mesh effectively solves this problem. Figure 3 presents the image of DLMM with a honeycomb and random arrangements. With the mesh period varying from 50 µm to 200 µm, the interference of the Moiré fringe arising from the honeycomb DLMM recedes gradually (Figs. 3(a)–3(e)); however, it cannot be eliminated. In contrast, the nonperiodic random DLMM indicates high imaging quality, as shown in Fig. 3(f), which perfectly eliminates the Moiré fringe. Therefore, the introduced nonperiodic random pattern mesh achieves uniform diffraction and effective elimination of the Moiré fringe generated by the DLMM film.

 figure: Fig. 3.

Fig. 3. Moiré fringe image for DLMM films based on honeycomb-structured Ni-mesh with period of (a) 50 µm, (b) 100 µm, (c) 150 µm, and (d) 200 µm. (e) Magnified part of film with period of 200 µm. (f) Image of DLMM film based on random structured Ni-mesh with the magnified part insert.

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The visible region performance was also taken into consideration by measuring the optical transmittance. To investigate the impact of the mesh period, randomly structured Ni meshes with different periods of 50, 100, 150, and 200 µm were fabricated, where the random mesh with nonperiodic pattern appearing different mesh space, so we adopted the average space that represented the randomly arranged mesh. Subsequently, we fabricated the corresponding SLMM and DLMM films based on the above random Ni meshes via an imprinting transfer process. For comparison, we designed Ni meshes with a unified thickness of 4 µm and line width of 6.5 µm, and the distance between the two layers of the Ni-mesh was fixed at 250 µm. The fabricated Ni meshes with periods ranging from 50 µm to 200 µm show excellent electrical conductivity with low sheet resistance from 0.126 Ω/sq to 0.841 Ω/sq, and the Ni-mesh with smaller period reveals higher conductivity. The optical transmittance of the metallic mesh film is described as: $T = {T_S} \times (1 - W/(W + G))^{\textrm{2}n}$, where ${T_S}$ is the transmittance of substrate, W is the line width, G is the mesh spacing, and n is the number of layers of metallic mesh. The SLMM and DLMM films with various periods exhibit optical transparency from 67.2%–86% and 55%–79.4% in the visible spectrum of 400–800 nm wavelength, respectively, as shown in Fig. 4(a). The DLMM with a period of 100 µm (DLMM-100) obtains a similar transmittance value (∼67.3%) as the SLMM with a period of 50 µm (SLMM-50), and the DLMM with period of 200 µm (DLMM-200) and the SLMM with period of 100 µm (SLMM-100) likewise have similar transmittance values (∼79.2%). The transmittance of the metallic mesh film can be further improved by coating with a thin layer of polyvinyl alcohol (PVA) gel [42]. The PVA gel was prepared by mixing 10 g of PVA powder in 100 mL deionized water followed by subsequent even coating on the films. The transmittance can be elevated by introducing the PVA gel with a refractive index of 1.4–1.5 between PET (∼1.65) and air (∼1), thus reducing the reflection loss at the air and PET interface. Figure 4(b) shows the improved transmittance of both SLMM and DLMM films with a varying period. The optical transmittance of the films was increased by around 10% in the wavelength range of 400–800 nm. For the higher transmittance films, the improvement of light transmittance is limited. An example is the SLMM-200 film, where the transmittance increases only by 6%. Furthermore, a similar transmittance was obtained between DLMM-100 and SLMM-50, and the transmittance between DLMM-200 and SLMM-100 was consistent with that of the films without PVA enhancement. Overall, the DLMM film with high image quality and optical transmittance is adequate for optical applications.

 figure: Fig. 4.

Fig. 4. (a) Optical transmittance of SLMM and DLMM films with periods varying from 50 µm to 200 µm. (b) Enhanced optical transmittance of SLMM and DLMM films with PVA gel coating for periods of 50, 100, 150, and 200 µm.

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3.2 Period variation effect on EMI SE

The EMI shielding by the SLMM film is mainly attributed to reflections on the surface owing to the high conductivity, and the SE is given by the following equation [43]:

$$S{E_1} = 20\lg \left[ {\frac{1}{{s\sqrt {{{({0.265 \times {{10}^{ - 2}}{R_f}} )}^2} + {{\left[ {0.265 \times {{10}^{ - 2}}{X_f} + 0.333 \times {{10}^{ - 2}}f(\ln \frac{s}{a} - 1.5)} \right]}^2}} }}} \right]$$
where s denotes the mesh space, a is the line width, f is the frequency, and ${R_f}$ and ${X_f}$ are the alternative current resistance and reactance for metallic mesh wire per unit length, respectively. Evidently, the metallic mesh with high conductivity, small mesh space, and broad line width provides a large SE value.

For the DLMM film, the EMI shielding is immensely improved, and the SE is described as follows [43]:

$$S{E_2} = S{E_\textrm{1}} + 10\lg \left\{ {4 + \frac{{\frac{{12l}}{s}\left[ {\frac{{0.38 \times {{10}^6}}}{f}{X_f} + 0.478\left( {\ln \frac{s}{a} - 1.5} \right)} \right] + 9{{\left( {\frac{l}{s}} \right)}^2}}}{{{{\left[ {\frac{{0.38 \times {{10}^6}}}{f}{X_f} + 0.478\left( {\ln \frac{s}{a} - 1.5} \right)} \right]}^2} + {{\left( {\frac{{0.38 \times {{10}^6}}}{f}{R_f}} \right)}^2}}}} \right\}$$
where l is the separation distance between the two layers of metallic meshes. Theoretically, the SE value of the DLMM film increases with widening of the separation distance.

Subsequently, we systematically studied the influence of a and l on the DLMM SE. The simulation of SE for Ni meshes based on SLMM and DLMM in the X-band were carried out using the Microwave Studio software. The corresponding experiments were performed via a vector network analyzer to confirm the simulation results. Figures 5(a)–5(d) present the simulated and measured SE values of SLMM and DLMM films with Ni meshes of different periods in the X-band varying from 8.2 to 12.4 GHz. Further, the results were plotted as shown in Fig. 5(e) for the SE at 8.2 GHz frequency. For the SLMM films with periods varying from 200 µm to 50 µm, the SE value increases gradually from 33 dB to 53 dB, which is consistent with the simulation results. Meanwhile, the DLMM films show a sharp increase in SE (46.9–80 dB) with a decreasing period. Moreover, the gap between the simulated and measured results becomes larger as the period decreases to 50 µm, while their increasing tendencies remain the same. This deviation-case can be attributed to the influence of ambient noise during the measurement on high-performance shielding. Overall, the measured results show good agreement with the simulation. For films with the same Ni-mesh period, the results exhibit an extremely high performance of the DLMM compared to the SLMM, exhibiting an almost 1.5 times improvement. To provide a more objective and evident analysis of the optical transmittance, we summarize the optical transmittance enhanced by the PVA gel (at 550 nm wavelength) and SE values (at the frequency of 8.2 GHz) in Fig. 5(f). Notably, the SLMM-50 yields the same transmittance as DLMM-100 (∼76%), while DLMM-100 with an SE value of 62 dB is significantly larger than the SLMM-50 with an SE value of 53 dB. An improvement in SE larger than 9 dB can be achieved in the X-band with no loss of transmittance. Similarly, DLMM-200 and SLMM-100 films yield a similar result, as the DLMM-200 film yields 5.2 dB more than SLMM-100, and the agreement with the identical transmittance of 89% is maintained. Moreover, SLMM-50 yields the same SE value of 53 dB with DLMM-150, and the transmittance of DLMM-150 ∼84% is larger than that of SLMM-50 ∼76.2%, indicating a higher transmittance of the DLMM film with the same SE. Because of the demand of high SE, the SLMM films sacrifice their transmittance for a higher shielding performance. The introduction of DLMM films tactfully balances the tradeoff between transmittance and SE which further proves that the DLMM can improve SE at the same optical transmittance as Lu et al. have done in Ku-band [37]. Therefore, the DLMM has an advantage over the SLMM in the high-level microwave shielding domain.

 figure: Fig. 5.

Fig. 5. EMI SE of SLMM and DLMM films with randomly structured Ni meshes in X-band. (a) Simulation and (b) experiment results of SLMM films with periods of 50, 100, 150, and 200 µm. (c) Simulation and (d) experiment results of DLMM films with periods of 50, 100, 150, and 200 µm. (e) Comparison of simulated and experimental results for SLMM and DLMM films with different periods at the frequency of 8.2 GHz. (f) Summarized SE at the frequency of 8.2 GHz and enhanced optical transmittance at 550 nm wavelength for SLMM and DLMM films with periods varying from 50 µm to 200 µm.

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3.3 Effect of separation distance on SE

The distance between the two layers meshes is a critical factor influencing the microwave shielding performance, the SE of a DLMM can be improved considerably by increasing the separation between its two mesh layers, with no loss of optical transmittance [37,44]. To verify this result in X-band and for flexible films, we employed PET films with different thicknesses as the separation between mesh layers, thus building DLMM films with separation distances of 100, 200, and 300 µm between two layers. The Ni meshes with a period of 200 µm, thickness of 4 µm, and line width of 6 µm were adopted to construct DLMM films with varying layer separation values. For the DLMM films with identical periods, the transmittance remains the same as the separation changes (Fig. 6(a)). The SE was evaluated though the varying separation distance using both theoretical and experimental methods (Figs. 6(b) and 6(c)), and the result is shown in Fig. 6(d). The simulation results are in good agreement with the experimental results; as the separation increases from 100 to 300 µm, an SE increase of 5.2 dB was obtained, while the visible transmittance remained unchanged. When the separation distance is further increased, the SE keeps increasing (Fig. 6(e)), and achieves the maximum value (∼112 dB) at the distance close to 9000 µm, which is approximately λ/4 at the frequency of 8.2 GHz (Fig. 6(f)). When the separation distance is less than λ/4 of the shielding frequency, the SE value of a DLMM film can be improved simply by widening the separation distance, which breaks off the inherent conflict between the transmittance and shielding effectiveness. For flexible films of micrometer thickness, the SE of DLMM films is considerably increased by increasing the separation distance between the two mesh layers, without affecting of optical transmittance. This indicates an efficient approach in the search for high shielding effectiveness in flexible shielding. However, as the distance further increases from the micrometer to millimeter scale, the two-layer film becomes rigid, which imposes restrictions on the applications in flexible electronics. Thus, to maximize functionality, it is important to strike a balance between the shielding efficiency and film thickness, which is critical to the mechanical flexibility for current flexible device.

 figure: Fig. 6.

Fig. 6. (a) Optical transmittance of DLMM films with various separation distances of 100, 200, and 300 µm. (b) Simulation and (c) experiment results of EMI SE for DLMM films at various separation distances of 100, 200, and 300 µm. (d) Summary of SE at 8.2 GHz frequency for SLMM and DLMM films with different separation distances. Simulation of DLMM SE with increasing separation distance (e) up to 20000 µm and (f) magnified logarithmic graph up to 1000 µm.

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4. Conclusion

We developed an embedded DLMM based on randomly structured Ni meshes on both sides of a flexible substrate. The facile and low-cost double-sided imprint transfer method contributes to the full utilization of the flexible substrate by arranging the two embedded Ni meshes on both sides, such that the thickness of a DLMM film is similar to the substrate-supported SLMM film, and provides the DLMM with good mechanical stability. We systematically investigated the effect of the pattern structure, mesh space, and separation distance for the DLMM film to determine an efficient approach for achieving high SE with transparent shielding in an optical window field. The introduction of randomly patterned Ni meshes provides the DLMM films with uniform diffraction and eliminates the Moiré fringe generated by periodic DLMM, thus ensuring high imaging quality for optical applications. Furthermore, the designed DLMM films simultaneously achieve shielding and high optical transmittance that is superior to the SLMM films. Moreover, the SE of DLMM films is considerably enhanced by increasing the separation distance between the two mesh layers, without compromising the optical transmittance. Consequently, the as-fabricated DLMM film is characterized with excellent transmittance, flexibility, excellent optical imaging quality, and an extraordinary EMI SE, providing an effective method in transparent EMI shielding material for further optical applications.

Funding

National Natural Science Foundation of China (61974100); Natural Science Foundation of Jiangsu Province (BK20181166); National Science Foundation of the Jiangsu Higher Education Institutions of China (18KJB510040); Collaborative Innovation Center of Suzhou Nano Science and Technology; Priority Academic Program Development of Jiangsu Higher Education Institutions.

Disclosures

The authors declare no conflicts of interest.

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Figures (6)

Fig. 1.
Fig. 1. (a) Fabrication of Ni-mesh. (b) Fabrication of SLMM and DLMM film. (c) Diagram of DLMM film. (d) Side view of DLMM film depicting the shielding mechanism.
Fig. 2.
Fig. 2. Diffraction pattern analysis of SLMM and DLMM films with different pattern structure. (a) Different structures, (b) simulation of diffraction distribution, (c) the three-dimensional intensity profile of the simulated diffraction spots, and (d) the experimental test of the diffraction distribution for SLMM and DLMM with honeycomb and random arrangement.
Fig. 3.
Fig. 3. Moiré fringe image for DLMM films based on honeycomb-structured Ni-mesh with period of (a) 50 µm, (b) 100 µm, (c) 150 µm, and (d) 200 µm. (e) Magnified part of film with period of 200 µm. (f) Image of DLMM film based on random structured Ni-mesh with the magnified part insert.
Fig. 4.
Fig. 4. (a) Optical transmittance of SLMM and DLMM films with periods varying from 50 µm to 200 µm. (b) Enhanced optical transmittance of SLMM and DLMM films with PVA gel coating for periods of 50, 100, 150, and 200 µm.
Fig. 5.
Fig. 5. EMI SE of SLMM and DLMM films with randomly structured Ni meshes in X-band. (a) Simulation and (b) experiment results of SLMM films with periods of 50, 100, 150, and 200 µm. (c) Simulation and (d) experiment results of DLMM films with periods of 50, 100, 150, and 200 µm. (e) Comparison of simulated and experimental results for SLMM and DLMM films with different periods at the frequency of 8.2 GHz. (f) Summarized SE at the frequency of 8.2 GHz and enhanced optical transmittance at 550 nm wavelength for SLMM and DLMM films with periods varying from 50 µm to 200 µm.
Fig. 6.
Fig. 6. (a) Optical transmittance of DLMM films with various separation distances of 100, 200, and 300 µm. (b) Simulation and (c) experiment results of EMI SE for DLMM films at various separation distances of 100, 200, and 300 µm. (d) Summary of SE at 8.2 GHz frequency for SLMM and DLMM films with different separation distances. Simulation of DLMM SE with increasing separation distance (e) up to 20000 µm and (f) magnified logarithmic graph up to 1000 µm.

Equations (2)

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S E 1 = 20 lg [ 1 s ( 0.265 × 10 2 R f ) 2 + [ 0.265 × 10 2 X f + 0.333 × 10 2 f ( ln s a 1.5 ) ] 2 ]
S E 2 = S E 1 + 10 lg { 4 + 12 l s [ 0.38 × 10 6 f X f + 0.478 ( ln s a 1.5 ) ] + 9 ( l s ) 2 [ 0.38 × 10 6 f X f + 0.478 ( ln s a 1.5 ) ] 2 + ( 0.38 × 10 6 f R f ) 2 }
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