## 3 Results and Discussion
What is different in this study is that the shielding performance of the mesh coating is balanced over a wide frequency range. For mesh coatings, the underlying cause of the frequency-dependent property of EMI shielding can be explained by analyzing the transmission (\(T\)) of electromagnetic waves, which can be expressed as follows in the case of normal incidence in free space [24]:  
\[T=\frac{4y^{2}}{1+4y^{2}} \tag{3}\]  
Figure 4: EMI shielding performance. (**a**) Schematic illustration of EMI SE measuring method based on waveguides. (**b**) The actual EMI SE measurement setup. (**c**) Measured EMI SE of transparent electromagnetic shielding window over wide frequency range of 1.7–18 GHz. where \(y\) is the normalized admittance of the individual mesh film without a substrate. When the linewidth (\(w\)) of the mesh is larger than its thickness and much smaller than the period (\(p\)), the normalized admittance can be expressed as [24; 43]:  
\[y=-\frac{p}{l}\bigg{[}\ln(\sin\frac{\pi w}{2p})\bigg{]} \tag{4}\]  
where \(\lambda\) is the wavelength of the incident electromagnetic wave. According to Equation (4), as the frequency gets higher and the wavelength gets smaller, the normalized admittance of the conductive mesh decreases. Therefore, the metal mesh exhibits a decrease in shielding efficiency at higher frequencies. In addition to the influence of the aperture structure on the transmission coefficient of the mesh, the variation of the sheet resistance of the mesh with frequency is also an important reason for the frequency dependence of its shielding effectiveness. The frequency dependence of sheet resistance for mesh coatings can be described as follows [30]:  
\[R_{mesh}=\frac{1}{\sigma\delta(1-e^{-t/\delta})}\frac{p}{w} \tag{5}\]  
Here \(\delta\) is the skin depth, \(\sigma\) is the conductivity of the metal, \(t\), \(p\), and \(w\) are the thickness, period, and linewidth of the mesh, respectively. As the frequency gets higher, the sheet resistance of the mesh film increases. According to the measured result, the average EMI SE of L- to Ku-band are 25.5 dB, 23.1 dB, 23.6 dB, 24.4 dB, and 20.9 dB, respectively. It can be seen that EMI SE is only weakly dependent on frequency, demonstrating that the thin metal film is beneficial to alleviate the dependence of EMI SE on frequency. Additionally, the irregular mesh pattern design also contributes to the stable shielding property, which has been experimentally verified by [PERSON] et al. [23]. The thin meal mesh with irregular patterns in this study not only ensures effective EMI shielding performance, but also reduces the frequency dependence of the shielding effectiveness, which is beneficial to obtain a balanced shielding effectiveness in a wide frequency band. The advantage of adopting the thin mesh is that a more stable shielding performance can be achieved over a wide frequency band. In addition, the design of the thin mesh facilitates costly and time-consuming mesh fabricating process, making it possible to achieve the desired shielding performance in an efficient manner. Figure 3a-f present the EMI shielding performance of metal meshes with different thicknesses in six measured frequency bands. One can see that the thickness variation has different effects on the shielding effectiveness in different frequency bands. A close inspection of the figures shows that the effect of thickness variation on shielding effectiveness is more evident at lower frequencies. In the frequency range of 1.7-2.6 GHz, the average EMI SE values of samples with thickness of 320 nm and 230 nm are 26.1 dB and 22.7 dB, respectively (Figure 5a). According to Figure 5f, however, the average EMI SE values of the two samples are 20.9 dB and 20.0 dB, showing that the effect of thickness variation on shielding effectiveness gradually weakens as the frequency increases.