# Deep Learning-Based FSS Spectral Characterization and Cross-Band Migration
## 2 FSS Structure Design and Spectral Characterization Analysis
Figure 6 shows that spectral properties of different thicknesses of the same substrate with the same FSS model. The thickness of the substrate in Figure 6a is \(h_{0}=5\) um, and the thickness of the substrate in Figure 6b is \(h_{0}=8\) um. The metal type of both models was Au and the type of substrate was high-resistance silicon. They are compared with Figure 2a. The high transmissivity resonance points of the different substrate thicknesses are shown in Table 3. The trend is that as the substrate thickness increases, the resonant frequency of FSS shifts towards lower frequencies and the overall trend is similar, but the transmittance decreases overall. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Conductivity \(\alpha\)/(10\({}^{7}\)S/m)** & **Skin Depth \(\delta\)/m** &
\begin{tabular}{c} **Skin Depth \(\delta\)/nm** \\ **(f = 1 THz)** \\ \end{tabular} \\ \hline Gold & 4.1 & \(0.078/\sqrt{f}\) & 78 \\ Silver & 6.17 & \(0.064/\sqrt{f}\) & 64 \\ Aluminum & 3.72 & \(0.083/\sqrt{f}\) & 83 \\ Brass & 1.6 & \(0.13/\sqrt{f}\) & 130 \\ Graphite & 0.01 & \(1.6/\sqrt{f}\) & 1600 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Conductivity and its skinning depth for various common metals. Figure 4: Spectral curves of different metal coatings for the same FSS model. (**a**) Gold, (**b**) silver, (**c**) brass, and (**d**) aluminum. The resonant frequency of the FSS shifted when a substrate of infinite thickness was loaded unilaterally, which is given as follows:  
\[f_{0}^{\prime}=\frac{f_{0}}{e_{eff}}=\frac{f_{0}}{\sqrt{\frac{(e_{r}+1)}{2}}} \tag{2}\]  
In the above analysis, either the increase in the relative permittivity of the substrate or the increase in the thickness of the substrate was equivalent to the increase in the equivalent permittivity \(e_{eff}\), which led to the shift of the resonant frequency of the FSS to the lower frequency. The simulation results are in good agreement with the theoretical results. As a subwavelength structure, the period length of FSS should be comparable to the wavelength corresponding to the highest frequency of the incident electromagnetic wave. When the wavelength was much smaller than the period length, the incident electromagnetic wave exhibited a geometrical optics-like property. When the wavelength  
Figure 5: Spectral profile of graphite coating with the same FSS model. Figure 6: Spectral curves of different thicknesses of the same substrate with the same FSS model. (a) \(h_{0}\) = 5 \(\upmu\)m (b) \(h_{0}\) = 8 \(\upmu\)m. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Substrate Thickness**} & **Resonance** & \multirow{2}{*}{**Transmissivity**} \\  & **Frequency/THz** & \\ \hline
3 \(\upmu\)m & 2.28 & 0.88 \\
5 \(\upmu\)m & 1.92 & 0.84 \\
8 \(\upmu\)m & 1.64 & 0.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of resonance points with different substrate thicknesses for the same FSS model. was longer than the period length, it could not control electromagnetic waves due to the drastic changes in its transmittance spectrum. Figure 6 shows the comparison results of the spectral properties of the FSS for the same FSS model by expanding its period length by a factor of 100 accordingly when the maximum frequency of the incident electromagnetic wave was reduced by a factor of 100. That is, when the corresponding wavelength was kept equal to it, the comparison results of the frequency spectrum characteristics of FSS. The comparison of the parameters of the cross-band FSS model is shown in Table 4 below. Comparing Figure 7a with Figure 7c, it can be found that the spectral curves of the two are very different due to the differences in the substrate thickness and relative dielectric constant. However, if the effect of substrate was excluded and the substrate thickness of both FSS models was set to 0, the spectral curves of the two would trend as-shown in Figure 7b with Figure 7d, respectively.