# Deep Learning-Based FSS Spectral Characterization and Cross-Band Migration
## 2 FSS Structure Design and Spectral Characterization Analysis
Figure 3 compares the computational results of the same frequency-selective surface (FSS) using two meshing strategies, demonstrating close agreement between the two approaches. In Figure 3, the dashed line represents the spectral curve obtained with the default physics-controlled meshing, while the solid line corresponds to the user-defined meshing, achieving a 56.7% reduction in computational time. The maximum and mean absolute errors (MAE) for key performance metrics were quantified as follows: (1) transmittance: maximum error = 0.0445, MAE = 0.0193; (2) reflectance: maximum error = 0.2425, MAE = 0.0291; and (3) absorptance: maximum error = 0.1265, MAE = 0.0173. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Meshing** & **Domain** & **Boundary** & **Edge** & **Single** \\
**Approach** & **Elements** & **Elements** & **Elements** & **Computation Time** \\ \hline Physical field & & & & \\ meshing & & & & \\ Custom & & & & \\ meshing & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of meshing element counts. Figure 2: Comparison of the polarization of the “circular” encoded FSS. (**a**) TE; (**b**) TM. The elevated reflectance error at 1.86 THz was attributed to sharp fluctuations in transmittance near the FSS resonance frequency, where field gradients challenge mesh resolution. Despite this localized discrepancy, the low MAE for reflectance (0.0291) confirmed that the slight resonance frequency shift caused by the reduced mesh density negligibly impacted the overall spectral characteristics of the FSS. This validates the applicability of the user-defined meshing strategy for large-scale dataset generation while significantly accelerating simulations. Further optimization was achieved by replacing the default MUMPS solver with the PARDISO solver, explicitly designed for parallel computing. This adjustment reduced the per-simulation computation time to 2 min and 22 s, enhancing workflow efficiency for the 26,000-sample dataset. The FSS parameters were mainly categorized into two types: geometrical parameters and material parameters. Geometrical parameters include the period length \(D\) of the FSS, the thickness \(h\) of the substrate, and the thickness \(h_{0}\) of the metal film layer. Material parameters include the metal conductivity and the refractive index of the substrate. For the convenience of later discussion, all FSSs in this paper used the encoding as shown in Figure 1b, unless otherwise stated. Figure 4 demonstrates the spectral properties of different metals of the same FSS surface model. Figure 4a-d are gold, silver, brass, and aluminum, respectively, whose conductivities are shown in Table 2. It can be found that the spectral properties were almost identical. This phenomenon is determined by the interaction between light and metal. The calculation of the skin depth \(\delta\) is as follows:  
\[\delta=\frac{1}{\sqrt{\pi f\mu\sigma}} \tag{1}\]  
where \(\delta\) is skinning depth of the metal, \(f\) is the frequency of electromagnetic wave, \(\mu\) is magnetic permeability of the metal, for non-magnetic media take \(4\pi\times 10^{-7}\), and \(\sigma\) is conductivity of the metal. Table 2 gives the common types of metal conductivity, the simplified skinning depth formula, and its skinning depth at 1 THz. It can be seen that the skinning depth at 1 THz of each type of metal was less than 200 nm. When the thickness of the metal was 200 nm, the effect of different metal types on the spectral characteristics of the FSS was relatively small and could be ignored. Figure 3: Comparison of simulation results of different mesh profiles. Figure 5 shows the spectral characteristics of the FSS when the surface coating was changed to graphite. Due to the difference of two orders of magnitude between the electrical conductivity of graphite and that of the metal, the skinning depth reached 1600 nm at the incident electromagnetic wave frequency of 1 THz, which is much larger than that of the coating thickness of 200 nm, resulting in an obvious change in the spectral curve.