# Deep Learning-Based FSS Spectral Characterization and Cross-Band Migration
## 2 FSS Structure Design and Spectral Characterization Analysis  
The FSS simulation structure is shown in Figure 1. Figure 1a shows the three-dimensional simulation schematic of the FSS with the following features: the substrate was of high-resistance silicon, in the terahertz band its refractive index was \(n=3.42\), the absorption can be ignored [28], and the thickness h of the substrate was 5 \(\upmu\)m. The external medium was air and the absorption can be ignored [28]. The surface of the dielectric substrate was covered with a thin layer of gold, and its conductivity was \(S=4.1\times 10^{7}[\text{S}/\text{m}]\), and its thickness was \(h_{0}=0.2\)\(\upmu\)m. The cycle length of the FSS was \(D=80\)\(\upmu\)m.  
The corresponding coding unit structure is shown in Figure 1b. The period unit is discretized into small squares with a side lengths of \(l=5\)\(\upmu\)m, in which the number \"1\" denotes the thin gold layer and the number \"0\" denotes the substrate. Therefore, the FSS was composed of 16 by 16 \"0/1\" matrices with one-to-one correspondence. Considering the polarization stability of FSSs, all FSSs were set as rotationally symmetric structures. Figure 1b demonstrates the four symmetry axes of the FSS, which reduced the degrees of freedom of the FSSs from \(2^{16\times 16}\) to \(2^{36}\). It reduced the difficulty of FSS optimization design greatly. Following the completion of the FSS symmetric structure model, the simulation was conducted utilizing COMSOL. The boundary condition was designated as the Floquet periodic condition, with a simulation frequency range of 0.5-3 THz and a step size of 0.02 THz, consequently yielding a total of 126 frequency points. The electromagnetic properties of the FSS were characterized in this study by means of the total transmittance, total reflectance, and total absorptance, in order to investigate its transmission and reflection characteristics. The spectra of the \"ring-shaped\" encoded FSS under TE and TM conditions are shown in Figure 2a,b, respectively. It can be observed that the two spectra are nearly identical. A similar conclusion can be drawn from the calculation results of other randomly encoded FSSs that satisfy rotational symmetry, thereby verifying the polarization stability of the rotationally symmetric structure. Figure 1: Schematic diagram of the FSS simulation structure. (**a**) 3D simulation structure and (**b**) FSS topological code. The dataset serves as the cornerstone of deep learning, where both the quantity and quality of data directly influence the training efficacy of neural networks. The dataset in this study comprised two components: the binary \"0/1\" matrices corresponding to the Frequency Selective Surface (FSS) configurations and their associated spectral responses. To optimize data generation efficiency, 26,000 unique pairwise-distinct \"0/1\" matrices were randomly generated. An automated workflow was implemented using MATLAB (Version R2021b) to control COMSOL (Version 6.0) Multiphysics, sequentially constructing FSS models for each matrix, performing electromagnetic simulations, and exporting the computed spectral responses to MATLAB for post-processing and archival storage. Due to the large amount of data required, and in order to save computation time, \"transition boundary conditions\" were used instead of thin metal layers to avoid mesh partitioning. Additionally, mesh partitioning settings were optimized to minimize the number of elements and accelerate the computation speed. Table 1 provides a comparative analysis of two meshing strategies in terms of element count and computational time. The physics-controlled meshing, an automated COMSOL algorithm that determines element size based on the highest frequency in the operational band, delivered higher numerical accuracy. In contrast, the user-defined meshing allowed researchers to manually specify element dimensions tailored to specific simulation requirements.