# Deep Learning-Based FSS Spectral Characterization and Cross-Band Migration
## 1 Introduction  
The frequency range of a terahertz wave is 0.1-10 THz between infrared and microwave, with its low energy, strong penetration, spectral information, and other characteristics. It has a wide range of applications in 6G communication [1], food safety [2, 3], and biomedicine [4, 5, 6]. Frequency Selective Surfaces (FSSs), a two-dimensional planar structure of metamaterials, can regulate terahertz amplitude, phase, polarization, and other covariates flexibly and diversely, which provides a brand new platform for the design of miniaturized, high-performance terahertz micro- and nano-optical devices [7, 8, 9]. The design of FSSs is faced with difficulties including numerous unit structures, parameter complexity, and time-consuming optimization. A simple, efficient, and unified method to complete the design of various FSSs is urgently needed. It is very important for FSSs to move from simulation to engineering. To address the challenge exposed by the diversity of unit cell structures, researchers have adopted a discretization approach for the periodic structural elements of Frequency Selective Surfaces (FSSs). By integrating full-wave simulation methods with optimization algorithms such as genetic algorithms (GAs) and particle swarm optimization (PSO), intelligent FSS design has been achieved [10; 11; 12; 13], effectively eliminating reliance on empirical expertise. However, this methodology exhibits a notable drawback: the iterative optimization process necessitates repeated calculations of FSS spectral characteristics, resulting in substantial computational time and resource consumption. With the rapid advancement of artificial intelligence, researchers have begun to explore the use of neural networks as alternatives to traditional analytical methods, numerical techniques, and full-wave simulation software [14; 15; 16; 17; 18; 19]. Leveraging the framework and principles of deep learning, once the neural network is trained, the spectral characteristics of Frequency Selective Surfaces (FSSs) can be directly obtained by inputting parameters such as discrete encodings of the FSS structure [20]. This approach has demonstrated an efficiency improvement of several orders of magnitude in the simulation process compared to conventional methods. In recent years, scholars both domestically and internationally have paid significant attention to research in this area [21; 22; 23]. In 2019, [PERSON] and colleagues from the Chinese Air Force Engineering Research Institute employed deep learning techniques to accurately predict discrete coding metasurface structures and design a tri-band absorber [24]. Their study utilized a training set comprising 70,000 data samples and a validation set of 10,000 data samples. Similarly, [PERSON] and collaborators from the Harbin Institute of Technology implemented a multifunctional transmit array metasurface design capable of frequency reuse and polarization reuse by integrating neural networks with genetic algorithms. Their approach involved a training set of 36,000 data samples and a validation set of 4000 data samples [25]. Deep learning-based FSS design methods, while significantly enhancing efficiency during the design phase, still require substantial time and resources for data collection. Consequently, scholars have begun exploring transfer learning to reduce data requirements and improve data utilization efficiency [26; 27]. [PERSON] [17] realized the transfer learning of FPN from rectangular meta-atoms to elliptical meta-atoms, which was used to predict real part spectra and imaginary part spectra in the range of 100-300 THz. Compared with the training process of the two neural networks, the former without transfer learning had a data size of 27,000, and the latter with transfer learning had a data size of 4500, and the training time was reduced from 4 h to 20 min, and the test error was reduced from 0.00076 to 0.00067. [PERSON] et al.