## 2 Fundamentals of Frequency-Selective Surfaces
### Methods for Evaluating the Performance of Frequency-Selective Surfaces (FSSs)  
Evaluating the performance of Frequency-Selective Surfaces (FSSs) requires a comprehensive analysis of their electromagnetic behavior, particularly in terms of frequency response, angular stability, and polarization sensitivity. These evaluations are typically conducted through a combination of numerical simulations and experimental measurements. The following methods are commonly employed to assess the performance of FSS structures:  
Numerical Simulation Techniques. One of the most widely used methods for evaluating the performance of FSSs is through numerical simulation, with full-wave electromagnetic solvers playing a critical role. These simulations are typically based on Maxwell's equations and employ techniques such as the Finite Element Method (FEM), the Finite Difference Time Domain (FDTD) method, or the Method of Moments (MoM). Each of these approaches provides a means of modeling the electromagnetic response of FSSs to incident waves across a wide range of frequencies. FEM, for example, divides the structure into small elements to solve complex field distributions, making it highly effective for analyzing intricate FSS geometries. FDTD, on the other hand, provides time-domain solutions, allow  
Figure 2: Basic FSS cell designs [9]: (**a**) cross cell; (**b**) patch cell; (**c**) loop/ring cell; and (**d**) meandered cell. ing for the analysis of transient behavior and broadband responses. These simulation tools enable researchers to predict key performance metrics such as transmission and reflection coefficients (S-parameters), resonant frequencies, and bandwidth, under various conditions, including changes in angle of incidence and polarization. Measurement of S-Parameters. To experimentally validate the performance of FSSs, measurements of scattering parameters (S-parameters) are conducted, typically in an anechoic chamber or a waveguide environment. The S-parameters, specifically S\({}_{11}\) (reflection) and S\({}_{21}\) (transmission), provide a direct measure of the FSS's filtering characteristics by quantifying how much power is reflected or transmitted at different frequencies. The FSS is illuminated with a plane wave, and the reflected and transmitted waves are recorded to obtain the frequency response. The key evaluation criterion is the resonant frequency at which maximum transmission or reflection occurs, as well as the bandwidth over which the FSS exhibits selective filtering. These measurements are critical for confirming the theoretical predictions made during the design phase and for ensuring that the FSS meets the specific frequency filtering requirements for its intended application. Angular and Polarization Sensitivity. Another important aspect of FSS performance evaluation is the analysis of angular and polarization sensitivity. Since the performance of an FSS can vary with the angle of incidence of the incoming electromagnetic waves, it is essential to evaluate how stable the transmission and reflection characteristics remain over a range of incident angles. Typically, this is done by simulating or experimentally measuring the response of the FSS at different angles, from normal incidence (0 degrees) to oblique angles, and plotting the variation in S-parameters as a function of the incident angle. Angular stability is especially important in applications where the orientation of incoming signals cannot be controlled, such as in satellite communications or radar systems. Similarly, the sensitivity of the FSS to the polarization of incident waves--whether the waves are linearly or circularly polarized--must be assessed to ensure consistent performance under different polarization conditions. Equivalent Circuit Models. In addition to full-wave simulations, equivalent circuit models are often used as a simplified method for understanding the behavior of an FSS.