## 2 Fundamentals of Frequency-Selective Surfaces
### Telecommunication Services Frequencies: Basic Design Constraints  
Table 1 provides a summary of the most-used telecommunication services and their typical frequency allocations below 6 GHz. While the table is not intended to be exhaustive, it serves as a helpful reference for understanding the various design objectives of the unit cells discussed in the following sections. Upon observing the frequency allocations of various telecommunication services (as seen in Table 1), one can appreciate the complexity of FSS design. The design goal may involve blocking certain services while allowing others to remain fully operational. For example, one might aim to block WiFi signals to prevent interference from neighboring networks, while maintaining cellular phone coverage to ensure uninterrupted smartphone connectivity. Such design objectives lead to the development of FSSs that exhibit alternating regions of high transparency (low attenuation) in some frequency bands and deep attenuation in others. This is particularly relevant, given that many telecommunication services operate in close proximity to one another within the spectrum, necessitating the design of multi-band FSSs. While early FSS designs provided spatial filtering at only a single frequency, numerous techniques have been developed to extend the FSS functionality to multiple frequency bands. These techniques include combined element methods [19; 20], fractal elements [21; 22], multi-layer cascaded structures [23; 24; 25; 26], lumped elements [27; 28], or a combination of several approaches [29; 30]. Once the unit cell design has been simulated, and, potentially, a finite sample measured, various manufacturing techniques can be employed to produce components for building \begin{table}
\begin{tabular}{c c} \hline \hline
**Frequency Band** & **System** \\ \hline
100 MHz & FM radio broadcasting \\
400–700 MHz & TV broadcasting \\
700 MHz & 5G \\
800 MHz & 4G \\
900 MHz & 2G and 3G \\
1800 MHz & 2G and 4G \\
2100 MHz & 3G and 4G \\
2.4 GHz & WiFi \\
2.6 GHz & 4G and 5G \\
3.5 GHz & 5G \\
5 GHz & WiFi \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Telecommunication services and their frequency band allocations. Figure 4: Samples of actual FSS designs. envelopes or internal partitions. A comprehensive review of these techniques can be found in [31]. While initial simulations and tests are typically conducted with radio waves incident at normal angles (perpendicular to the FSS), real-world conditions are far more complex. In practice, radio waves strike the FSS at various angles. Therefore, it is crucial to assess the stability of the FSS's performance across different angles of incidence. It is common to observe a shift in the frequency peak of each attenuated band as the incidence angle moves from normal to oblique. This tuning frequency can deviate from the nominal frequency obtained at normal incidence. Such behavior can be evaluated through a series of simulations or measurements of the FSS prototype under varying angles of incidence. An FSS design is considered stable when it shows minimal frequency variation, even at large incidence angles (e.g., 70\({}^{\circ}\) or 80\({}^{\circ}\), where 0\({}^{\circ}\) represents normal incidence) [32]. The more stable the FSS, the more useful it would be in practical applications, as radio signals can impinge the surface from any angle. Additionally, the more symmetrical the unit cell design, the more stable the FSS will be in response to changes in polarization. This stability is essential in real-world scenarios, where the polarization of incoming radio waves may be unpredictable. Although FSS designs are typically simulated as infinite arrays, in practice, they consist of a finite number of unit cells. This truncation can affect the FSS's performance, which is closely related to the electric dimensions of the surfaces (i.e., their sizes, measured in wavelengths). For example, according to [32], for a square loop aperture to resonate, its perimeter should be approximately one wavelength.