# Frequency Selective Surfaces: A Review
## 2 Periodic Structures  
When identical elements are arranged in an infinite array of one or two-dimensions, a periodic surface is formed [2]. Two basic means to excite a periodic array are known: one is through an incident plane wave (a passive array type) or by the attached generators to individual element (an active array type). In the former type, the incoming plane wave (E\({}_{i}\)) will partially be transmitted (E\({}_{t}\)) in the forward direction and in part reflects (E\({}_{r}\)) specularly. In the condition of resonance and without grating lobes, the amplitude of the reflected wave E\({}_{r}\) may be equal to incident wave E\({}_{i}\), while the transmitted signal E\({}_{t}\) is equal to zero. The specular reflection coefficient (\(\Gamma\)) can be defined by (1). \[\Gamma=\
icefrac{{E_{r}}}{{E_{i}}} \tag{1}\]  
Similarly, the transmission coefficient (\(\Gamma\)) can be defined by (2). \[\Gamma=\
icefrac{{E_{t}}}{{E_{i}}} \tag{2}\]  
In the active array type, the voltage generators must possess the same amplitude and also a linear variation of the phase across whole active array elements so that it may be regarded as a periodic \begin{table}
\begin{tabular}{l l} \hline \hline
**Focused Topics** & **Description** \\ \hline Theoretical Analysis & \(\bullet\) & FSS circuit modeling; fully analytical and semi-analytical formulation is elaborated to confirm the range of validity for various models and their accuracies [4]. \\  & \(\bullet\) & Theoretically analysis of FSS as a filter at microwave and optical regime by different techniques is reviewed. Key properties of FSS and various approaches for the prediction of frequency response are presented [37]. \\  & \(\bullet\) & Most common FSS elements are reviewed and simplified model to analyze complex FSS systems is focused. Lumped equivalent models of most common FSS are presented at normal/oblique incidences, and for fixed/varying periodicities [40]. \\ \hline Evolution of FSS & \(\bullet\) & Evolution of FSSs is outlined, briefing a few of its forms and applications [43]. \\ \hline FSS based EM structures & \(\bullet\) & FSS based advanced EM structures have been reviewed with the description of few FSS geometries used in FSS based radomes, absorbers, antennas textile, active high impedance surfaces and fractal based 2D EM band gap structures [41]. \\ \hline Individual type of FSSs & \(\bullet\) & Frequency selective metasurfaces are reviewed in which electric polarisability is used to show the resonant, multiband and high order response with miniaturized surfaces [1]. \\  & \(\bullet\) & Recent developments in the field of FSS integrated patch antennas are surveyed [44]. \\  & \(\bullet\) & All-dielectric metamaterial FSSs with existing fabrication techniques are thoroughly described [42]. \\  & \(\bullet\) & Emerging class of three-dimensional FSS is outlined while highlighting their unique features [22]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of focused topics of frequency selective surfaces (FSSs) covered by existing surveys. surface [2]. Dipole and slot arrays with a similar shape of elements constitute complementary arrays so that when both of these arrays are positioned on top of one another (cascaded), a perfect conducting plane is created. The transmission coefficient of one array is equal to the specular reflection coefficient of its complementary array and is simply termed as Babinet's principle. In order to obtain a stable resonance with variation in the angle of incidence for a periodic surface, the inter-element spacing must be kept very small (!0.4\(\lambda\)) [2]. High impedance surfaces (HISs) [45] are electrically smart, two-dimensional arrays that are designed to totally reflect an in phase incoming plane wave and reject bounded surface waves. They can be employed to suppress propagation of surface modes. EBG possess such characteristics and similar type of structures, named photonic band gap structures (PBG), explain an impulsive and forbidden emission.