# Frequency Selective Surfaces: A Review
## 1 Introduction
Extensive research is going on to miniaturize the FSSs and improve the frequency response with broader bandwidth (BW) at higher incidence angles and dual polarization. However, single layered FSS structures have been proved inefficient due to unstable performance with the variation of EM wave incident angle. To overcome the limitations of conventional single layer FSSs, multilayered FSSs have been introduced, which offer additional flexibility of varying parameters for desired performance [12; 13; 14; 15; 16; 17]. At present, FSSs based on fractal elements and miniaturized arrays (2.5 dimensional) are employed for compactness [18; 19; 20]. Three-dimensional FSS structures and active FSSs have opened new doors in microwave technology [21; 22; 23; 24]. Additionally, embedded FSS (with inserted metallic rods and plates based on stepped-impedance resonator) [25], integrated FSS and Electromagnetic band gap structures (EBG) [26], and metamaterial FSSs [27; 28] are the most recent advances implemented by microwave researchers. In the past, dispersion properties of FSSs have been explored through approximate analytical techniques, for example, which involve equivalent circuit method to analyze the transmission line characteristics (By Quasi-static approximation). However, with the growth of more complex structures, state-of-the-art numerical methods have been introduced, which use periodic boundary conditions (PBC) allowing for the design analysis quite straightforward. Some of these include finite element method (FEM), method of moments (MoM), finite difference time domain method (FDTD), and the integral equation (boundary element) method (IEM/BEM) [29; 30; 31; 32; 33; 34; 35]. A well-known technique is IEM/BEM used in combination with the MoM [36; 37; 38; 39]. Various designs of FSSs and schemes to examine their EM characteristics are well presented in [2; 3]. Regardless of its importance, a detailed review of the various types FSS is undeniably in its infancy. Particularly, an adequate demonstration of recent advancements in innovative FSS structures that are linked with their frequency responses is required. In fact, a detailed overview of different varieties of FSS from the standpoint of structure design, applications, and types of array elements, is yet to emerge in the literature. Although a few review articles are available on FSSs or FSS based EM structures in broad frequency regimes [4; 22; 37; 40; 41; 42], however, in this article we specifically discuss the different kinds of FSSs operating at wavelengths in microwave range. Figure 1 depicts a comparison of presented review with already available survey articles on FSSs. A more detailed assessment of existing surveys in the literature is outlined in Table 1.  
As shown in Figure 1, the category 1 details theoretical reviews; for example, which discusses a number of techniques to analyze FSSs as filters in the microwaves and optical ranges, and circuit analytical review to underline the range validity of some model with their accuracies. In category 2, while there exist some survey articles that target architectures of particular types of FSS, more focus has been set in the literature toward the specific FSSs types (including metamaterials or metasurfaces FSSs), FSS based antennas, and other FSS based EM structures. On the other hand, researchers have less considered the survey on the different types of FSSs that have recently evolved based on structural design, applications, and nature of array element used and have taken this lack as for granted. Therefore, in this review paper, we provide an outlook of skyrocketing research field of FSSs by assessing the progress during the past years primarily focusing on categorizing the FSSs as mentioned above. The contributions of our effort in this review paper are as follows. 1. Through a careful study of the existing surveys on the FSSs, we identify the survey gap in the existing reports, as briefed in Table 1, which accentuates the requirement to report most up-to-date FSS types, especially in the microwave regime. 2.