## 3 Parametric Simulations  
The performances of the proposed FSS filters were simulated and optimized with the CST Microwave Studio(r) (MWS) using the FSS unit cell (frequency domain) solver. By utilizing the CST's Floquet-mode ports, the FSS structures were simulated as an infinite array of the unit cell of square and circular loops in CST MWS. The boundary conditions were set as unit cell boundary conditions and the meshing was set as tetrahedral spatial meshing. The frequency response of the FSS is determined by the structure shape and its dimension parameters. The key dimension parameters that largely affect the performance of the FSS filters are the loop length \"\(d\)\" (loop side length for the square-loop and outer diameter for the circular-loop), the loop width \"\(w\),\" the unit cell period \"\(p\)\" and the gap between the loops \"\(g\)\" as shown in Figure 2a,b. For the parameters of square and circular loops, the subscripts \"\(s\)\" and \"\(c\)\" represent the square and circular structures, respectively, as shown in Figure 2.  
A typical frequency response of the loop-type FSS including the effects of the oblique angle incidence of a plane wave is shown in Figure 3. The main and accompanying effects of the aforementioned parameters (\(d\), \(w\), \(p\), \(g\)) are also summarized. By adjusting these design parameters, the following FSS properties can be selected: resonant frequency, quality factor (Q-factor) and the frequency where grating lobes occur. Figure 1: Single-layer double-sided FSSs: (**a**) Layout of a square-loop structure, (**b**) Layout of a circular-loop structure; (**c**) Equivalent circuit model. As for a design example, the FSS parameters are optimized for square-loop and circular-loop FSS structures to have the resonant frequency of 105 GHz as shown in Figure 4a. The design parameters selected for square-loop and circular-loop FSSs are \(d_{s}\) = 23, \(d_{c}\) = 26.9, \(w_{s}\) = 4, \(w_{c}\) = 4, \(p_{s}\) = 60, \(p_{c}\) = 60, \(g_{s}\) = 37, \(g_{c}\) = 33.1 (units: mil). It can be seen that both square- and circular-loop structures possess very similar frequency responses at the normal incidence of a plane wave for both TE and TM excitations. However, in the case of the oblique angular incidence, a slightly downward shift in the resonant frequency is observed for the TM excitation with no occurrence of grating lobes as compared with the TE excitation within the incidence angle of 20 degrees up to the frequency range of 125 GHz. Within 20 degrees of angular incidence, the shifts in the resonant frequency of the square-loop FSS were 0.1 GHz and 0.72 GHz for TE and TM polarizations, respectively. However, the shifts in the resonant frequency of the circular-loop FSS were 0.09 GHz and 0.88 GHz for TE and TM polarizations, respectively, as shown in Figure 4b,c. The effects of the design parameters on the frequency responses of the square- and circular-loop FSSs are described as the following. Figure 3: Typical characteristics of an FSS filter with effects of design parameters. Figure 2: Dimension parameters: (**a**) Square-loop structure, (**b**) Circular-loop structure. In the design, firstly, the loop width \"\(w\)\" should be chosen, since \(w\) strongly affects both the resonant frequency and the Q-factor of the FSS filter as shown in Figure 5. Figure 5a shows the variation of resonant frequencies as changing \(w\) with fixing \(d\), \(p\) and \(g\) parameters. When \(w\) is increased, the inductance of the loop becomes smaller and thereby the resonant frequency is significantly increased with some improvement of rejection level. The Q-factor of the FSS filter, however, is decreased with the increase of \(w\) as shown in Figure 5b, which shows the FSS frequency responses by changing \(w\) and adjusting \(d\) with fixing \(p\) and \(g\) parameters to have the resonant frequency of 105 GHz. As can be seen, the higher Q-factor from the FSS filter can be obtained with a smaller value of \(w\), which can be often limited by the fabrication tolerance.