## 3 Results and Discussions
### Angular Stability Analysis  
Angular stability is a phenomenon in which the EM behavior of an FSS surface is rigorously investigated over different oblique incident angles and polarization states. Since the design is four-fold symmetric, perpendicular, and parallel polarizations of the incident plane waves, results in a similar response. Furthermore, angular stability also depends on the unit cell periodicity '\(P\)' in an FSS array, and to prevent grating lobes, the following relation must be satisfied:  
\[P<\frac{\lambda_{o}}{1+sin\theta}, \tag{2}\]  
where \(\lambda_{o}\) represents the free-space wavelength, and (\(\theta\)) is the incident angle. Therefore, the value of '\(P\)' in Equation (2) should be minimal to minimize the angle sensitivity. In this study, for the incident angle (\(\theta=75^{\circ}\)), '\(P\)' should be smaller than 13.2 mm. Theoretically, with the increase in incidence angle, the value of '\(P\)' is reduced, and the array becomes densely packed, and vice versa. In addition, the relative deviation in frequency response due to angle variations can be calculated using Equation (3). \[\triangle f=\frac{f_{Z}-f_{oblique}}{f_{Z}}, \tag{3}\]  
where \(\Delta\)f, \(f_{z}\), and \(f_{oblique}\) represent the relative deviation, the transmission zero frequency, and the oblique angle frequency, respectively. Figure 4a specifies the SE of the unit cell at a normal incidence for the TE and TM polarized waves. It is noticed that the FSS exhibits an identical response for TE and TM wave modes. Thus, the unit cell accomplishes SEs of at least 48 dB and 45 dB at the 7.9 GHz and 11.9 GHz frequencies in the X- and Ku-bands. Moreover, the FSS offers a 10 dB bandwidth of more than 2.60 GHz and 2.70 GHz at its operating bands. In addition, Figure 4b,c illustrates the effective shielding characteristics of the FSS as a function of oblique angle under TE and TM polarization up to \(75^{\circ}\). The results reveal that the angle variations do not affect the unit cell EM performance. The FSS ensures highly selective and angularly stable spectral responses at its operating bands for the TE and TM polarized waves. However, after \(60^{\circ}\), the rejection bandwidth varies within the acceptable limits as the incident angle increases to \(75^{\circ}\). Further, it is observed that the notch selectivity also improves over angle variations. The bandwidth and fractional bandwidth can be calculated as follows:  
\[BW\ (\mathrm{GHz})=f_{H}-f_{L}, \tag{4}\]  
\[FBW(\%)=\frac{BW}{f_{C}}\times 100, \tag{5}\]  
In Equations (4) and (5), \(f_{H}\), \(f_{L}\), and \(f_{C}\) represent the higher, lower, and center frequencies, respectively. Based on Equations (4) and (5), the 10 dB fractional bandwidth of the FSS as a function of angle variations for the TE and TM modes is summarized in Table 2. Furthermore, Figure 4d,e reveals the SE curves of the FSS at various polarization angles at a normal incidence. As the FSS structure is four-fold symmetric, thus it manifests identicalresponses for the TE and TM polarization states up to 90\({}^{\circ}\). Thus, the FSS unit cell exhibits highly selective, angularly insensitive, and similar responses.