## 2 Unit Cell Design and Proposed FPC Antenna
However, intuitively, below the resistive ring the presence of a constant patch on top of a gradated mesh would have been more suitable, in that the variation of mesh aperture would have least affected the desiredabsorption frequency response. In fact, initial unit cell simulations were performed with that configuration; however, two problems arose:  
1. The achieved reflection phase gradient was meagre and seemed insufficient to achieve significant beam tilt. 2. The reflection phase values were not supportive of reduced cavity height. Henceforth, the configuration of the PRS was flipped below the AFSS (gradient mesh above constant patch), and interestingly, the unit cell simulations showed encouraging results for fulfilling all objectives, and are discussed next in detail. The high frequency structure simulator (HFSS) unit cell parametric simulations employing periodic boundaries and Floquet ports were performed to compute the finalized scattering (S) parameters. While optimizing the S-parameters, the following guidelines were followed [25; 28]:  
* For incoming wave absorption (port 1 to port 2), reflection (S\({}_{11}\)) magnitude as well as transmission (S\({}_{21}\)) magnitude had to be below \(-\)10 dB over a wide range of frequencies, to achieve at least 80% of incident wave absorption. * In the transmission mode (port 2 to port 1), reflection coefficient (S\({}_{22}\)) had to show high partial reflectivity as well as progressive phase over the gradated apertures, at operating frequency, to achieve high gain as well as off-broadside radiation. The plots in Figure 2 are of TE (transverse electric) wave polarization, and it is important to note that due to the symmetry of the unit cell structure, the plots for TM (transverse magnetic) wave polarization are expected to be similar as well, and hence have not been shown here. The co-/cross-polarized reflection and transmission plots for a wave incident towards \(-\)z-axis are shown in Figure 2a,b, respectively. Solid lines depict the co-polarized components, while the dashed lines represent the cross-coupled components. Different curves correspond to the varying aperture sizes (AP\({}_{\rm L}\): 2 mm to 10 mm). For the co-polarized S\({}_{11}\) and S\({}_{21}\) responses shown in Figure 2a,b, it can be seen that starting from 7 GHz (out-of-band) and extending well into high frequency region, more than 80% absorption (A) (A = \(1-1S_{11}\,|^{2}-1S_{21}\,|^{2}\)) is being achieved for all aperture sizes. This owes to the values of the incoming wave reflection and transmission, which are below \(-10\) dB over a wideband. S\({}_{11}\) and S\({}_{21}\) magnitudes around operating frequency (6 GHz) show partial absorption, which means a reasonable extent of RCS reduction should occur at in-band frequencies also. For the cross-coupled S\({}_{11}\) and S\({}_{21}\) responses shown in Figure 2a,b, it is evident that their magnitudes are significantly low, hence establishing the efficiency and purity of absorption. S\({}_{22}\) magnitude response is shown in Figure 2c for gradating aperture values. At operating frequency, the reflection magnitudes lie between 0.64-0.99 (linear). Figure 2d depicts the phase response of S\({}_{22}\). It shows that the reflection phase values range between 104\({}^{\circ}\) to \(-114^{\circ}\) over aperture variation of 2 mm to 10 mm, realizing a significant phase gradient at 6 GHz. Furthermore, the extents of phase range closely follow \(\pm 90^{\circ}\), a reflection phase range criteria of the PRS to reduce the cavity height to \(\lambda/4\)[40]. From Figure 2c,d, it  
Figure 2: Unit cell scattering parameters for \(\pm\)z-axis incident wave (TE polarization). (**a**) S\({}_{11}\) magnitude response. (**b**) S\({}_{21}\) magnitude response. (**c**) S\({}_{22}\) magnitude (linear) response. (**d**) S\({}_{22}\) phase response. (Note: The dashed traces shown in (**a**,**b**) represent cross-coupled/polarized reflection and transmission components).