# Two-Dimensional Scanning of Circularly Polarized Beams via Array-Fed Fabry-Perot Cavity Antennas
## 3 FPCA: Element Patterns and Far-Field Polarization  
At this stage, one can evaluate the far-field components \(E_{\theta}\) and \(E_{\phi}\) over different directions and, thus, obtain the corresponding \(E_{\text{RHCP}}\) and \(E_{\text{LHCP}}\) quantities through (2). The desired co-polar, far-field pattern of the \(E_{\text{RHCP}}\) component is reported in Figure 3a-e for different frequencies in the overall 27-28.5 GHz range. As expected, in Figure 3a, a broadside pencil beam is observed at 27 GHz. The \(-3\) dB gain and 3 dB AR isolines are reported with a dashed black line and solid magenta line, respectively. It is manifest that the design process effectively led to a CP narrow beam at broadside for 27 GHz. As expected, as the frequency increases, the pencil beam turns into a conical beam, preserving its CP features. As shown in Figure 3b, at 27.3 GHz, an almost azimuthally symmetric beam pointing at \(\theta=12^{\circ}\) is obtained with a half-power beamwidth (HPBW) well within the 3 dB AR range, thus demonstrating that the CP condition is maintained over the main beam. At higher frequencies, namely up to 28.2 GHz, one may observe from Figure 3c,d that a CP beam is maintained at elevation angle as large as \(\theta=32^{\circ}\). However, in this latter operating condition, the azimuthal symmetry of the beam is affected and the CP condition compromised around \(\phi=-50^{\circ}\) and \(\phi=130^{\circ}\). Such behavior is more evident at even larger frequencies (see results for 28.5 GHz in Figure 3e), where the CP condition is compromised over larger azimuthal ranges, with the radiation maximum occurring for \(\theta=37^{\circ}\). An additional increase in frequency, although not shown, further enlarges the regions outside the CP regime, thus worsening the antenna radiation performance. Finally, in Figure 3f, the importance of choosing the unit-cell design parameters in a _cavity_ environment is stressed. The colormap shows the AR considering the PCM in a _free-standing_ environment, after the reciprocity-driven optimization process. As is manifest, the AR levels are completely outside those limits that enclose the CP region, thus suggesting that the ground plane presence strongly modifies the PCM behavior. The _in-cavity_ optimization procedure, while being uncommon for FPCA modeling, constitutes a simple and precise technique to account for multiple reflections, which otherwise would provide a detrimental effect on preserving satisfactory AR values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(l_{c}\) (mm) & \(l_{u}\) (mm) & \(l_{e}\) (mm) & \(l_{b}\) (mm) & \(h_{s}\) (mm) \\ \hline
3.33 & 3 & 1.33 & 2.53 & 0.46 \\ \hline \(h_{d}\) (\(\mu\)m) & \(d_{v}\) (mm) & \(d_{o}\) (mm) & \(s_{y}\) (mm) & \(s_{x}\) (mm) \\ \hline
5 & 0.42 & 0.63 & 0.18 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Unit -cell design parameters. Figure 2: A comparison of the phases of the PCM reflection coefficient is presented. The blue dashed line represents the optimized configuration, while the red solid and black dotted lines correspond to sub-optimal cases, reflecting variations in the dimensions of the transmitting patch, the via holes, and their mutual distance. Considered patterns of the co-polar right-hand component are also reported as 3-D radiation patterns in Figure 4a-e, where the elevation scan is evident as we depart from the broadside condition at 27 GHz in Figure 4a and approach an elevation angle of almost \(\theta=40^{\circ}\), Figure 4e. For comparison, at corresponding frequencies, the cross-polar \(E_{\text{LHCP}}\) component (normalized to the co-polar radiation maximum) is shown in Figure 5a-e to be \(-20\) dB under the \(E_{\text{RHCP}}\) component.