## 5 Comparison between Infinite and Finite Approaches  
The results reported in this paper have been computed at the aperture level with an infinite array approach. As far as the aperture full-wave analysis in a periodic environment is concerned, the critical aspects are related to the high number of required modes in the Floquet ports to allow for proper field absorption at high scan angles and to the significant performance variation (mainly ARC) observed in Section 4. The latter is the relevant characteristic that requires validation. We know that experimental verification is the final goal for fully independent verification, however, it would require the design and manufacturing of polarizers [26], launchers and, in general, matching sections. Such components will  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Radiating Element**} & \multirow{2}{*}{**Lattice**} & \multirow{2}{*}{**BW (\%)**} & \multicolumn{2}{c}{**Scan Angle, \(\theta\)**} & \multirow{2}{*}{\(\mathbf{S}_{11}\)**} & \multirow{2}{*}{\(\mathbf{S}_{21}\)**} & \multirow{2}{*}{**Scan (dB)**} & \multirow{2}{*}{**XPD**} \\  & & & & (\({}^{\circ}\)) & & & **Loss (dB)** \\ \hline \multirow{4}{*}{\ \begin{tabular}{c} Evanescent \\ quadridge [5] \\ \end{tabular}  } & \multirow{4}{*}{Square} & \multirow{4}{*}{4.5} & 0 & \(-40\) & \(-12\) & - & 40 \\  & & & \(30\) & \(-15\) & \(-13\) & 1 & 15 \\  & & & \(40\) & \(-12\) & \(-9\) & 1 & 10 \\  & & & \(50\) & \(-10\) & \(-6\) & 2 & 8 \\  & & & \(60\) & NA & NA & NA & NA \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Evanescent \\ quadridge [5] \\ \end{tabular}  } & \multirow{4}{*}{Square} & \multirow{4}{*}{13.2} & 0 & \(-53\) & \(-4\) & - & 40 \\  & & & \(30\) & \(-11\) & \(-6\) & 2 & 12 \\  & & & \(40\) & \(-9\) & \(-6\) & 2 & 7 \\  & & & \(50\) & \(-4\) & \(-6\) & 8 & 0 \\  & & & \(60\) & \(-3\) & \(-7\) & 7 & 6 \\ \hline \multiadd additional design parameters and uncertainties in the overall verification process. Moreover, the experimental validation should be performed by implementing a finite array with either a reconfigurable BFN or additional post-processing to achieve ARC, scan loss and XPD from measurements at the element level (scattering matrices and embedded element patterns). Both BFN and such post-processing methods would introduce additional uncertainties in the overall verification process. All these considerations led us to the full-wave analyses on finite structures reported in this section. Convergence of such finite array results is assessed by varying both the number of elements and the distance between the structure and the boundary conditions. This analysis is also useful to assess the minimum number of elements that should be considered for array prototyping. Provided that there is good agreement between the infinite and finite array approaches, there are several papers demonstrating good agreement between simulations and measurements in finite arrays (see, for example, [7; 9]). As far as metal waveguide components are concerned, we already compared the adopted full-wave software with measurements up to W-band in previous papers (see, for example, [26; 31]). Two relevant configurations have been selected, i.e., the quadridge in the square lattice and the hexagon with three ridges in the triangular lattice. The quadridge is significant because of its scan blindness. The hexagon with three ridges is interesting because of its one-fold symmetry and the triangular lattice arrangement. The validation has been carried out comparing three sets of results: an infinite approach (unit cell) in both CST Studio Suite 2021 and HFSS 2022, and a finite array simulation in CST. For the hexagonal structure, a simple transition with two steps from a smaller waveguide to the aperture has been introduced to avoid overlapping the waveguide ports in the finite array configuration. The same transition has also been included in the infinite simulation for consistency. Therefore, the presented results are slightly different from the ones presented in Section 4.2.