# Two-Dimensional Scanning of Circularly Polarized Beams via Array-Fed Fabry-Perot Cavity Antennas
## 2 Unit-Cell Design and Analysis Strategy  
The antenna structure is presented in Figure 1, as well as a detailed zoom on the PCM unit cell. Three main components should be distinguished: the PCM, the ground plane, and a simple horizontal electric dipole (HED) oriented along the \(y\) axis and placed in the middle of the cavity to have maximum gain [44; 45]. Here, we consider both the ground plane and the PCM of infinite extent without taking into account possible truncation effects, as is typical for leaky-wave antennas with high aperture efficiency [14]. As concerns the source, an FPCA is commonly fed by any LP dipole-like radiator [22]. The use of a horizontal magnetic dipole (HMD), typically implemented through a resonant slot on the ground plane [46], or an HED, usually in the form of an L-shaped probe [22], allows for obtaining the broadside pencil beam, which are instead not possible with vertical dipole sources [14]. Concerning the PCM, this has been designed on the basis of the one proposed in [36], which has been suitably improved in order to ensure a good performance at different elevation and azimuth angles to allow for an efficient electronic scan of the beam. In particular, the PCM consists of three metallic patches sandwiching two square Rogers RO3203 dielectric substrates, whose dimensions are reported in Table 1. The bottom metallic square patch is responsible of field reflections inside the cavity [36], while the top metallic patch is shaped to obtain an LP-to-CP conversion [35]. The symmetry of the upper metallic patch with respect to the diagonal plane (see Figure 1) is instrumental to obtain the right-hand circular polarization (RHCP) [35; 36]. The two top/bottom metallic sheets are separated by a further metallic layer located between them; the electrical coupling between the top and bottom layers is ensured by a pair (rather than a single, as in [36]) vertical via holes, whose symmetric location with respect to the center of the unit cell helps in improving the scanning performance of the resulting antenna. As in [36], thanks to the stratified geometry of the PCM, one may optimize transmission features by tailoring the top patch without significantly affecting the reflection features,  
Figure 1: Pictorial representation of the proposed FPCA. The insets on the left show the PCM unit cell through different perspective views, indicating the main design parameters. which are essentially established by the bottom patch. The central metallic patch that separates the dielectric substrates decouples the transmission and reflection patches so that their optimization can be carried out independently. Moreover, it has been shown that the position of the vias (see Figure 1), whose reciprocal distance accounts for the required phase quadrature between horizontal and vertical radiated components, does not modify the reflectivity of the bottom patch seen by the resonating field, both in terms of magnitude and phase. Hence, the phase of the reflection coefficient can be used, in particular, to design the cavity height \(h\) for maximum radiated power at broadside, according to [PERSON]'s formula [21], and it is not affected by further calibration steps. In the case under analysis, a broadside pencil beam is obtained for \(h=3.5\,\mathrm{mm}\). Since typical multiple reflections inside an FPCA are supposed to modify the conversion properties of the free-standing PCM, we directly optimize the polarization-conversion properties of the latter in a reciprocity-based scenario. The latter accounts for multiple bounces that define the actual behavior of the device. The optimization of the PCM top patch is performed by tuning the dimensions of its constituent elements on a given azimuthal plane, here the \(xz\) plane, such that the CP conditions are fulfilled, i.e., \(|E_{\phi}|\)=\(|E_{\phi}|\), and \(\angle E_{\theta}-\angle E_{\phi}=\pm 90^{\circ}\).