# Circularly Polarized High-Gain Fabry-Perot Cavity Antenna with High Sidelobe Suppression
## 2 Proposed FPCA Design and Operation
### Mechanism of the CP-PRS as a Polarizer  
The simulated model of the CP-PRS unit cell is depicted in Figure 5 in the form of floquet ports and boundary conditions, which are used to excite and analyze the unit cell to attain impedance characteristics and realize an infinite planar periodic structure [see Figure 5c]. Figure 3: AMC unit cell with reflection magnitude (\(0.95<\lvert\Gamma_{n}^{AMC}\rvert<1\)): (**a**) top square patch layer, (**b**) bottom ground layer, \(p=\lambda_{0}/2=15\) mm, \(a=0.1\) to \(14.9\) mm. The CP-PRS works as a conventional polarizer, which transmits only the \(x\)-polarized components of the incident waves coming from the feeder and converts them to CP waves after penetrating the CP-PRS. Only the \(x\)-polarized waves can be transmitted through the CP- PRS due to the rectangular patch, which is installed along the \(x\)-axis on the bottom side of the PRS unit cell as shown in Figures 2c and 5a. To form a perfect CP wave in the broadside direction, the orthogonal components of the transmitted waves should be equal in magnitude \(\left|\mathrm{T}_{(x,x)}^{PRS}\right|=\left|\mathrm{T}_{(y,x)}^{PRS}\right|\) and have \(\pm 90^{\circ}\) phase differences \(\Delta\phi=\phi_{\mathrm{T}(x,x)}^{PRS}-\phi_{\mathrm{T}(y,x)}^{PRS}\) for the left-handed and right-handed circular polarization. Here, \(\left|\mathrm{T}_{(x,x)}^{PRS}\right|\), \(\left|\mathrm{T}_{(y,x)}^{PRS}\right|\), \(\phi_{\mathrm{T}(x,x)}^{PRS}\), and \(\phi_{\mathrm{T}(y,x)}^{PRS}\) are the magnitudes and phases of the orthogonal components of the transmitted waves. The labeled subscripts are (\(x\),\(x\)) and (\(y\),\(x\)) on the right and left of the comma \",\" representing the incidence of \(x\)-polarized waves and the orthogonal \(x\)- and \(y\)-components of the transmitted waves, respectively. These transmission characteristics of the circularly polarized wave are controlled independently by the arm length, width, diameter, and corners (\(l_{1}\), \(l_{2}\), \(w_{1}\), \(w_{2}\), \(d_{1}\), \(c\)) of the upper PRS metal layer, due to the deployment of the reflective ground between the top and bottom patches [as depicted in Figures 1, 2b and 5a]. Moreover, the reflective ground provides high reflection within the resonance cavity, which is favorable for increasing antenna gain due to the more realistic illumination environment of the PRS. For CP waves  
Figure 5: Simulated model of the PRS unit cell: (**a**) lower metallic patch, (**b**) upper metallic patch, (**c**) boundary conditions. as an output above the PRS superstrate, the axial ratio (AR) [20,26] can be determined within the operating frequency band using the equations  
\[AR=\left(\frac{\left|\mathbb{T}_{(x,x)}^{PRS}\right|^{2}+\left|\mathbb{T}_{(y,x)} ^{PRS}\right|^{2}+\sqrt{m}}{\left|\mathbb{T}_{(x,x)}^{PRS}\right|^{2}+\left| \mathbb{T}_{(y,x)}^{PRS}\right|^{2}-\sqrt{m}}\right)^{\frac{1}{2}} \tag{1}\]  
\[m=\left|\mathbb{T}_{(x,x)}^{PRS}\right|^{4}+\left|\mathbb{T}_{(y,x)}^{PRS} \right|^{4}+2\cdot\left|\mathbb{T}_{(x,x)}^{PRS}\right|^{2}\cdot\left|\mathbb{ T}_{(y,x)}^{PRS}\right|^{2}\cdot\cos(2\Delta\phi) \tag{2}\]  
The reflection and transmission characteristics of the PRS unit cell are shown in Figure 6. The optimized reflection magnitude \(\left|\mathbb{T}_{(x,x)}^{PRS}\right|\) and phase \(\phi_{\Gamma(x,x)n}^{PRS}\) characteristics of the CP-PRS unit cell are 0.95 and \(-135^{\circ}\), respectively, at design frequency \(f_{0}=10\) GHz. For circular polarization, this cell satisfies the equal magnitude of \(\left|\mathbb{T}_{(x,x)}^{PRS}\right|=\left|\mathbb{T}_{(y,x)}^{PRS}\right|=0.26\), and a phase difference of \(\Delta\phi=\phi_{\Gamma(x,x)}^{PRS}-\phi_{\Gamma(y,x)}^{PRS}=-115^{\circ}-155^ {\circ}=-270^{\circ}\) (i.e., \(90^{\circ}\) in the counterclockwise direction) between the orthogonal components of the transmitted waves shown in Figure 6a,b. To confirm perfectly circularly polarized wave generation, the Ex-field distribution and surface current density are illustrated in the Supplementary Materials [see Figure S3].