## 2 Transmit-Array Element Structure  
A transmit-array lens element that can realize phase modulation and polarization conversion functions at the same time is shown in Figure 1. The element consists of six layers of metal patterns, five layers of dielectric substrates, and a metalized via. The first four-layer metallic patterns with substrates form a phase modulation part, as shown in Figure 1a. The split ring resonator with substrate functions as a linear-to-circular polarization conversion part. The fifth layer is a metal ground with circular holes to isolate these two parts as shown in Figure 1b, and the phase modulation and polarization conversion parts are electrically connected through a metallic via. All layers of the metal patterns are printed on dielectric substrates of Rogers RT5880 with \(\varepsilon\)r = 2.2, tan\(\delta\) = 0.0009, and M1 = 0.75 mm. The period of the element is S = 3.6 mm. In the electromagnetic simulation software HFSS, we optimized the geometric dimensions of nine elements under periodic boundary conditions and Floquet port excitations. In the frequency range of 24.5-27 GHz, the element provides a phase shift of 40\({}^{\circ}\), covers 360\({}^{\circ}\) with three-bit phase modulation, and demonstrates horizontally linear polarization to right-hand circular polarization. The geometric dimensions of all unit-cells are shown in Table 1. The phase shift varies with the size parameters of the unit cell. Among them, the radius of the metalized via R_via and the outer radius of the metallic open ring R_out are sensitive to the axial ratio, transmitted amplitude, and phase modulation of the unit cells. According to the state-of-the-art fabrication processing, the minimum fabrication size is 25 \(\upmu\)m for the multilayer PCB. The variations in transmission coefficient with R_via and R_out are shown in Figure 2. When R_via and R_out change \(\pm\)25 \(\mu\)m, the axial ratio, transmission coefficient, and phase of the unit cell change about \(\pm\)0.4 dB, \(\pm\)0.5 dB, and \(\pm\)5\({}^{\circ}\) over the frequency range of 24.5-27 GHz, respectively, which is tolerated for the transmit-array phase distribution. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline  & **L1** & **L2** & **L3** & **L4** & **W1** & **W2** & **W3** & **W4** & **R\_in** & **R\_out** \\ \hline Unit-cell1 & 2.58 & 2.34 & 2.3 & 2.92 & 0.1 & 0.18 & 0.1 & 0.13 & 0.4 & 1.69 \\ Unit-cell2 & 2.85 & 2.71 & 2.67 & 2.89 & 0.18 & 0.18 & 0.1 & 0.13 & 0.39 & 1.7 \\ Unit-cell3 & 2.56 & 2.7 & 3.11 & 3.09 & 0.18 & 0.19 & 0.14 & 0.12 & 0.39 & 1.69 \\ Unit-cell4 & 2.14 & 1.98 & 1.62 & 2.68 & 0.19 & 0.25 & 0.15 & 0.18 & 0.39 & 1.7 \\ Unit-cell5 & 3.12 & 3.16 & 3.08 & 3.1 & 0.13 & 0.11 & 0.08 & 0.14 & 0.39 & 1.71 \\ Unit-cell6 & 3.22 & 3.18 & 3.16 & 3.13 & 0.12 & 0.11 & 0.14 & 0.39 & 1.705 \\ Unit-cell7 & 2.18 & 2.11 & 1.5 & 2.25 & 0.35 & 0.1 & 0.15 & 0.1 & 0.4 & 1.7 \\ Unit-cell8 & 2.7 & 2.7 & 3.13 & 3.15 & 0.1 & 0.18 & 0.09 & 0.13 & 0.55 & 1.7 \\ Unit-cell9 & 2.33 & 2.2 & 1.1 & 2.9 & 0.17 & 0.25 & 0.15 & 0.18 & 0.39 & 1.7 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters of the nine unit cells. Figure 1: Schematic diagram of the proposed lens element: (**a**) phase modulation part; (**b**) polarization modulation part; (**c**) 3D view. The simulated reflection coefficients, transmission phase, and axial ratio responses of the proposed transmit-array element versus the frequency are shown in Figure 3. The reflection coefficients of all lens unit cells are lower than \(-10\) dB, the transmission phase of the lens unit-cells shifts with a step of 40\({}^{\circ}\) and covers 360\({}^{\circ}\), and the axial ratio of all unit cells is less than 3 dB for the whole frequency range, from 24.5 GHz to 27 GHz. With the incident angle varying from 0\({}^{\circ}\) to 30\({}^{\circ}\), the change in the transmission phase shift is less than nine degrees, as shown in Figure 3e. The element has no air layer and is easy to fabricate with PCB manufacturing.