## 2 The Principle and Components of CPFTA
### The Unit Cell of Transmitarray  
The receiver-transmitter structure is adopted to construct transmitarray. The schematic geometry of the unit cell is shown in Figure 2. The unit contains three metallic layers separated by two identical substrates (TACONIC-TLX-8). The substrates are bonded together with ROGST-4450F. The top and bottom metallic layers are connected by metallic via. The middle layer is a metallic ground etched with circular hole. The periodicity (\(p\)) of the unit cell is 10 mm (about 0.33 \(\lambda\) at 10 GHz) and the profile of the unit cell is 3.1 mm (about 0.1 \(\lambda\) at 10 GHz). The parameters are tabulated in Table 1.  
The structure of the unit cell can be regarded as back-to-back combination of two microstrip antennas. The bottom metallic layer is a E-shaped patch used to be a linearly polarized receiving antenna. The top metallic layer is an anisotropic patch used to be a circularly polarized transmitting antenna. The transmitarray works as follows. Firstly, the bottom E-shaped patch receives the linearly polarized electromagnetic wave radiating from the feed antenna. Then, the electromagnetic energy is transferred to the top anisotropic patch by the metallic via. Finally, the top anisotropic patch radiates circularly polarized electromagnetic wave. Under _x_-polarized incident waves, \(T_{xx}\) and \(T_{yx}\), represent the components of co-polarized and cross-polarized transmission, respectively. Analogously, \(R_{xx}\) and \(R_{yx}\) represent the components of co-polarized and cross-polarized reflection. \(\Delta{\varphi}\) represents the phase difference between \(T_{yx}\) and \(T_{xx}\). Defining AR [24] of circularly polarized waves and transmission ratio (TR) of the unit cell as:  
\[\text{AR}=\left|20 log_{10}\tan\left[0.5 arcsin\left(\frac{2\,T_{xx}\,T_{yx}}{T _{xx}^{2}+T_{yx}^{2}}sin\Delta{\varphi}\right)\right]\right| \tag{1}\]  
\[\text{TR}=\frac{\left(T_{yx}x^{2}+T_{xx}x^{2}\right)}{\left(T_{yx}x^{2}+T_{xx} ^{2}+R_{yx}x^{2}+R_{yx}x^{2}\right)} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline Parameter & \(w\) & \(l\) & \(l\) & _l1_ & _w1_ & _r2_ & _r1_ \\ \hline Value (mm) & 8 & 7.8 & 2 & 1.8 & 1.4 & 0.9 \\ \hline Parameter & _r3_ & _w2_ & _dh_ & _dl_ & \(h\) & \(p\) \\ \hline Value (mm) & 1.4 & 1.1 & 0.1 & 3.6 & 1.5 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of transmitarray unit cell. Figure 2: The schematic geometry of transmitarray unit cell. Figure 3a plots the reflection and transmission amplitudes under _x_-polarized incident waves. Two obvious resonance frequencies of \(R_{xx}\) are observed at 9.4 GHz and 10.8 GHz. The two resonance frequencies correspond to two TR peaks, as shown in Figure 3c. Around 9.2 GHz, the amplitude of \(T_{xx}\) and \(T_{yx}\) are equal, which satisfies the amplitude condition for generating circularly polarized waves. Similarly, \(T_{yy}\), \(T_{xy}\), \(R_{yy}\) and \(R_{yy}\) can be obtained under _y_-polarized incident waves. Since the polarization direction of incident waves is orthogonal to the E-shaped patch, the E-shaped patch hardly receives energy [25]. Hence, Figure 3b shows that the _y_-polarized incident waves are totally reflected. The AR and TR are calculated under _x_-polarized incident waves, as shown in the Figure 3c,d. In the range of 8.9-9.5 GHz, the _x_-polarized incident waves are converted to circularly polarized transmission waves with the AR less than 3-dB. Furthermore, the TR of oblique incident waves is also studied. The simulated results show that the TR is larger than 80% in the range of 8.9-11.4 GHz with incident angle less than 45\({}^{\circ}\). Due to the feature of the receiver-transmitter structure, the top and bottom metallic layers are relatively independent. Hence, rotating the bottom E-shaped metallic patch with 180\({}^{\circ}\) can realize 1-bit transmission phase adjustment. This is the key for radiation beam focusing.