## 2 Beam Steering/Beam Forming Principle of Transmitarray
A high gain transmission antenna using a metasurface composed of 10 \(\times\) 10 circular patch array unit cells is presented. The total size of the transmitarray is 200 mm (about 4 \(\lambda_{0}\)), and the distance between the source antenna and the metasurface is 50 mm (about 1 \(\lambda_{0}\)). Figure 1: Generic radiation model of transmitarray antenna. The total wavefront of the transmitarray antenna can be conceptually expressed as the sum of the wavefront of the source antenna and the transmission phase of the transmitarray, as illustrated in Figure 2. When the focal source antenna and transmitarray antenna are fixed for phase implementing high gain and shape of the wavefront, a straight line is demonstrated in Figure 2a. The focal source antenna is fixed, whereas phase change is implemented by an active transmitarray in Figure 2b. A high gain variable phase change is achieved in this scenario by changing the wavefront of the active transmitarray. It is illustrated in Figure 3 that the wavefront of the transmitarray antenna is fixed through the change in the wavefront shape of the source antenna using the phase transformation surface that helps to implement the change of phase and achieve the high gain steering transmitarray. Aperture efficiency is an important performance indicator of a transmitarray antenna. Aperture efficiency (\(\eta_{a}\)) is defined in terms of the taper efficiency (\(\eta_{t}\)), spillover efficiency (\(\eta_{s}\)), polarization efficiency (\(\eta_{pol}\)), transmission efficiency (\(\eta_{trans}\)), phase efficiency (\(\eta_{plt}\)), and random surface as in Equation (4). It can be calculated as the product of the error efficiency (\(\eta_{r}\)) [72]. \[\eta_{a}=\eta_{t}\,\eta_{s}\,\eta_{pol}.\eta_{trans}.\eta_{ph}.\eta_{r} \tag{4}\]  
Here, the efficiencies that mainly affect the aperture efficiency of the transmitarray antenna are the taper efficiency and the spillover efficiency. These two efficiencies are determined by the size and spacing of the source antenna and the metasurface. Taper and spillover efficiencies are related to the uniformity and amount of power reaching the metasurface from the source antenna, respectively, and are calculated by Equations (5) and (6). \[\eta_{t}=\frac{\eta_{a}}{S}\frac{\left|\int\ E(x,y)^{2}.dS\right|^{2}}{\int \left|E(x,y)^{2}dS\right|^{2}} \tag{5}\]  
\[\eta_{s}=\frac{\int\left|E(x,y)^{2}dS\right|}{P_{rad}} \tag{6}\]  
where \(S\) and \(P_{rad}\) are the area of the metasurface and the radiation power of the source antenna, respectively. It is vital to determine the source antenna, the distance between the source antennas and the plane array (F), and the size (D) of the transmitarray to optimize the aperture efficiency of the transmitted antenna using the TA. When the distance between the source antenna and the plane array is short, the spillover efficiency is high but the taper efficiency is low. Conversely, if F becomes longer, taper efficiency is high but spillover efficiency is lower. In addition, as the size of the transmitarray increases, the spillover efficiency is high but the taper efficiency decreases. Therefore, to maximize the aperture efficiency of the transmit antenna, it is necessary to optimize F/D. Maximum numerical aperture efficiency and the optimum gain of the source antenna following various F/D are shown in [42]. In this case the gain of the source antenna has become relatively low, the maximum value of the aperture efficiency decreases, but the distance F with maximum efficiency is reduced and a low-profile transmitarray antenna can be designed. In addition, a source antenna with a high gain may be applied to secure the maximum aperture efficiency, for example, when a patch antenna having a gain of 7.5 dBi is applied to a transmission antenna as a source antenna, the maximum aperture efficiency is about 62%, and F/D can be designed to 0.2.