## 2 Beam Steering/Beam Forming Principle of Transmitarray  
The transmitarray antenna is an antenna that is capable of modifying the radiation pattern of a directional antenna such as a patch antenna or a horn antenna. A transmitarray has the capability of adjusting the wavefront of the source antenna and the incident wave. By using a structure that can adjust the size and phase of the incident wave, the transmission antenna can be used in various fields such as beam steering, beam focusing, and polarization control. Figure 1 shows a typical radiation model of a transmission antenna composed of a source antenna and a transmitarray. A transmitarray is formed by a feed, which is labeled as a source antenna where the source antenna is placed at a distance F from transmitarray. Focal distance (F) is calculated as a tradeoff between spillover losses and an increase in gain, aperture efficiency, and other parameters. The source antenna illuminated by incident wave to the first part of the array is called the receiver. The receiver is directly connected to group of phase shifters to control the beam wave front in the required direction. The other end of the phase shifters are coupled with a transmitter layer, which produces a phase shift in the incident wave that works in transmitter mode. The phase shifter of each unit cell provides \(\gamma\)n path difference to the source point to obtain the desired scan angle \(\theta\). As shown in Figure 1, the direction of the incident wave is determined by radiation controlled by the transmission phase of the transmitarray. Transmitarrays are generally composed of several resonant unit cells with a spatial periodicity that forms a planar arrangement. The principle of beam forming/beam steering transmitarrays is reported in [57; 58; 59; 60; 61; 62]. There are incident EM waves generated from a feed source that passes through a transmitarray made up of nth (n = 0, 1,... ) elements of periodicity of \"a\" and produces phase change \(\varphi_{n}\) shown in Equation (1). \[\varphi_{n}=k_{o}n\ \Delta s+\varphi_{0} \tag{1}\]  
where \(k_{o}=\frac{2\pi}{\lambda_{0}}\) is the propagation constant of the free space-waves. \(\Delta s\) is the path difference between the nth and (n + 1 th) elements after they pass through the transmitarray. \(\Delta s\) is defined here for the deflection angle \(\theta\) of the transmitted wave with element dimensions a that is the path difference with the deflection angle \(\Delta s\) = a.sin\(\theta\). Now we can write the phase change as \(\varphi_{n}\) = \(\varphi_{n+1}-\varphi_{n}\). \[\Delta\varphi=k_{o}\Delta s=\frac{2\pi}{\lambda_{0}}a.sin\theta \tag{2}\]  
\[\sin\theta=\frac{\lambda_{0}}{2\pi a}.\ \Delta\varphi \tag{3}\]  
Equations (2) and (3) demonstrate that if we define the deflection angle \(\theta\), we can calculate the phase change \(\Delta\varphi\) from Equation (2). Thus, both equations show inter-dependent relations for each other [63]. Similarly, the design and implementation of beam switching in arrays using a butler matrix have also been reported [64; 65; 66]. Transmitarray unit cells are usually designed based on microstrip patches, metamaterials [67; 68], and frequency selective surfaces (FSS) [69; 70]. The microstrip patch metasurface of the unit cell and its permeation characteristics are shown in [71]. The unit cell comprises of four dielectrics and five circular metal patches, and the equivalent circuit model can be expressed by series inductance and parallel capacitance in the passband. The transmission characteristics of the metasurface can be controlled by the radius (a) of the metal circular patch and the transmittance and transmission phase of the circular microstrip patch array transmitarray at 5.8 GHz. In this case, the size (W) of the square unit cell is 20 mm (0.38 \(\lambda_{0}\)), the dielectric constant (\(\varepsilon\)r) and thickness (h) of the dielectric substrate are 2.2 and 3.2 mm, respectively. From 1 mm to 9.1 mm, a transmittance of 0.8 or more and a change in transmission phase of about 400 degrees can be obtained.