## 2 Transmitarray Antenna Design
### Array of MS
However, the elements on the TA are all block structures with the same volume, and we just regard the elements as volumetric free and put the center-point coordinate of every element on the array into the (1) to calculate the required phase and use those phases to build the model, so the phase values are presented in the form of cubes in Figure 6b. As a result of which, the phase shifting will be discontinuous, some phase errors will be caused inevitably. Third, the adjacent elements on the array are different from those around them and there is a feed source in the TA antenna so the mutual coupling are complex. However, in the analysis of unit cell, the data are acquired under the situation of periodic boundary condition with the plane wave excited. In general, we ignore the impacts of oblique incidence, discontinuity, and actual mutual coupling to design the TA. After the optimization of unit cell, we can keep all the transmission coefficient in the level of \(-2\) dB, which is shown in Figure 5b. From that plot, it is obvious that the most part in Unit Cell B has a higher and smoother tendency changing with the length of slots than the magnitude tendency of Unit  
Figure 6: **(a)** The top view of the fabricated transmitarray (TA), and (b) the phase distribution of TA calculated by Equation (1). Cell A. Additionally, according to the first and second approximation discussed before, the farther from the center, the greater the design error may occur. Hence, we should put the elements with less transmission loss around the center as much as possible. In this situation, the Unit Cell B with the length of 1.29 mm (\(L_{2}\) = 1.29 mm) is selected as the four identical elements in the center because of the symmetrical distribution of elements. Other elements are determined based on the relationship between the length of slots and the related phase in Figure 5a; therefore, the distribution of elements with different dimensional information is presented in Figure 6a. Figure 7 presents the positional relation between TA and the feed horn. As described above, \(D\) is the diameter of TA, which has the value of 160 mm, and \(f\) is the distance from the center of source antenna to the center of TA, and the ratio between \(f\) and \(D\) (/\(D\)) is an important criterion to judge the SLL and low-profile of a TA antenna. The smaller value of /\(D\), the better low-profile performance of a TA antenna and the worse of the backward radiation, so there is a tradeoff needed to be made. For the working principle, the TA is aimed to imitate the function of lens and the feed source is placed at the virtual focal point. When the quasi-spherical wave emitted by the feed crosses over the TA, it will compensate the phases and form a uniform wave front similar to a plane wave. Reversely, when the TA is illuminated by the plane wave, the wave will gather at one point theoretically just like the optical reversibility in the Fermat's principle. In this way of analysis, a plane wave is placed at one transmission side of the TA like shown in Figure 8a, and the power density on the E-plane and H-plane of the other TA side will be shown as in Figure 9. Obviously, the energy is focused at an area, and this area is the approximate position to place the feed. The normalized energy distribution along the intersection line of E-plane and H-plane is proposed in Figure 8b. The peak in Figure 8b is the theoretical optimum of the feed position (\(f\)) which has a value of 104.1 mm, so the theoretical ratio of /\(D\) will be around 0.65, and slight changing near 0.65 will be needed in the simulation to find the best position of feed. The simulation result is shown in Figure 10, in which the far-field gain of TA antenna is 27 dB at 28 GHz, SLL in E-plane is \(-\)19.6 dB and in H-plane is \(-\)21.7 dB, and compared with the radiation pattern of horn, the focusing effect of TA is significant in two cut planes. Figure 8: (**a**) TA with plane wave and (**b**) the normalized power distribution along intersection line of E-plane and H-plane.