## 2 Transmitarray Antenna Design
### Design of Unit Cell of MS  
The proposed unit cells with two identical conductive layers printed on the both sides of the substrate and the slots control the changing of transmission coefficients; the whole structure is presented in Figure 4. The material of substrate is Rogers 4003C, which has the dielectric constant (\(\varepsilon_{\mathrm{r}}\)) of 3.38 and loss tangent of 0.0027. To get the phase and amplitude of transmission coefficient (S\({}_{21}\)), CST Microwave Studio is used to simulate the unit cell structure with period boundary condition in X and Y direction and the excitation of the normal plane wave in Z direction. In Figure 4c, the side length of square substrate (\(P\)) is 5.3 mm, the thickness (\(T\)) of substrate is 1.524 mm, and four vias are inserted in the substrate to connect the upper and bottom metallic layers.  
The unit cells can be classified into two group: Unit Cell A as shown in Figure 4a and Unit Cell B as shown in Figure 4b. For Unit Cell A, \(r_{1}\) = 2.55 mm, \(L_{1}\) changes from 1. 28 to 1.85 mm, and a phase shift range from 360\({}^{\circ}\) to 156\({}^{\circ}\) is covered. For Unit Cell B, \(r_{2}\) = 1.83 mm, \(L_{2}\) varies from 0.61 to 1.29 mm, while the phase shifts from 156\({}^{\circ}\) to 0\({}^{\circ}\). The residual parameters like the position of vias (\(d\)) and the width of slots (\(w\)) are kept the same in both Unit Cell A and Unit Cell B: \(d\) = 1.1 mm and \(w\) = 0.2 mm. Each unit cell has four vias at the symmetric positions away from the center. Only two different sizes of circular metallic patches are used to build the TA, and meanwhile, the length of slot is changed to get different transmission phase, which will be used to focus the beam. Unlike in the Ref. [28], the 304\({}^{\circ}\) phase shift is achieved by changing the side length of square patch and the position of vias is varied with the patch size proportionally; the TA in this paper can cover the 360\({}^{\circ}\) phase shift with sweeping the length of slots on Unit Cell A and B, correspondingly. What's more, the positions of  
Figure 4: The structure of unit cell: (**a**) Unit Cell A, (**b**) Unit Cell B, and (**c**) side view of unit cell.  
Figure 3: The electric field magnitude at the cross sections inside the optimized horn antenna: (**a**) inside the circular waveguide, (**b**) at the first abrupt change part, (**c**) at the second abrupt change part, and (**d**) at the flared aperture.  
via do not change with the dimension of patches, which means the positions of via are fixed on the array, and those will reduce the cost and the difficulty in the procedures of design and fabrication.  
Figure 5 shows that the transmission coefficients change with the length of slots while other parameters remain unchanged in this process. Apparently, in Figure 5a, there is a seamless connection between the phase shift of Unit Cell A and Unit Cell B and the full 360\({}^{\circ}\) can be covered with a gentle slope to realize the requirement of focusing effect of transmission wave. The transmission magnitudes are all over \(-2\) dB, which is proposed in Figure 5b, and for the high gain of TA design, design with less transmission loss is desirable; it is also be helpful in the optimization of SLL reduction in the following research of TA antenna.  
The length of slots is varied from 1.28 to 1.85 mm with a 0.03 mm step in Unit Cell A, whereas in Unit Cell B, it is varied from 0.61 to 1.29 mm with a step of 0.02 mm, thus the relationship between the length of slots and the transmitted phase will be built for Unit Cell A and Unit Cell B, separately. In this way, it will be easier to confirm the specific length of slot at different positions on the array according to the phase distribution, which will be discussed in the next part.