## 3 Non-Uniform Phase Distribution for Directional Radiation
The absolute value of the electric field strength is plotted in a pseudo-color way, and the results are obtained at 9.7 GHz. Figure 10a-c shows the radiation patterns. Different properties can be observed. In Figure 10b,c, the main power is directed toward the \(-x\) direction, and the reflection is larger for \(h=50\) mm. In Figure 10a, there are several peaks in the radiation pattern. This is caused by the excitation of the higher-order modes, as shown in Figure 8d. The power flow inside the high-permittivity region is directed toward four corners of the block and result in four lobes both for the transmission pattern and the reflection pattern. It should be mentioned that similar dielectric waveguides were used for direction coupler by Refs. [11,16,17]; however, in this work, the 2-D periodic dielectric bars were used as a reflect array with directional reflection. The excited radiation pattern are presented in Figure 10a. The power is mainly scattered perpendicularly, and only a little microwave power is reflected toward the \(-x\) direction. It is expected that a reflect-array structure will have a similar radiation pattern for decreasing the reflection returning back to the microwave antenna. The simulation model of the reflect-array structure containing the metal wall was built and is shown in Figure 11a. The simulated radiation pattern at 9.7 GHz is shown in Figure 11b. It can be found that the peaks toward the \(-x\) direction in Figure 10a correspond to the peaks toward the \(z\) direction in Figure 11b due to the reflection of the metal wall. The appropriate value of \(h\) is of course important for optimizing the radiation pattern. As a result, the acceptable radiation pattern is obtained when \(h=9\) mm and is shown more clearly in Figure 11c,d. The  
Figure 10: Radiation pattern of structure in Figure 8 with (**a**) \(h=40\) mm, (**b**) \(h=45\) mm, and (**c**) \(h=50\) mm. Figure 9: Simulated phase distribution using the model in Figure 8 at (**a**) 7.7 GHz, (**b**) 8.7 GHz, and (**c**) 9.7 GHz. simulated values of the radiated electric field are obtained at a distance of 1 m and the pitch angles denoted as 'phi' in Figure 11b are 0\({}^{\circ}\) and 90\({}^{\circ}\) for Figures 11c and 11d, respectively. The reflected fields are concentrated toward the directions with a pitch angle of 90\({}^{\circ}\) and azimuth angles of 50\({}^{\circ}\), 130\({}^{\circ}\), 230\({}^{\circ}\), and 310\({}^{\circ}\), as shown in Figure 11c. The aim of the design is to decrease the reflection toward the \(x\) direction. From Figure 11d, it can be observed that the field strength in dB toward the \(x\) direction is \(\sim\)\(-\)37 dB, and this value is more than 7 dB lower than that of the concentration directions mentioned above. The height of the structure, denoted by \(h\), is 9 mm, which proves the robustness of the structure when it is applied in wind tunnel experiments. When the gap length \(g\) changes from 15 mm to 13.5 mm, the phase distribution on the interface is obtained and is shown in Figure 11e. The two values in the centers of two dielectric materials have a difference of \(\sim\)182 degrees; however, the difference is close to 180 degrees when \(g\) is \(\sim\)15 mm. The phase difference of 180 degrees can depress the reflection toward the normal direction. So, for \(g\) = 13.5 mm, the reflection is higher in  
Figure 11: Radiation pattern of the reflect-array structure: (**a**) simulation model of the reflect array, (**b**) radiation pattern of the electric field, (**c**) radiation pattern with ’phi’ = 0\({}^{\circ}\), (**d**) radiation pattern with ’phi’ = 90\({}^{\circ}\), (**e**) phase distribution on the interface when \(g\) is 13.5 mm, and (**f**) distribution of the amplitude of the \(E_{y}\) component on the interface when \(g\) is 17.5 mm. Figure 11c when phi = 0\({}^{\circ}\) and theta = 90\({}^{\circ}\), and the peak strength of the main lobe is weaker in Figure 11d when phi = 90\({}^{\circ}\) and theta = \(\sim\)45\({}^{\circ}\).