## 3 Metasurface Simulation and Experimental Measurement Results  
### Metasurface Simulation and Results  
As the method of calculating the compensation phase for generating a single off-axis pseudo Bessel beam and multiple pseudo Bessel beams by a metasurface has been proposed, we can use the suitable unit cell to compose the needed metasurfaces. A miniaturized subwavelength unit cell with a periodicity \(P=8\) mm (0.27\(\lambda\)) [13] is selected as the unit cell of the metasurface, as show in Figure 2. The unit cell comprises two concentric circular rings, while the inner ring is connected to a cross, and is also separated by four identical gaps with an angle of 20\({}^{\circ}\). The radiuses of the outer ring and the inner ring are \(R_{o}\) and \(R_{i}\), which has the relationship of \(R_{i}=0.7\times R_{o}\), and the width of both the rings and the cross is \(w=0.3\) mm. This unit cell is printed on a F4B (\(\varepsilon_{r}=2.65\)) dielectric substrate with a thickness of \(t=3\) mm, and the model of it is built in the simulation software ANSYS HFSS, with periodic boundary conditions. The reflection phase and reflection coefficient characteristics of the unit cell versus the length of \(R_{o}\) at the center frequency of 10 GHz are shown in Figure 2.  
As shown in Figure 2, by varying \(R_{o}\) from 0.85 to 3.9 mm, the reflection phase variation range of the unit cell can cover the whole 360\({}^{\circ}\), and it can be seen that the phase-shift changes are less than 17\({}^{\circ}\) when the incidence angle varies from 0\({}^{\circ}\) to 30\({}^{\circ}\). Meanwhile, the reflection coefficient keeps above \(-0.2\) dB when the incidence angle varies, so that this miniaturized unit cell has the characteristics of both high efficiency and good angle stability; it is also polarization-insensitive because of its symmetrical structure. According to the method mentioned and the relationship between the unit cell size and its reflection phase curves shown in Figure 2, the metasurfaces to generate off-axis pseudo Bessel beams can be designed. All of the metasurfaces have a size of 390 mm \(\times\) 390 mm, and the distance from the feed horn to the metasurfaces is 300 mm. The azimuth angle of the beam is set to be \(\varphi_{k}=45^{\circ}\), and the angle between the inward conical wave and the propagation axis is \(\alpha=10^{\circ}\). In order to show the universality of this method, we chose the pitch angles to be 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), respectively. The designed metasurfaces were simulated by ANSYS HFSS, and the models and simulated results of the generated off-axis pseudo Bessel beams are shown in Figure 3.  
The normalized E-field amplitude distributions in Figure 3 show that the off-axis pseudo Bessel beams, which have the predetermined orientations, were generated successfully. As the energy is concentrated along the propagation axis without leakage in other directions, the method we use shows its effectiveness. To demonstrate the superiority of the proposed method, we can compare it with the traditional method, which realizes the off-axis pseudo Bessel beam by adding the compensation phases of the on-axis Bessel beam and the deflected beam. As the differences between these two methods will become more obvious when the pitch angle becomes larger, we set the pitch angle to be 60\({}^{\circ}\), and the other settings are just the same as in Figure 3. The normalized E-field amplitude distributions and corresponding compensation phase distributions of the off-axis pseudo Bessel beams using the two different methods are shown in Figure 4.  
Figure 2: Geometry (top view) of the designed unit cell and the reflection phase and reflection coefficient versus the length of \(R_{o}\) in an infinite periodic model with different incidence angles. It is easy to find that the compensation phase distributions of the two methods have the same trend, but the difference is also obvious.