## 3 Results and Discussion
### Multichannel FOV Generation and Detection  
A transmission-mode multichannel FOV (MCFOV) generator design principle based on metasurfaces is demonstrated. The phase distribution profile \(\phi_{m}(x,y)\) of the MCFOV generator of the _x-y_ cross section at z = 0 is the synthetic phase of the multiple FOV beam interference.  
\[\phi_{m}(x,y)\ =\ arg(\sum_{i\ =\ 1}^{n}E_{i}(x,y)e^{ip_{i}}) \tag{5}\]  
\[\theta(x,y)\ =\ \phi_{m}(x,y)/2 \tag{6}\]  
where  
\[\varphi_{i}(x,y)\ =\ -\frac{2\pi}{\lambda}(\sqrt{(x-x_{i})^{2}+(y-y_{i})^{2}+f^{2 }}-\sqrt{x_{i}^{2}+y_{i}^{2}+f^{2}})+l_{i}\times\arctan(\frac{y}{x}) \tag{7}\]  
Here, \(E_{i}(x,y)\) is the amplitude distribution of the \(i^{th}\) targeted beam, \(\varphi_{i}\) is the phase profile of the \(i^{th}\) targeted beam, where these two factors determine the intensity distribution of the transmitted light beam in the focal plane, \(l_{i}\) is the topological charge number of the \(i^{th}\) targeted beam, \(f\) is the distance between the metasurface and the focal plane, \((x_{i},y_{i})\) is the \(i^{th}\) designed coordinate of the focal spot in the focal plane, and \(n\) is the total number of the targeted beam. It is worth mentioning that if the metasurface is large enough, both \(n\) and \(||\) can be any arbitrary large positive integer. Here, for simplicity, we assume that \(n\) = 5, \(E_{i}\ =\ \sqrt{1/n}\), and \(l\ =\ [-2,-1,0,1,2]\). Through adjusting the rotation angle \(\theta(x,y)\) of optimized nanobars on the metasurface, the design of the MCFOV can be obtained.  
As schematically depicted in Figure 6a, the elaborately designed metasurface with a radius of 6 \(\upmu\)m can generate five-channel FOV beams with topological charges from \(-2\) to \(2\) under the RCP plane wave incidence at 355 nm. The corresponding focal spots are generated on the focal plane 10 \(\upmu\)m away from the metasurface. The simulated result of the multichannel FOV generator is shown in Figure 6a. The topological charges change from \(-2\) to \(2\), and the corresponding focal spots are located at \((0,-3\upmu\)m), \((-3\upmu\)m, \(0)\), \((0,0)\), \((3\upmu\)m, \(0)\), \((0,3\upmu\)m) on the focal plane, respectively. This device can realize a high efficiency of over 12% in every channel, which is much higher than the previous work [39].  
Figure 6: Numerical simulated result of a multichannel FOV generator operating in transmission mode. (**a**) The RCP incident wave illuminates the generator along the positive _z_-axis and divides into five FOV beams with different orbital angular momentum (OAM) values. (**b-e**) The incident waves with different topological charge numbers of (**b**) \(l\) = 1, (**c**) \(l\) = \(-1\), (**d**) \(l\) = 2, and (**e**) \(l\) = \(-2\) illuminate the generator. (**b-e**) The corresponding intensity profiles on the focal plane at \(z\ =\ 10\ \upmu\)Besides, the designed metasurface is capable of interacting with incident OV beams. These OV beams can be obtained by a traditional OV generator [8] and a metasurface. When the OV beam with topological charge \(l\ =\ l_{in}\), illustrated in the metasurface mentioned above, the transmitted beam carries the orbital angular momentum (OAM) \(l_{out}\hbar\ =\ (l_{in}+l_{i})\hbar\), where \(\hbar\) is the reduced [PERSON]'s constant. The annihilation of the OAM occurs when \(l_{out}\) equals zero, resulting in a solid spot on the focal plane. One can identify the OAM of the incidence by recognizing the solid spot's position according to the metasurface design. For better understanding, the previously designed metasurface is illuminated by normal incident RCP OV beams (RCP plane wave with a phase evolution in the form of \(e^{i\theta}\)) with different topological charges from \(-2\) to \(2\) and the corresponding simulation results are shown in Figure 6b-e, respectively. It is necessary to mention that an optical vortex with a larger topological charge can be identified with more sizeable metasurfaces.