# Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces
## 3 Metasurfaces for OAM Generation
### Artifical PEC-PMC Metasurface  
We propose a composite perfect electric conductor (PEC)-perfect magnetic conductor (PMC)-based anisotropic metasurface [84]. A PEC surface is designed for \(x\) polarization so we have \(J_{xx}=-1\). An artificial PMC surface is put beneath the PEC surface so that \(J_{yy}=1\) is satisfied. The proposed novel metasurface is depicted in Figure 1. The metasurface has two dielectric layers and a ground plane. It is composed of scatterers shown in Figure 1b. The metal strips on the top layer function as a parallel plate waveguide and allow the perfect transmission of \(y\) polarized wave while the \(x\) polarized wave will be totally reflected with \(\pi\) phase shift. The metal patch in middle together with the via and ground plane forms the well-known mushroom-like high-impedance surface. By operating at its resonant frequency, it can be considered as a PMC surface and will reflect the transmitted \(y\) polarized wave from the metal strips with a zero phase shift. The whole metasurface is built by distributing the scatterers with varying orientations according to their azimuthal locations. It should be noted that the mushroom-like high-impedance surface is isotropic, therefore, there is no need to change the orientations of mushrooms. For the PEC surface, by setting the rotation angle \(\alpha=\phi\), rotation of the strips will lead to a series of concentric loops. The resultant generated OAM order is 2 or \(-2\), where the sign depends on the incident circular polarization state. The metasurface is designed at 6.2 GHz and can be conveniently fabricated using printed circuit board (PCB) technique. Full-wave simulation was done in CST MWS. The right circularly polarized plane wave is used as incident wave. Figure 2 shows the amplitude and phase distributions of the reflected electric fields at a transverse plane of \(z=20\) mm. An amplitude null can be observed in Figure 2a, which results from the phase singularity at the center for an OAM-carrying wave. In Figure 2b, the phase accumulated along a full circular path around the center is \(4\pi\), indicating an OAM of order \(-2\). A unique feature for the PEC-PMC metasurface is that the scatterers on top layer are not on resonance or discrete but continuously connected. Thus, the near-field pattern is quite smooth without any evanescent field component scattered by discrete scatterers. For the generation of OAM of other orders, a similar PEC-PMC metasurface but with discrete dipole scatterers on the top layer is proposed. The dipoles are designed to totally reflect the \(x\) polarized wave with \(\pi\) phase shift at 6.2 GHz. Two cases for generation of OAM of order \(-2\) and \(-4\) are shown in Figure 3. The amplitude and phase of the reflected field are drawn at a transverse plane of \(z=40\) mm. The distributed dipole scatterers are also depicted in Figure 3a,c. The field patterns verify the desired OAMs have been generated. However, due to the influence of the discrete dipoles, the amplitude  
Figure 1: Schematic pattern of the perfect electric conductor (PEC)-perfect magnetic conductor (PMC) anisotropic metasurface for orbital angular momentum (OAM) generation. With a nearly 100% conversion efficiency, the metasurface perfectly converts a left (right) circularly polarized plane wave carrying zero OAM to a right (left) circularly polarized vortex beam carrying \(\pm 2\hbar\) OAM: (**a**) Top view of the whole metasurface; (**b**,**c**) A scatterer in the metasurface. The scatterer is composed of artificial PEC (purple) and PMC (blue and red) surfaces. The period of the scatterer is \(p=7\) mm. The permittivity and thickness of the dielectric substrate are set to \(\epsilon_{r}=2.2\), \(d_{1}=2\) mm and \(d_{2}=3\) mm. For the artificial PEC surface (top-right inset), the width and gap for the strip is \(t=1\) mm and \(g=2.5\) mm, respectively. For the mushroom-based artificial PMC surface (bottom-right inset), the square patch size is \(a=6\) mm.