## 4 Metasurfaces for OAM Beam Generation
### Reflective Metasurfaces
The N-shaped resonator based on PB phase is employed to achieve nearly 100% conversion efficiency in Reference [56]. The unit cell is suitable for broadband design which transmits 98% energy of incident CP wave to its cross-polarized wave (Figure 9b). Besides, when the incident angle varies from 0\({}^{\circ}\) to 50\({}^{\circ}\), the conversion efficiency is higher than 90% in 8 GHz frequency bandwidth. The metasurface generates vortex beams with OAM mode \(l=1\) from 12 GHz to 18 GHz. Similarly, the polarization conversion bandwidth can also be expanded with a double layer unit cell. Figure 9: Reflective OAM metasurfaces based on geometric (PB) phase. (**a**) Double arrow-shaped metasurface [55]. (**b**) N-shaped resonator metasurface [56]. (**c**) Double-layered cross dipoles metasurface for a wideband vortex beams [57]. (**d**) OAM metasurface based on perfect electric conductor-perfect magnetic conductor (PEC-PMC) elements [60]. A dual-layer meta-atom that can manipulate phase shift independently for \(x\)- and \(y\)-polarized waves is proposed in Reference [57]. The unit cell consists of five symmetric parallel dipoles with different parameters in each layer, as shown in Figure 9c. The reflection phase can be controlled independently without much crosstalk by arranging the dual-layer orthogonally. It is much easy to achieve CP wave polarization conversion over large bandwidth. The bandwidth of the metasurface generating vortex beams with OAM mode \(l=1\) ranges from 6.95 GHz to 18 GHz. A perfect electric conductor-perfect magnetic conductor (PEC-PMC) anisotropic metasurface for OAM generation is proposed in Reference [60] and is illustrated in Figure 9d. The top surface of the unit cell acts as a PEC surface which consists of two metal strips behaving like a parallel-plate waveguide. The \(x\)-polarized wave is totally reflected with an offset phase of \(\pi\), while the \(y\)-polarized wave will transmit through it. The bottom surface acts as a PMC surface which is realized by the mushroom-like high-impedance surface. It reflects the \(y\)-polarized wave with zero phase shift. In this way, the unit can realize the perfect polarization conversion of CP wave. Two types of metasurface carrying an OAM mode \(l=2\), consisting of azimuthally continuous loops and azimuthally discontinuous loops, are designed based on the proposed unit cell. It can be observed that the continuous one shows smoother phase distribution than the discontinuous one. A series of unit cells with continuous phase shift constitutes some difficulties in the design process. Though the introduction of PB phase can simplify the design, it can only operate under CP wave. Recently, digital metamaterials have been presented to create a new connection between the physical structure and digital information. The beams can carry specific information with only a few unit cells by digital coding. When the concept comes to the two-dimensional metasurface, the coding can be implemented by the reflected or transmitted phase and amplitude of the unit cells. The simplest one-bit code can be realized by the reflection phases \(0^{\circ}\) and \(180^{\circ}\). A one-bit coding metasurface was proposed to generate vortex beams in Reference [61]. The elementary cell is composed of a metallic patch and a metallic ground plane printed on the two faces of a dielectric substrate. The reflection phase of two unit cells are \(0^{\circ}\) and \(180^{\circ}\), respectively. The reduction of the coding number does not influence the divergence angle of main lobe, but the existence of quantization error will raise the side lobes. Besides, the one-bit quantization method does not have enough resolution to generate the vortex beam without any additional compensation in the normal direction for plane wave incidence. However, if other phase profiles, such as the spherical wave phase, are introduced into the vortex beam, then the quantization error will show pseudo-random distribution.