## 4 Metasurfaces for OAM Beam Generation
### Transmissive Metasurfaces  
For transmissive OAM metasurfaces, generation efficiency needs to be considered since there is no ground plane to reflect all energy. It has been demonstrated that only 25% efficiency can be achieved in a single layer structure due to no excitation of magnetic resonance [69; 70]. The design of a high efficiency transmissive metasurface is therefore a challenging problem that merits to be considered. Figure 11: Multiplexed OAM reflective metasurfaces. (**a**) Single linear polarization reflective metasurface to generate multiple vortex beams [65]. (**b**) Circular polarized (CP) wave decoupling to achieve multiplexed vortex beams [66]. (**c**) Full polarization multi-beams [67]. (**d**) A decoupling method to generate dual CP vortex beams at different frequencies [68]. A unit cell consisting of a cylindrical dielectric resonator and a metallic rod to manipulate the EM wavefront was proposed in Reference [71]. The metallic rod provides the necessary broadband electric polarization, and the cylindrical dielectric resonator provides the necessary broadband magnetic polarization. By tuning the unit parameters, 2\(\pi\) phase shift can be covered with high transmission magnitude. According to the concept of gradient phase discontinuity, a vortex beam carrying an OAM mode \(l=1\) can be generated by the flat spiral gradient phase with high efficiency at in the 8 GHz-9.8 GHz frequency band. However, to have strong electric and magnetic resonances, the length of the cylindrical rod must not be too short. The overall thickness of the metasurface is 10 mm (0.3\(\lambda_{0}\)). Miniaturized element frequency selective surfaces (MEFSS) were proposed to generate high efficiency vortex beams in Reference [72]. The elementary cell is composed of four layers of patches and three layers of wire grids alternately separated by dielectric substrates (Figure 12a). The patches are considered as capacitors while the wire grids are considered as inductors. The cascading distance can be effectively reduced by the strong coupling of the two kind of components. By tuning the size of patches, eight unit cells can be obtained with a transmission phase gradient of 45\({}^{\circ}\) and nearly 100% efficiency at 10.6 GHz. Even though the amplitude is non-uniform, the efficiency of vortex beams with \(l=1\) exceeds 60% in the 10 GHz-11.3 GHz frequency band. The overall thickness is only 0.15\(\lambda_{0}\). A subwavelength scatterer based on photon spin Hall effect (PSHE) to generate high efficiency OAM waves was proposed in Reference [73]. The proposed unit cell consists of two double-headed arrows printed on the top and bottom of the dielectric substrate (Figure 12b). By introducing the magnetic resonance, the unit cell can effectively convert CP wave to its cross-polarized component in transmission. The conversion efficiency attains 84.6% at 10 GHz. However, when the unit cell is rotated to introduce PB phase, the amplitude of cross-polarized component cannot be kept constant, resulting in a reduction of the efficiency of the vortex beams excitation. The metasurface generating vortex beams with \(l=2\) presents an efficiency of 45% with a thickness of 0.05\(\lambda_{0}\). In Ref. [74], a unit cell consisting of complementary split ring resonators (CSRRs) for full phase control in a 0.8 mm (0.05\(\lambda_{0}\)) thick metasurface was presented (Figure 12c). The proposed unit cell transmits a circularly polarized wave to its cross-polarized component with a high efficiency of 81%. The calculated conversion efficiency of OAM beams with \(l=1\) in the transmitted wave is up to 81.8% while the total transmission efficiency is only 15.2% and it becomes lower for higher modes. This is mainly due to the fact that compared to the whole metasurface, the scatterers are too few to satisfy the periodicity along \(x\)- and \(y\)-directions. In Reference [75], the efficiency was enhanced by dual-layer Z-shaped metallic patterns shown in Figure 12d.