## 4 Metasurfaces for OAM Beam Generation
### Transmissive Metasurfaces
The unit cell has nearly the same polarization conversion efficiency as two double-headed arrow unit, but the amplitude is more stable when it is rotated. A transmission efficiency of 55% is achieved for the same OAM mode \(l=2\). An ultrathin unit cell was proposed in Reference [76] to generate high efficiency vortex beams. The unit consists of a cross-bar structure with positive permittivity and holey metallic ring resonator with negative permittivity on both sides of a dielectric substrate (Figure 12e). The transmission amplitude and phase can be controlled independently by the length of the cross bar. When the transmission phase in the two orthogonal directions has a phase difference of \(\pi\), 95% conversion efficiency of the cross-polarized component can be obtained at 10.6 GHz. The maximum excitation efficiency reaches 87% for OAM mode \(l=1\) and the overall thickness of the metasurface is only 0.07\(\lambda_{0}\). A nearly 100% efficiency photonic spin hall effect (PSHE) PB meta-atom named as ABA structure, with A and B representing two metal layers, was proposed in Reference [70]. The unit cell is composed of three metallic layers. Layer A is realized by an anisotropic resonator of rectangular patch while Layer B is realized by a holey metallic film coupled with a metallic bar (Figure 12f). The conversion efficiency could reach 91% at 10.5 GHz. Three vortex beam carrying OAM modes 1, 2, 3 were constructed by the ABA units in different metasurfaces of thickness 0.125\(\lambda_{0}\), respectively. The polarization state of EM wave can be set as a convenient switch to alter the different output wavefronts generated by bi-functional meta-devices. In Reference [77], the authors designed a multilayer unit cell that was inspired from the patch antenna (Figure 13a). The unit cell has five metallic layers and four dielectric layers. The top patch can couple the linear-polarized wave into the guided mode in the stripline structure, and the bottom patch decouples the guided wave into its cross-polarized component. Different transmission phase distributions are introduced by different length of the stripline with low transmission losses. Two metasurfaces of thickness 0.074\(\lambda_{0}\) with different OAM modes of 1 and 2 were designed through the transmission phase steps of 45\({}^{\circ}\) and 90\({}^{\circ}\), respectively. Due to the asymmetry of the polarization conversion, the metasurfaces were able to excite two opposite modes simultaneously, +1 and +2 modes for \(x\)-polarized wave and \(-1\) and \(-2\) modes for \(y\)-polarized wave at 5.14 GHz. An active metasurface to separately generate vortex beams carrying different modes is proposed in Reference [78] (Figure 13c). The unit cell consists of a patch and a metallic loop. Two varactor diodes are placed in the gaps between them which is controlled by a DC bias voltage with a low transmission loss. When the reverse voltage bias varies from 0 V to 30 V, the maximum voltage of the \(x\)-polarized wave is reached to 0.001 V.  
\(2\pi\) phase coverage can be easily obtained. Three different orders of OAM modes \(l=+1\), \(l=-1\) and \(l=0\) are separately excited at 5.35 GHz. The efficiency of the three modes are about 45%. In Reference [79], a multiplexed CP vortex beam generator is proposed by overlapping the phase masks of a harmonic spatial light modulator and spiral phase plates. The unit cell cascades three anisotropic impedance surfaces with custom-designed anisotropy to achieve high efficiency of circular polarization conversion, as shown in Figure 13b. A single vortex-beam PB transmitarray (\(l=1\)) was designed which could bend the wave towards the direction of a particular diffraction mode with a high purity. The efficiency of the generated vortex beams was 88% at 29.4 GHz and over 50% in a non-narrow bandwidth of 17%. A dual vortex beam transmitarray was designed by incorporating spiral phase profiles into a harmonic-response spatial light modulator with tailored intensity.