## 4 Metasurfaces for OAM Beam Generation
### Reflective Metasurfaces  
In Reference [51], a propagation phase reflective metasurface is designed to effectively generate single vortex beam with orbital angular momentum in the radiofrequency domain, as shown in Figure 8a. The unit cell consists of three patch dipoles. By controlling the length of the three patches and the distance between them, the reflected wave has a continuous reflection phase range of more than \(2\pi\). Based on the proposed unit cell, a reflective metasurface with \(20\times 20\) elements is designed to generate vortex beam carrying an OAM mode with topological charge \(l=2\) at 5.8 GHz. A metasurface composed of ring-surrounded bowtie patch resonators is proposed in [52]. The structure is inspired by the bowtie antenna which has wideband characteristics (Figure 8b). A linear phase variation is obtained when varying the radius of the bowtie patch under TM wave incidence. Several metasurfaces have been designed to generate OAM modes with \(l=0\), \(1\), \(2\) over about 3 GHz bandwidth. Single layer resonant structures are easy to fabricate, but the phase varies drastically at the resonant frequency, resulting usually in a narrow bandwidth. In Reference [53], double-layered elements are used to design MS for the generation of broadband vortex beams. The unit cell is composed of two square patches separated by a dielectric substrate instead of only one patch in a single layer structure, as illustrated in Figure 8c. For one patch element, a strong magnetic resonance occurs between the patch and ground plane of the reflective MS, while for double-layered element, the magnetic resonance is due to the interaction between the two patches and the ground plane for low frequency and to the interaction between mainly the two patches for high frequency. Therefore, the phase response is more flat and the operational bandwidth is enhanced. The proposed metasurface generates vortex beams carrying an OAM mode \(l=1\) in the 8.5 GHz-11.5 GHz frequency range. Due to limitation of unit cell topology, the metasurface in [51] and [52]  
Figure 8: Reflective OAM metasurfaces based on propagation phase. (**a**) Linear polarized (LP) vortex beams [51]. (**b**) Wideband linear polarized vortex beams [52]. (**c**) Double-layered unit for wideband vortex beams [53]. (**d**) Polarization insensitivity OAM metasurfaces [54]. can only operate under single polarized incident waves. By properly designing the elementary cell pattern (Figure 8d), a polarization-insensitive OAM metasurface is proposed in [54]. Two concentric rings guarantee structural symmetry when introducing enough phase-shift range. The spiral phase distribution is realized by changing the radius of the inner and outer rings. A reflectarray-type prototype with \(l=1\) is fabricated to demonstrate the design at 5.8 GHz. The phase shift of the metasurfaces in [51; 52; 53; 54] can be controlled not only through varying structure parameters to introduce propagation phase, but also through rotation of the orientation of the meta-atom to introduce geometric phase. Compared to propagation phase, geometric phase which is usually called Pancharatnam-Berry (PB) phase is easier to implement. When the unit cell is rotated, the emitted phase of the cross-polarized component will have a phase shift as twice as the rotated angle under circular polarized (CP) incident wave. Therefore, only single-sized unit cell is needed which has the ability to convert CP wave to its cross polarization rather than a plurality of different-sized unit cells [55; 56; 57; 58; 59]. Besides, the unit cells with different rotation angles have the same dispersion characteristics and hence, the bandwidth of the vortex beams are usually broad. In Reference [55], an ultra-broadband reflective metasurface based on PB phase to generate vortex beams is proposed. A double arrow-shaped metallic layer is applied to achieve perfect CP wave conversion (Figure 9a). The metasurface presents an efficiency of 75.76% to excite vortex beams with OAM mode \(l=2\) in the 12 GHz-18 GHz frequency range.