## 4 Metasurfaces for OAM Beam Generation
### Divergence Reduction of OAM Vortex Beams  
Vortex waves present divergence characteristics in propagation, which become worse when the OAM topological order increases and also when propagation distance increases. It might limit the practical applications of vortex beams for long distance communications or transmitting systems. A common solution is to converge the vortex beam. However, the limitation of this method is that it can only focus the beam to a point close to the metasurface rather than propagating over a long distance. In Reference [47], a flat metalens was proposed to collimate the vortex waves (Figure 14a). The converging lens system is excited by an OAM beam generator composed of a conventional circular patch antenna array source consisting of eight patches with the same phase shift between each of the neighboring elements. The metasurface is placed at a distance \(2\lambda\) above the antenna source to compensate the phase of vortex beams. The divergence characteristics of vortex beams are obviously improved as they transmit through the metalens around 10 GHz frequency. Meanwhile, the propagation directivity and gain are also enhanced from 9 dBi to 15 dBi. The transmission efficiency is over 75% and reaches 88.14% at 10 GHz. Moreover, the purity of OAM mode \(l=1\) is degraded by only 1%. In Reference [50], a broadband all-dielectric 3D-printed cylindrical collimating lens was proposed to solve the divergence characteristics drawback of vortex beams (Figure 14b). The design comes from the transformation optics concept. By solving the transformation equations of Laguerre-Gaussian (LG) to high-order Bessel (HOB) beam, the permittivity distribution of the metamaterial medium is obtained. The equivalent permittivity was varied by considering air holes in a bulk dielectric medium. The permittivity decreases when the radius of the cylindrical cavity increases. The divergence angle and diameter of the vortex beams can be greatly reduced through the metamaterial medium. The frequency bandwidth was about 8 GHz around 10 GHz operating frequency thanks to the use of all-dielectric non-resonant unit cells.  
The integration of the vortex beam excitation and the non-diffraction function can be realized by phase compensation. In Reference [81], a reflective metasurface was presented to generate a non-diffractive Bessel beam carrying OAM modes. The system consists of three parts; a circular cavity  
Figure 14: Non-diffraction OAM metasurfaces and metamaterials. (**a**) A collimating metalens [47]. (**b**) A collimating all-dielectric metamaterial medium [50]. (**c**) A metasurface to generate non-diffraction vortex beams and convert the polarization of the LP wave [81]. (**d**) A converging OAM metasurface and a non-diffracting OAM metasurface [82].  
backed substrate-integrated waveguide (SIW) source, a polarizer, and the metasurface, as shown in Figure 14c. The metasurface converts the linear polarized incident wave to its cross-polarized component carrying non-diffraction vortex beams at 40.25 GHz. In Reference [82], the authors proposed a general scheme to optimize the divergence constraints of vortex beams (Figure 14d). Firstly, the converging phase distribution has been imposed into the vortex beam, which can effectively focus the OAM with required mode into preset plane, where the radius of converged vortex beam in focal plane can be decreased by nearly four times. This focused OAM can be effectively applied in communication systems, where the propagation distance is specifically fixed. On the other hand, the spatial phase profile of Bessel beam has been added into a vortex beam, which can produce quasi-non-diffractive OAM beam within a long propagation distance. It can be obviously seen that the combination with different functional wavefronts can effectively optimize the divergent property of traditional vortex beam, and realize OAM carrying new and useful properties.