## 4 Metasurfaces for OAM Beam Generation
### Reflective Metasurfaces
Such a coding metasurface with OAM mode \(l=1\) was fabricated to demonstrate the effectiveness of the concept at 6 GHz and is shown in Figure 10a. A tunable metasurface generating vortex beams with any OAM modes is proposed in Reference [62]. A positive intrinsic negative (PIN) diode is utilized as a switch between the two rectangular patches constituting the unit cell of the metasurface, as presented in Figure 10b. The two states \"0\" and \"1\" are realized by switching the PIN diode, controlled by direct current (DC) voltage, to ON and OFF states. Therefore, any OAM mode can be realized by switching the states of each unit cells judiciously on the metasurface. In Reference [63], a multiple OAM vortex beams is generated by one-bit coding metasurface. Combining the phase distribution of vortex beam with the phase distribution required for beam steering functionality, the incident energy can be redirected into desired directions. Due to the periodic variation of the phase, \(0^{\circ}\) phase is also regarded as \(2\pi\) phase. In other words, the variation of phase from 0 to \(\pi\) also means variation of phase from \(2\pi\) to \(\pi\). Therefore, for one-bit coding beam steering, a vortex beam will reflect into two opposite directions under normally incident plane wave. The cross-dipole structure is utilized to manipulate \(x\)-polarized and \(y\)-polarized wave, respectively (Figure 10c). Then, by combining the coding of two orthogonal directions, the incident waves are simultaneously converted to vortex beams with \(l=\pm 1\) and \(l=\pm 2\) in different directions at 8.5 GHz. Another method to design coding OAM metasurface based on polarization bit was proposed in Reference [64]. The unit cell can cover \(2\pi\) reflection phase for linearly polarized waves by adjusting each parameter (Figure 10d). Besides, when rotating the structure by \(\pm 45^{\circ}\), the polarization state of the reflected wave is converted to its cross-polarized component. The metasurface is divided into two regions: inner region and outer region. Each region determines whether to convert the polarizations of incident beam or not and modulate the OAM modes into the reflected beam. Under illuminating \(x\)-polarized wave, two vortex beams carrying OAM modes \(l=1\) and \(l=2\) in the \(x\)- and \(y\)- polarized component can be clearly observed at 15 GHz, respectively. To enhance the information capacity of a metasurface, a single linear polarization reflective metasurface generating multiple vortex beams with different OAM modes in different directions was proposed in Reference [65]. The unit cell consists of only one patch element, as shown in Figure 11a. The reflected phase has a continuous change when the length of patch is increased or decreased. When vortex beams with different OAM modes are excited in the same direction, the mode order will be the sum of them. Therefore, different vortex beams can only be generated in different directions. Besides, interference may occur if the beams are close to each other. By compensating the phase of different OAM modes and diffraction direction, the metasurface generates two vortex beams with \(l=2\) in opposite propagation directions (\(\theta=\pm 30^{\circ}\)). The operational frequency range of the metasurface spans from 5.5 GHz to 6.5 GHz. Another way to expand the channel capacity is to control the polarization of wave freely. For linear polarized wave, it can be easily realized by a unit cell that can control phase shift for \(x\)- and \(y\)-polarized waves independently. However, for CP wave, it is hard to control LHCP and RHCP independently when only geometric phase is utilized because they are constrained to be conjugate values in the electric field form. In other words, vortex beams will have opposite mode number for LHCP and RHCP. To overcome the limitation, a metasurface merges propagation phase and geometric phase together in Reference [66].