# Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces
## 1 Introduction
Although there are various designs in different types and suitable for different application scenarios, the design principles for OAM generation lead to one common rule: the introduction of the azimuthal phase term \(e^{il\phi}\) to EM waves. Generally, they fall into two categories: independent and dependent on the wave polarization. The first scheme employs isotropic materials, such as SPPs, CGHs. \(e^{il\phi}\) is introduced in a SPP based on the accumulated spatially varying optical path [43; 44; 45]. They are usually implemented at optical frequencies. At lower frequencies, the device would become bulky unless some flatten techniques are employed [46; 47; 48]. CGHs are diffractive optical elements and they produce light with different OAMs according to the diffraction orders [49; 50; 51; 52]. Alternatively, the excitation of an antenna or antenna array can be modulated directly to satisfy the required phase condition so that an OAM wave can be radiated out [53; 54]. \(e^{il\phi}\) can also be produced based on the abrupt phase shift at scatterers on a metasurface. By varying the geometry of the scatterer, its resonant frequency is changed so that the phase shift varies at the designed frequency. A total \(2\pi\) phase shift is achieved after optimization; and successful generation of different OAM states has been reported in [55; 56]. Lately, tunable scatterers loaded by varactor diodes are proposed for convenient multiple OAM-mode generation [57]. Scatterers can also be made anisotropic to achieve independent control of different polarizations. However, even if the response of scatterers is polarization dependent, the helicity of the produced OAM does not depend on the polarization state of incident wave. In other words, the helicity is fixed. While for the second scheme, it is an opposite scenario. The second scheme is based on the conversion and coupling between SAM and OAM. This process occurs in inhomogeneous and anisotropic media, such as q plates [58; 59]. Q plates shift the circular polarization state from left to right or right to left and have spatially varying optical axis [60]. Their behaviors can be explained by AM conservation law. The flip of the circular polarization state indicates a change of \(\pm 2\hbar\) in SAM. When the q plate is cylindrically symmetric, the total AM is conserved so that the output wave must carry an OAM of \(\mp 2\hbar\). When the q plate is not cylindrically symmetric, it introduces extra AM to the system so that different orders of OAM can be generated in the output wave. Q plates are usually made by liquid crystals, owning to their flexibility and anisotropic properties. By tuning the temperature or external voltage, the birefringent retardation in liquid crystals varies, so that the conversion efficiency can be tuned [61; 62]. The maximum efficiency is obtained when the retardation is \(\pi\). Metasurfaces have been used to implement the feature of q plates [63; 64; 65; 66; 67]. The flip of the circular polarization state achieved by anisotropic scatterers and rotation of the scatterers is an analogue to the rotation of optical axis of a q plate, along with the introduction of geometric phase. Therefore, this type of metasurfaces is known as geometric-phase metasurfaces. Unlike the metasurfaces employing the first scheme, geometric-phase metasurfaces produce OAM along with the change of the polarization state of the output wave, which is fundamentally different from the first scheme. The hardness of the produced OAM depends on the incident SAM. Hence, geometric-phase metasurfaces show their high flexibility in the manipulation of OAM because they enable the coupling and interchange between SAM and OAM. In communications, detection of OAM at the receiver side is required. Although OAM detection is just a reciprocal process of OAM generation, it is much more challenging due to the degraded OAM states after the propagation.