# Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces
## 1 Introduction  
It is well known that electromagnetic (EM) wave carries linear momentum which is associated with the poynting vector. Besides the linear momentum, EM wave has been demonstrated to possess angular momentum (AM), including spin angular momentum (SAM) and orbital angular momentum (OAM) [1]. Circularly polarized wave carries SAM. The SAM is \(\hbar\) per photon for left-handed circular polarization (LHCP) and \(-\hbar\) per photon for right-handed circular polarization (RHCP), where \(\hbar\) is the reduced Planck constant. The SAM characterizes the spin feature of photon. Different from the SAM, OAM manifests the orbital rotation of photon and each photon has an OAM of \(l\hbar\), where \(l\) is known as the OAM index and can be any integer. Different values of \(l\) correspond to mutually orthogonal OAM states and the number of allowable OAM states for photons is unbounded. Different OAM states have been used to encode information in communications to enhance the channel capacity, both in free space [2; 3; 4; 5; 6; 7; 8; 9] and optical fibers [10]. The main problem of practical application of OAM in communications is the significant crosstalk between OAM modes [11; 12]. The spatial-dependence and divergency nature of OAM-carrying waves result in the their vulnerability to the atmosphere [13; 14] and limited power received at the receiver side [15]. All these facts will degrade the purity of OAM modes. Still, OAM offers a new attractive degree of freedom to EM waves, extending beyond the existing wave features. The optical vortices of OAM beams also find their applications in super resolution imaging [16; 17]. OAM can be transferred to particles, which has been applied in optical tweezers [18; 19; 20]. The exchange of OAM with matter can also be utilized in detecting the rotation of particles [21]. In quantum mechanics, at a single-photon level, OAM modes can be utilized for high-dimensional entanglement [22; 23]. Overall, OAM has received great attentions in multidisciplinary research areas [24; 25; 26; 27]. Since OAM has great potentials in various applications, research has been undertaken extensively on its generation. In 1992, [PERSON] et al. first found that a Laguerre-Gaussian (LG) beam with helical wavefront carries well defined OAM [28]. That beam possesses an azimuthal phase term, \(e^{il\phi}\), where \(\phi\) is the azimuthal angle. Before that, [PERSON] et al. created structured light with helical wavefront byforked gratings [29]. This grating forms the basis of the computer generated holograms (CGHs) for producing light beams with OAM. Afterwards, many other devices for OAM generation have been proposed, such as the cylindrical lens in 1993 [30], spiral phase plates (SPPs) in 1994 [31], q plates in 2006 [32]. Lately, OAM has been analyzed at radio frequencies. Antenna arrays [33], traveling-wave antennas [34] and circularly polarized patch antennas [35] which radiate EM waves carrying OAM have been demonstrated. Recent advances in versatile metasurfaces also expedite powerful and convenient design routes for OAM generation [36; 37; 38; 39]. The concept of metasurface originates from the conventional frequency selective surfaces (FSSs) [40]. They are composed of man-made subwavelength scatterers with varying geometry and orientation. Therefore, they go beyond the conventional FSSs due to the high feasibility of tailoring the geometry and orientation of the ultracompact scatterers. Metasurfaces locally alter the wave properties by the abrupt phase change at the scatterers. By varying the geometry or orientation, scatterers can cover a total \(2\pi\) phase shift so that arbitrary beam forming can be achieved. Meanwhile, scatterers can be designed to simultaneously change the wave amplitude [41]. Besides the electric response, they can have the magnetic response. Scatterers have both electric and magnetic responses form the Huygens metasurface [42]. The magnetic response helps to compensate the impedance mismatch at the metasurface interface so that nearly perfect efficiency can be achieved.