Spin- and orbital-Hall effect in cyclic group symmetric metasurface
  Light possesses both spin and orbital angular momentum (AM). While spin AM is determined by helicity of circular-polarization, orbital AM is characterized by topological charge of vortex beam. Interaction of AM with optical beam orbit leads to optical spin Hall or orbital Hall effect, exhibited as spin-dependent or topological charge-dependent transverse shift of optical beam. Conservation of AM enables spin-to-orbital AM conversion, where circular-polarized Gaussian beam is converted to opposite-helicity circular-polarized vortex beam with topological charge $\pm 2$, an example of controlling spatial beam profiling by spin flip. However, the resultant vortex beam has the beam center of gravity unchanged, the same as that of incident Gaussian beam, meaning a null transverse shift. Here we introduce a cyclic group symmetric metasurface to demonstrate generation of vortex beam exhibiting spin-dependent transverse shift, namely, spin- and orbital-Hall effect, attributed to an alteration of dynamical phase of scattered beam according to the order $n$ of cyclic group while keeping geometric phase constant. Capability of spin-controlled spatial beam profiling with a transverse shift via spin- and orbital-Hall effect has important implications for spatial demultiplexing in optical communication utilizing orbital AM mode division multiplexing as well as for optical vortex tweezer and signal processing involving vortex beams. 
Yeon Ui Lee, Igor Ozerov, Frederic Bedu, Ji Su Kim, Frederic Fages,   Jeong Weon Wu
physics.optics