Generation of pure Laguerre-Gaussian vector beams on the higher-order Poincaré sphere by hollow Gaussian beams through dielectric metasurfaces

Abstract It is a longstanding challenge for the extracavity generation of vector beams (VBs) to have pure Laguerre-Gaussian (LG) modes due to diffraction. Here we propose theoretically and realize experimentally the generation of pure LG VBs by using hollow Gaussian beams (HGBs) through q -plates. A general expression for the VB generated by the HGB with arbitrary polarization is derived. It is found that when the order of the HGB is two times the topological charge of the q -plate, the VB possesses a pure LG mode and that any desired polarization distribution on the higher-order Poincare sphere can be realized by tuning the incident polarization. Further we implement the q -plates with dielectric metasurfaces and experimentally verify the theoretical results. The generated pure LG VB may find applications in the situations where high mode purity is required.