  The purity of an optical vortex beam depends on the spread of its energy
among different azimuthal and radial modes. The smaller is this spread, the
higher is the vortex purity and the more efficient are its creation and
detection. There are several methods to generate vortex beams with well-defined
orbital angular momentum but only few exist allowing to select a pure radial
mode. These typically consist of many optical elements with rather complex
arrangements, including active cavity resonators. Here we show that it is
possible to generate pure vortex beams using a single metasurface plate in
combination with a polarizer. We generalize an existing theory of independent
phase and amplitude control with birefringent nanopillars considering arbitrary
input polarization states. The high purity, sizeable creation efficiency and
impassable compactness make the presented approach a powerful complex amplitude
modulation tool for pure vortex generation, even in the case of large
topological charges.
