To exploit the full potential of the transverse spatial
structure
of light using the Laguerre–Gaussian basis, it is necessary
to control the azimuthal and radial components of the photons. Vortex
phase elements are commonly used to generate these modes of light,
offering precise control over the azimuthal index but neglecting the
radially dependent amplitude term, which defines their associated
corresponding transverse profile. Here, we experimentally demonstrate
the generation of high-purity Laguerre–Gaussian beams with
a single-step on-axis transformation implemented with a dielectric
phase-amplitude metasurface. By vectorially structuring the input
beam and projecting it onto an orthogonal polarization basis, we can
sculpt any vortex beam in phase and amplitude. We characterize the
azimuthal and radial purities of the generated vortex beams, reaching
a purity of 98% for a vortex beam with l =50 and p = 0. Furthermore, we comparatively show that the purity
of the generated vortex beams outperforms those generated with other
well-established phase-only metasurface approaches. In addition, we
highlight the formation of “ghost” orbital angular momentum
orders from azimuthal gratings (analogous to ghost orders in ruled
gratings), which have not been widely studied to date. Our work brings
higher-order vortex beams and their unlimited potential within reach
of wide adoption.