  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 neglect 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 polarisation basis, we can sculpt any vortex beam in phase and
amplitude. We characterize the azimuthal and radial purity of the generated
vortex beams, reaching a purity of 98% for a vortex beam with $\ell=50$ and
$p=0$. Furthermore, we comparatively show that the purity of the generated
vortex beams outperform 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.
