  Longitudinal electromagnetic fields generally become comparable with the
usually dominant transverse components in strongly-focussed, non-paraxial
beams. For optical vortex modes it is highlighted here how their angular
momentum properties produce longitudinal fields that in general must be
accounted for, even within the paraxial regime. First-order longitudinal
components of quantized Laguerre-Gaussian modes are derived and numerically
studied with respect to the paraxial parameter, highlighting light-matter and
spin-orbit interactions that stem from longitudinal fields of weakly-focussed,
paraxial beams in free space. New restrictions are cast on the validity of the
paraxial approximation for optical vortices interacting with atoms, molecules
and other nanostructures.
