  We show that propagating optical fields bearing an axial symmetry are not
truly hollow in spite of a null electric field on-axis. The result, obtained by
general arguments based upon the vectorial nature of electromagnetic fields, is
of particular significance in the situation of an extreme focusing, when the
paraxial approximation no longer holds. The rapid spatial variations of fields
with a "complicated" spatial structure are extensively analyzed in the general
case and for a Laguerre-Gauss beam 2 as well, notably for beams bearing a |l| =
2 orbital angular momentum for which a magnetic field and a gradient of the
electric field are present on-axis. We thus analyze the behavior of a atomic
size light-detector, sensitive as well to quadrupole electric transitions and
to magnetic dipole transitions, and apply it to the case of Laguerre-Gauss
beam. We detail how the mapping of such a beam depends on the nature and on the
specific orientation of the detector. We show also that the interplay of mixing
of polarization and topological charge, respectively associated to spin and
orbital momentum when the paraxial approximation holds, modifies the apparent
size of the beam in the focal plane. This even leads to a breaking of the
cylindrical symmetry in the case of a linearly polarized transverse electric
field.
