  Neglecting the electric field component along the light's propagation
direction is a common practice, known as paraxial approximation. However,
experimental evidence and theory on the head-on excitation of atoms by
Laguerre-Gaussian beams reveal that the full vector character of the light
field has to be taken into account. Optical vortices are a large family of
fields, being Laguerre-Gaussian only one particular case. Now we extend the
study of the applicability of the paraxial approximation to a broader set of
optical vortices by considering the interaction of atoms with generalized
Laguerre-Gaussian and generalized Bessel beams. We demonstrate that all vortex
beams here considered look the same close to the beam axis, where the atom is
placed. From this, we conclude that the paraxial approximation fails for the
large set of vortex beams, and that a full understanding of the interaction of
optical vortices with atoms requires the inclusion of all vector components of
the electric field.
