  The efficient interaction between single photons and single matter objects in
free space is of key importance for quantum technologies. An experimental setup
for testing this possibility involves single two-level ion trapped at the focus
of a parabolic metallic mirror. We study the conditions for the setup, under
which the assumption about the free-space mode structure of the radiation field
in the vicinity of the atom is justified. In our analysis we apply vectorial
properties of light by including polarization degree of freedom. We look for
possible changes in the spontaneous emission rate of the atom resulting from
the presence of the parabolic boundary conditions.
