  A novel design for a vectorial vortex beam launcher in the microwave regime
is devised. The beam is formed by launching a single guided transverse electric
(TE) mode of a metallic circular waveguide into free-space. Excitation is
achieved by the mean of an inserted coaxial loop antenna. Modal expansion
coefficients are computed, and the resulting electric and magnetic fields are
determined. The effect of the antenna location inside the waveguide on its
effective input impedance is modelled using transmission-line relations and
location for optimal matching is established. The analytical results are
confirmed using multi-level fast multipole method full-wave simulations.
