  We resonantly excite exciton-polariton states confined in cylindrical traps.
Using a homodyne detection setup, we are able to image the phase and amplitude
of the confined polariton states. We evidence the excitation of vortex states,
carrying an integer angular orbital momentum m, analogous to the transverse
TEM01* "donut" mode of cylindrically symmetric optical resonators. Tuning the
excitation conditions allows us to select the charge of the vortex. In this
way, the injection of singly charged (m = 1 & m = -1) and doubly charged (m =
2) polariton vortices is shown. This work demonstrates the potential of
in-plane confinement coupled with selective excitation for the topological
tailoring of polariton wavefunctions.
