We optically excited the eigenmodes of an elliptic resonator in a semiconductor microcavity. Using a pulsed excitation, we created a superposition of eigenmodes, and imaged the temporal evolution of the coherent emission pattern. A semiconductor quantum well was embedded in the microcavity structure. The system was operated in the strong light matter coupling regime, where the eigenmodes are hybrid half-photonic half-excitonic quasiparticles called exciton polaritons. Oscillations between orbital angular momentum states (or vortex states) were observed, and turned out to be remarkably well described within the Poincaré sphere representation.