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In this experimental work, we optically excite the eigenmodes of an elliptical resonator in a semiconductor micro-cavity. Using a pulsed excitation, we create a superposition of eigenmodes, and image the time evolution of the coherent emission pattern. Oscillations between vortex and anti-vortex states are observed, and remarkably well described within the Poincar sphere representation for an eigenmode containing an orbital angular momentum. A semiconductor quantum well is embedded in the microcavity structure. The system is operated in the strong light matter coupling regime, where the eigenmodes are hybrid half-photonic half-excitonic quasiparticles called exciton polaritons.