Optical centroid ellipses beyond polarization ellipses

Polarization ellipses are well-known as the result of coherent superposition of photonic spin states. As orbital counterparts, in this Letter, we introduce centroid ellipses that are geometrically mapped from optical orbital angular momentum (OAM) superpositions on a modal Poincaré sphere (PS) by coaxial interference. Different from not easily observable polarization ellipses, these centroid ellipses can be directly observed from dynamical interferograms with broken rotational symmetry. We demonstrate the results of a proof-of-concept experiment and the complete quantification of arbitrary OAM superpositions on the first- and second-order modal PSs, respectively, using modal Stokes parameters inferred from centroid ellipses. Our findings provide a unified geometric perspective into optical angular momenta and may offer new opportunities to develop high-dimensional optical metrology based on these detectable centroid ellipses.