Observation of the topological aberrations of twisted light

When reflected from an interface, a laser beam generally drifts and tilts away from the path predicted by ray optics, an intriguing consequence of its finite transverse extent. For twisted light, such beam shifts manifest even more dramatically: upon reflection, a field containing a high-order optical vortex is expected to experience not only geometrical shifts, but an additional splitting of its high-order vortex into a constellation of unit-charge vortices, a phenomenon known as topological aberration. In this article, we report on the experimental observation of the topological aberration effect, verified through the deformation of vortex constellations upon reflection. We develop a general theoretical framework to study topological aberrations in terms of the elementary symmetric polynomials of the coordinates of a vortex constellation, a mathematical abstraction which we prove to be the physical quantity of practical interest.