Spin-orbit interactions in vortex singularimetry

On scattering, the high strength singularity of a vortex beam breaks into a configuration of single charge vortices. The precise geometry of such a vortex constellation depends on the angle of incidence and the material properties of the scatterer, but also on the optical spin-orbit coupling as choosing different input and output polarization results in a family of vortex constellation. Measuring the position of the individual vortices allows us to reconstruct elements in an systematic expansion of the scattering matrix, in an analogy to optical aberration theory. We discuss in detail the dependence of the constellation geometry on external parameters, which is the basis for an optical metrology based on vortices.