Extracting topological features of skyrmionic light: a tutorial

Abstract

Optical topologies have become highly topical of late, manifesting in paraxial and nonparaxial light, single-photon and entangled quantum states, and in plasmonic and evanescent fields. A major attraction is their perceived immutability to disturbance, but unfortunately, the path to study this is fraught with difficulty. The standard approaches to measuring and computing topological features of light are highly sensitive to noise, the very thing one wishes to probe. In this tutorial, we outline the practical toolkit for extracting topological features of light, focusing on optical skyrmions, with embedded phase and polarization singularities, as an example. We show with worked examples how to process topological data in a manner that is consistent, agnostic, and topologically allowed, i.e., that it does not disturb the thing one wants to extract. We highlight the common pitfalls that will result in erroneous outcomes and provide all the codes for the reader to immediately implement the tutorial approach themselves. We expect this tutorial to set the standard for extracting topological features of light, accelerating new studies in topology through complex media and its applications.