Chiral moments make chiral measures

Abstract

We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only via its angular shape consistently with existing multipolar-moment approaches, but also its radial dependence. We combine these tensorial moments into a rotationally-invariant pseudoscalar using a newly-defined cross product and triple product for arbitrary symmetric tensors. We analyze these measures for a variety of toy-model distributions, providing intuition for the geometry and guiding the choice of chiral measure optimal for a given distribution. We also apply our measures to a physically-motivated example coming from photoionization in polychromatic chiral light. Our work provides a robust, flexible, intuitive, highly geometrical, and physically-driven framework for understanding and quantifying the chirality of a wide variety of distributions, together with an open-source software package that makes this toolbox readily applicable for the analysis of numerical or experimental data.