Multidimensional measures of electromagnetic chirality and their conformal invariance

Abstract

Proper assignment of left- and right-handed labels to general chiral objects is known to be a theoretically unfeasible problem. Attempts to utilize a pseudoscalar function to distinguish enantiomers face two unavoidable difficulties: false chiral zeros and unhanded chiral states. In here, we demonstrate how both of these problems can be solved in the context of light-matter interactions. First, we introduce a two-dimensional quantity called complex electromagnetic chirality that solves the problem of false chiral zeros. Next, we define an infinite-dimensional pseudovector called chirality signature that completely quantifies the multidimentional nature of electromagnetic chirality, does not have false global chiral zeros, and allows to continuously distinguish any pair of enantiomers. We prove that the introduced measures are invariant under the largest group of symmetries of Maxwell’s equations – the conformal group. The complete and conformally invariant quantification of electromagnetic chirality provided by the chirality signature distinguishes it as a particularly suitable tool for the study of chirality and its applications.