Generalized Polarization Matrix Approach to Near-Field Optical Chirality

TL;DR

This paper develops a comprehensive framework for characterizing optical chirality in arbitrary electromagnetic fields, extending existing polarization matrix methods to include non-paraxial and near-field scenarios, with applications to chiral emission and focused beams.

Contribution

It introduces a generalized polarization matrix approach for optical chirality applicable to complex three-dimensional fields, including near- and far-field regimes.

Findings

Framework applicable to near- and far-field optical chirality

Demonstrated relevance to chiral dipole emission

Applicable to tightly focused beams

Abstract

For paraxial light beams and electromagnetic fields, the Stokes vector and polarization matrix provide equivalent scalar measures of optical chirality, widely used in linear optics. However, growing interest in non-paraxial fields, with fully three-dimensional polarization components, necessitates an extended framework. Here, we develop a general theory for characterizing optical chirality in arbitrary electromagnetic fields, formulated through extensions of the polarization matrix approach. This framework applies to both near- and far-field optical helicity and chirality. As examples, we demonstrate its relevance to near-zone fields from chiral dipole emission and the focal plane of tightly focused beams.