Generalized Polarization Matrix Approach to Near-Field Optical Chirality

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.