Near-field measure of optical chirality

Both the Stokes vector and polarization matrix descriptions of optical polarization have found widespread application throughout paraxial optics. Recently there has been a significant interest in adapting these formulations to account for electromagnetic fields that are non-paraxial and have components polarized in three dimensions. Of topical interest are the conserved properties of electromagnetic fields known as the optical helicity and optical chirality. In paraxial optics the optical helicity and optical chirality can be inferred from the pure electric field polarization matrix and Stokes vector S3. In this work we provide the general theory of how these characteristics of arbitrary electromagnetic fields can be calculated using either a polarization matrix or Stokes vector approach. Our formulation provides a general theoretical framework applicable to both near- and far-field optical helicity and optical chirality.