Generalized (two-point) stokes-parameters representation in terms of the radial and azimuthal field components

Within the paraxial framework, a generalization of the Stokes representation is introduced in terms of the radial and azimuthal field structure of the beam cross-section. These generalized parameters depend on two spatial variables and are closely related with the cross-spectral density (CSD) matrix of the field. The propagation law of such parameters through general first-order optical systems is also given. It allows to describe, in terms of the radial and azimuthal field components, the coherence and polarization behavior of partially-polarized, partially-coherent beams.