Jones and Stokes parameters for polarization in three dimensions

For partially polarized three-dimensional electromagnetic fields, the polarization state is usually expressed in terms of nine generalized Stokes parameters, the coefficients of the nine Gell-Mann matrices in the expansion of the coherency matrix. We consider fully polarized fields, for which the Jones vector for the polarization state can be expressed in terms of five real parameters. Relationships between these five parameters and the nine generalized Stokes parameters are derived. For partially polarized three-dimensional fields there are four additional parameters that describe the partial polarization, two that specify the degree of polarization, and two that specify its orientation.