Extended Stokes parameters for cylindrically polarized beams

The extended Stokes parameters for arbitrary cylindrically polarized beams are newly introduced to evaluate their quality. A set of the parameters, expressing a cylindrically polarized state, permits the definition of the degree of polarization that indicates the purity of the spatial symmetry of polarization of a light beam. In addition, the Pancharatnam–Berry phase related to the cylindrically polarized states is described by the new Stokes parameters.