Spectral Stokes singularities of partially coherent radially polarized beams focused by a high numerical aperture objective

The dynamic behavior of spectral Stokes singularities of partially coherent radially polarized beams focused by a high numerical aperture (NA) objective is studied by using the vectorial Debye diffraction theory and complex spectral Stokes fields. It is shown that there exist s(12), s(23), and s(31) singularities, as well as P (completely polarized) and U (unpolarized) singularities. The motion, pair creation and annihilation, and changes in the degree of polarization of s(12), s(23), and s(31) singularities, and the handedness reversal of s(12) singularities (C-points) may appear by varying a controlling parameter, such as the truncation parameter, NA, or spatial correlation length. The creation and annihilation occur for a pair of s(12) singularities with opposite topological charge but the same handedness, and for a pair of oppositely charged s(23) or s(31) singularities. The critical value of the truncation parameter, at which the pair annihilation takes place, increases as the semi-angle of the aperture lens (or, equivalently, NA) or spatial correlation length increases. The collision of an s(12) singularity with an L-line (s(3) = 0 contour) leads to a V-point, which is located at the intersection of contours of s(12) = 0 and s(23) = 0 (or s(31) = 0) and is unstable.