Stokes singularity relations.

Polarization singularities in paraxial vector optical fields are analyzed in terms of the phase singularities of complex Stokes scalar fields. Six independent relationships are obtained that connect the topological charges of these singularities on special closed contours with the charges of singularities that are enclosed by these contours. These relationships, which have been confirmed by experimental data and computer simulations, imply topological polarization correlations of an infinite range.