  It was recently realized that the polarization bases of the plane-wave modes
in the integral representation of a light beam need to be determined by a
degree of freedom arising from the divergence-free Maxwell's equation. This is
a frequently introduced real unit vector in the literature, called Stratton
vector. The polarization bases so determined are singular at the momentum that
is parallel to the Stratton vector. Here we show that the polarization
singularity of vector vortex beams given by the integral representation comes
from the singularity of the polarization bases in association with the Stratton
vector. The consistency of the polarization structure of the vector vortex
beams with their polarization bases is also discussed.
