Rotational transformations of polarization singularities in three-dimensional optical fields: I. Ordinary points

In three-dimensional (3D) optical fields every ordinary point is a polarization singularity, here an ordinary polarization singularity, or O point, in three orthogonal planes oriented normal to the three principal axes (major, minor, and ellipse normal) of the polarization ellipse at the point. The canonical point polarization singularities: points of circular polarization, C points on C lines, and points of linear polarization, L points on L lines, are embedded in, and interact with, this sea of O points. O, C, and L points undergo a variety of democratic reactions in which O points collide with and replace C or L points, inverting the sign of the “topological charge” associated with the point. These reactions highlight the fact that not only must a consistent description of 3D light include O points and their reactions, but also that the charge of a C or L line segment is not an invariant, but is context dependent.