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 OO 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 OO points. OO, C, and L points undergo a variety of democratic reactions in which OO 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 OO points and their reactions, but also that the charge of a C or L line segment is not an invariant, but is context dependent.