Lines of circular polarization in electromagnetic wave fields

A monochromatic fully polarized electromagnetic wave propagating in free space possesses, in general, two families of singular lines (C lines) on which the transverse field is circularly polarized. The distribution of polarization ellipses around a C line shows that it obeys the same classifi­cation scheme as the isotropic points of a two-dimensional symmetric tensor: that is, a given section of a C line may belong to one of three different line patterns and it may be elliptic or hyperbolic. In addition it may be left-or right-handed. However, the way in which the polarization ellipses are executed in time shows that C lines may also be regarded as singularities of phase, analogous to line dislocations or interference fringes in scalar waves. From this point of view, a given line is of edge or screw type, according to its orientation, or, more generally, is a curved line of mixed edge-screw type. The whole field is divided into regions of opposite hand by surfaces S of linear polarization, and each family of C lines is confined to just one of these regions.