Lines of circular polarization in electromagnetic wave fields

Abstract

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.