Vortex strings in electric dipole radiation near a mirror

The energy flow pattern of the radiation emitted by an oscillating electric dipole near a mirror has a complicated structure, including numerous singularities and vortices. We consider the flow lines of energy in the plane through the surface normal and the oscillation direction of the dipole. It is shown that the vortices are due to the vanishing of the magnetic field at their centers. The locations of the vortices have the appearance of beads on strings, and there are four such strings. The rotation direction of the energy flow for each vortex on a given string is the same. There are two strings with clockwise rotation and two strings with counterclockwise rotation. Field lines of energy flow either start or end at the center of a vortex. For a given string, field lines end at each vortex or field lines start at each vortex. There are two strings on which field lines end at the centers of the vortices, and there are two strings on which field lines start inside the vortices.