Energy flow lines for the radiation emitted by a dipole

An oscillating electric dipole emits radiation, and the flow of energy in the electromagnetic field is represented by the field lines of the Poynting vector. In the most general state of oscillation the dipole moment vector traces out an ellipse. We have evaluated analytically the field lines of the Poynting vector for the emitted light, and it appears that each field line lies on a cone, which has its axis perpendicular to the plane of the ellipse. The field lines exhibit a vortex structure near the location of the dipole, and they approach a straight line in the far field. It is shown that due to the spiraling of the field lines near the source, the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. Both the spatial extent of the vortex in the near field and the magnitude of the displacement of the image in the far field are of nanoscale dimension.