Chapters authored
Vortices and Singularities in Electric Dipole Radiation near an Interface
An oscillating electric dipole in free space emits its energy along straight lines. We have considered the effect of a nearby interface with a material medium. Interference between the directly emitted radiation and the reflected radiation leads to intricate flow line patterns. When the interface is a plane mirror, numerous interference vortices appear, and when the distance between the dipole and the mirror is not too small, these vortices lie on four strings. At the center of each vortex is a singularity, and these singularities are due to the fact that the magnetic field vanishes at these locations. When the interface is a boundary between dielectric media, reflection leads again to interference. The pattern for the transmitted radiation depends on whether the medium is thicker or thinner than the material in which the dipole is embedded. For thicker dielectrics, the field lines bend toward the normal, reminiscent of, but not the same as, the behavior of optical rays. For thinner media, oscillation of energy across the interface appears, and above a crossing point, there is a tiny vortex. We have also considered the case of a dipole in between two parallel mirrors.
Part of the book: Vortex Dynamics and Optical Vortices