Vortices in Electric Dipole Radiation

Abstract

In the geometrical optics limit of light propagation, light travels from a source to an observer along straight lines, known as optical rays. On the other hand, the energy in an electromagnetic field flows along the field lines of the Poynting vector. It can be shown (Born & Wolf, 1980) that in the geometrical optics limit, where variations in the radiation field on the scale of a wavelength are neglected, the optical rays coincide with the field lines of the Poynting vector, and both are straight lines. In nanophotonics and near-field optics, where sub-wavelength resolution of the energy transport is of interest, the optical rays lose their significance. Energy flows along the field lines of the Poynting vector, and these field lines are in general curves. When sub-wavelength resolution is required, we need the exact solution of Maxwell’s equations. In order to study the fundamental aspects of energy propagation, we consider the simplest and most important source of radiation, which is the electric dipole. When a small object, like an atom, molecule or nanoparticle, is placed in an external electromagnetic field (usually a laser beam), oscillating with angular frequency  , a current will be induced in the particle, and this gives the particle an electric dipole moment of the form