Vortices in the near field of optical dipole radiation
AdvisorArnoldus, F. Henk
Pierce, M. Donna
An oscillating electric dipole emits radiation, and the flow of energy 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 and numerically 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. The spatial extent of the optical vortex is well below the wavelength of the emitted radiation. It is shown that the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. This near-field vortex pattern will also lead to a shift of the intensity distribution of the radiation in the far field. The emission of radiation by a linearly oscillating electric dipole is drastically altered when the dipole is close to a mirror. The energy is not emitted along optical rays, as for a free dipole, but as a set of four optical vortices. At a larger distance from the dipole singularities and isolated vortices appear. It is shown that most of these interference vortices are due to the vanishing of the magnetic field at their centers. In the plane of the mirror there is a singular circle with a diameter which is proportional to the distance between the dipole and the mirror. Inside this circle, all energy flows to a singularity on the mirror surface. We have also demonstrated a peculiar property of energy transport of optical dipole radiation in a negative index of refraction material (NIM). When the particle is embedded in a NIM and the dipole moment is rotating, the direction of rotation of the field lines of energy flow is reversed as compared to the rotation of the field lines for emission in a dielectric.