Energy flow in light scattering by a small conducting sphere

Abstract

Radiation energy scattered by a small particle can be expected to travel from the particle to a detector in the far field along the field lines of the Poynting vector. We consider the scattering off a small conducting sphere, for which only the induced electric and magnetic dipole moments contribute to the emitted radiation. Field lines of the energy flow due to interference between fields radiated by the electric and magnetic dipoles appear to form closed loops in the vicinity of the particle. Energy flows out of the particle at one side and then returns to the particle at the other side, and as such, this energy flow does not contribute to the radiated power. At larger distances, energy flows away from the particle at one side of the particle, but on the other side, radiation flows from infinity toward the particle. The energy for the scattered radiation is provided by the incident field. The energy flow is due to interference between the incident field and the scattered radiation, known as extinction. The flow pattern of this energy exhibits numerous singularities and vortices, and closed-loop flows near the particle. In the far field, energy flows along counter-oriented field line bundles, with only the net power flowing inward.