Power Flow of Electric Dipole Radiation Extinction in an Absorbing Host Medium

We have studied the extinction power flow for a dipole in a laser beam, and embedded in a dissipating medium. The power flows along the field lines of the Poynting vector. We have shown that near the particle, the field lines form closed loops, which start and end at the location of the dipole. A closed-form expression for these loops has been derived, and we have shown how the orientation direction of a loop is determined by the permittivities and permeabilities of the host medium and the particle. It is also shown that the spatial extent of these loops is determined by singularities in the flow pattern. It is shown that the extent of the loop structure near the dipole diminishes strongly when there is dissipation in the medium. This is due to the appearance of singularities very close to the particle, which are due to the damping. At greater distances, flow lines run off to the far field or they come in from the far field. Most flow lines change from incoming to outgoing, or vice versa, so they turn around somewhere in the flow field. Singularities, points where the Poynting vector vanishes, appear on the coordinate axes. At these points, field lines split. Off the axes, singularities appear as the centers of vortices. Near a vortex, energy swirls around the singular point. Field lines can come out of the center of a vortex or end there.