Damping of the dipole vortex

When a circular electric dipole moment, rotating in the x-y plane, is embedded in a material with relative permittivity ε(r) and relative permeability μ(r), the field lines of energy flow of the emitted radiation are dramatically influenced by the surrounding material. For emission in free space, the field lines swirl around the z axis and lie on a cone. The direction of rotation of the field lines around the z axis is the same as the direction of rotation of the dipole moment. We found that when the real part of ε(r) is negative, the rotation of the field lines changes direction, and hence the energy counter-rotates the dipole moment. When there is damping in the material, due to an imaginary part of ε(r), the cone turns into a funnel, and the density of the field lines diminishes near the location of the source. In addition, all radiation is emitted along the z axis and the x-y plane, whereas for emission in free space, the radiation is emitted in all directions. It is also shown that the displacement of the dipole image in the far field depends on the material parameters and that the shift can be much larger than the shift of the image in free space.