Propagation of Electric Dipole Radiation through a Medium

When electromagnetic energy propagates through a material medium, the paths of energy flow may be altered, as compared to propagation in free space. We consider radiation emitted by an electric dipole, embedded in a medium with permittivity and permeability . For a linear dipole in free space, the field lines of energy flow are straight, but when the imaginary part of is finite, the field lines in the material become curves in the near field of the dipole. Therefore, the energy flow is redistributed due to the damping in the material. For a circular dipole in free space, the field lines of energy flow wind around the axis perpendicular to the plane of rotation of the dipole moment. When has an imaginary part, this flow pattern is altered drastically. Furthermore, when the real part of is negative, the direction of rotation of the flow lines reverses. In that case, the energy in the field rotates opposite to the direction of rotation of the dipole moment. It is indicated that in metamaterials with a negative index of refraction this may lead to an observable effect in the far field. 1. Introduction When optical radiation from a localized source is observed at a large distance, it appears as if the light travels along straight lines. Similarly, light scattered or reflected by an object seems to travel from the object to an observer along straight lines, known as optical rays. These lines are the flow lines of the energy in the radiation field. In close vicinity of the source, however, these flow lines are in general curves, and intricate field line patterns may appear. Such structures can be found when the flow of radiation is resolved on a scale smaller than a wavelength. Particularly interesting is the possible presence of singularities and optical vortices. The first prediction of the existence of an optical vortex was made by Braunbek and Laukien in 1952 [1]. They considered the diffraction of a plane wave around the edge of a conducting half plane, and they found that a vortex should appear at the illuminated side of the plane, and close to the edge. Another mechanism that may lead to singularities and vortices in the energy flow is interference. We have shown recently [2, 3] that when a point source is located near a reflecting surface, numerous vortices are present in the energy-flow pattern when the source is about a wavelength away from the surface. A different type of vortex in the energy-flow pattern results from a rotation inside the source. We shall show in the next section that radiation emitted by an electric dipole may have such a vortex