Propagation of magnetic dipole radiation through a medium

An oscillating magnetic dipole moment emits radiation. We assume that the dipole is embedded in a medium with relative permittivity ϵ_r and relative permeability μ_r, and we have studied the effects of the surrounding material on the flow lines of the emitted energy. For a linear dipole moment in free space the flow lines of energy are straight lines, coming out of the dipole. When located in a medium, these field lines curve toward the dipole axis, due to the imaginary part of μ_r. Some field lines end on the dipole axis, giving a nonradiating contribution to the energy flow. For a rotating dipole moment in free space, each field line of energy flow lies on a cone around the axis perpendicular to the plane of rotation of the dipole moment. The field line pattern is an optical vortex. When embedded in a material, the cone shape of the vortex becomes a funnel shape, and the windings are much less dense than for the pattern in free space. This is again due to the imaginary part of μ_r. When the real part of μ_r is negative, the field lines of the vortex swirl around the dipole axis opposite to the rotation direction of the dipole moment. For a near-single-negative medium, the spatial extent of the vortex becomes huge. We compare the results for the magnetic dipole to the case of an embedded electric dipole.