Dipole radiation near a reflecting corner

We consider a radiating electric dipole, located near the joint of two orthogonal mirrors. The field lines of energy flow in the neighborhood of the dipole have an intriguing structure due to interference between the dipole radiation and the reflected light by the mirrors. Numerous singularities and vortices appear in the sub-wavelength region between the dipole and the surfaces. We present a method to find the locations of the vortices and singularities without regard to the details of the flow pattern. The radiation field induces a surface current density in the mirrors. The direction of the current is predominantly in the radial direction for a linear dipole, but it alternates between outgoing and incoming across singular curves. We show that the field line pattern expands with a phase velocity larger than the speed of light. For a circular dipole, there appears a spiral which runs inward. The current initially flows in along this spiral. Then the current leaves again along an outgoing spiral, which spirals inside the incoming spiral. Current can flow from one mirror to the other, and we show that the current always crosses the intersection line at a 90° angle.