Spherical lens as a launcher of electromagnetic missiles

A uniform dielectric sphere, under transient excitation by a point source, is found to be capable of launching an electromagnetic missile, i.e., there is a direction where the decay of the total energy transmitted to a receiver is slower than r−2. The conditions for the presence of an electromagnetic missile have a natural interpretation, which in turn leads to a classification of electromagnetic missiles according to the singularities of differentiable maps in two dimensions.