Diffraction of electromagnetic pulses in a single-resonance Lorentz model dielectric

We study the behaviour of a plane-wave delta-function pulse that is diffracted at an edge in a dispersive medium. In particular, we show that the edge-diffraction process by itself is dispersive and adds to the dispersion induced by the medium in such a way as to completely change the behaviour of the Brillouin precursor. The dispersion associated with edge diffraction manifests itself through the appearance of a new algebraic singularity near the origin. Since the Sommerfeld precursor field is due to asymptotic contributions from saddle points that always stay far from the origin, the character of this field is not changed by the new singularity induced by edge diffraction. The Brillouin precursor field, however, is due to asymptotic contributions from saddle points that are close to the origin, and therefore the new singularity changes its behaviour dramatically. Numerical illustrations of the evolution of the edge-diffracted pulse are given and the behaviour of the Brillouin precursor field is explained both mathematically and physically.