Transient processes for incidence of a light signal on a vacuum-medium interface

We extend the classical Brillouin-Sommerfeld treatment of precursors in several ways: We consider oblique incidence on an interface, the vector nature of the field, the effect of different forms of the incident signal, and the different refractive indices of the media. The amplitudes, frequencies, directions of propagation, and duration of the signal at all stages of the transient process are calculated. The steepness of the form of signals is one of the crucial factors for the experimental detection of the phenomena under consideration. The different possibilities of the experimental detection of the refracted and reflected signals are discussed.