  This article mainly deals with the propagation of step-modulated light pulses
in a dense Lorentz-medium at distances such that the medium is opaque in a
broad spectral region including the carrier frequency. The transmitted field is
then reduced to the celebrated precursors of Sommerfeld and Brillouin, far
apart from each other. We obtain simple analytical expressions of the first
(Sommerfeld) precursor whose shape only depends on the order of the initial
discontinuity of the incident field and whose amplitude rapidly decreases with
this order (rise-time effects). We show that, in a strictly speaking asymptotic
limit, the second (Brillouin) precursor is entirely determined by the
frequency-dependence of the medium attenuation and has a Gaussian or
Gaussian-derivative shape. We point out that this result applies to the
precursor directly observed in a Debye medium at decimetric wavelengths. When
attenuation and group-delay dispersion both contribute to its formation, we
establish a more general expression of the Brillouin precursor, containing the
previous one (dominant-attenuation limit) and that obtained by Brillouin
(dominant-dispersion limit) as particular cases. We finally study the
propagation of square or Gaussian pulses and we determine the pulse parameters
optimizing the Brillouin precursor. Obtained by standard Laplace-Fourier
procedures, our results are explicit and contrast by their simplicity from
those derived by the uniform saddle point methods, from which it is very
difficult to retrieve our asymptotic forms.
