  A method is proposed for the analysis of the propagation of electromagnetic
waves through a homogeneous slab of a medium with Drude-Lorentz dispersion
behavior, and excited by a causal sinusoidal source. An expression of the time
dependent field, free from branch-cuts in the plane of complex frequencies, is
established. This method provides the complete temporal response in both the
steady-state and transient regimes in terms of discrete poles contributions.
The Sommerfeld and Brillouin precursors are retrieved and the corresponding set
of poles are identified. In addition, the contribution in the transient field
of the resonance frequency in the Drude-Lorentz model is exhybited, and the
effect of reflections resulting from the refractive index mismatch at the
interfaces of the slab are analyzed.
