  We combine scattering theory, Fourier, traveling wave and asymptotic analyses
together with numerical simulations to present interesting and practically
useful properties of femtosecond pulse interaction with thin films. The
dispersive material is described by a single resonance Lorentz model and its
nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of
the Lorentz dielectric function is that its real part becomes negative between
its zero and its pole, generating a forbidden region. We illustrate numerically
the linear interaction of the pulse with the film using both scattering theory
and Fourier analysis. Outside this region we show the generation of a sequence
of pulses separated by round trips in the Fabry-Perot cavity due to multiple
reflections. When the pulse spectrum is inside the forbidden region, we observe
total reflection. Near the pole of the dielectric function, we demonstrate the
slowing down of the pulse (group velocity tending to zero) in the medium that
behaves as a high-Q cavity. We use the combination of analysis and simulations
in the linear regime to validate the delta function approximation of the thin
layer; this collapses the forbidden region to a single resonant point of the
spectrum. We also study the single cycle pulse interaction with a thin film and
show three distinct types of reflection: half-pulse, sinusoidal wave train and
cosine wavelet. Finally we analyze the influence of a strong nonlinearity and
observe that the film switches from reflecting to trasparent.
