  We present an exact treatment of wave propagation in some inhomogeneous thin
films with highly space-dependent dielectric constant. It is based on a space
transformation which replaces the physical space by the optical path. In the
new space, the dispersion equation is that of a normal progressive wave. We
will show that the dispersion properties of such films are plasma- or
waveguide-like, the characteristic frequency being determined by the spatial
characteristics of the dielectric constant's variations only. The theory is
scalable, so that it can be applied in any wavelength range : optical, IR,
radiofrequency, etc. depending only on the characteristic space scales. Several
applications will be presented, concerning the reflection properties of such
films (broadband anti-reflection, or dichroic coatings) or to the propagation
and transmission through the film. We will show that depending on the type of
space dependence, an incident wave can either propagate or tunnel through such
films. We will investigate the behaviour of the light group-velocity and
tunneling time inside or through such films. Though we can reproduce the
phase-time saturation corresponding to the Hartman effect, analysis of the
group velocity in the tunneling case shows no sign of superluminal propagation.
A strong frequency dependence can be obtained in some situations, which allows
to anticipate a strong reshaping of brodband laser pulses.
