  With the increasing use of ultrashort laser pulses and nanoscale-materials,
one is regularly confronted to situations in which the properties of the media
supporting propagation are not varying slowly with time (or space). Hence, the
usual WKB-type approximations fail, and one has to resort to numerical
treatments of the problems, with a considerable loss in our insight into the
physics of laser-matter interaction. We will present a new approach which
allows a fully analytical solution of such problems, based on a transformation
of the propagation equations into a new space where phase accumulation is
linear with either time or space, which greatly simplifies their treatment.
Though this method is restricted to some special models of the time or space
varying dielectric constant, those are however general enough to encompass
practically all experimental situations. It allows to introduce the concept of
"non-stationarity induced" (or "inhomogeneity induced") dispersion. We will
analyse the problem of reflection and propagation in two types of media whose
dielectric constant vary rapidly at either the laser period or the laser
wavelength scale. Extension of such techniques to the case of arbitrarily high
non linearities will be considered too.
