Exactly solvable models : a solution to different problems of laser matter interaction

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.