Laser pulse propagation in relativistically time-dependent media

Nonlinear optics and, in general, the interaction of light with matter is usually studied in the context of a stationary medium that does not change in time or changes slowly on the time scale of the optical frequency cycle. However, there are a number of interesting effects that arise when the medium is allowed to change at very rapid rates. We first discuss the recent experimental discovery of a new kind of resonant radiation emission from laser pulse shock fronts and consider its main features in terms of a possible route to investigate light scattering from a relativistically moving scatterer. As a second example we consider the case of a periodically changing medium: such a situation bears a close resemblance to the dynamical Casimir effect.