Generic propagation of sharp boundaries electromagnetic signals in any linear dispersive medium

A generic formalism for the propagation of a pulse with sharp boundaries in any linear medium is derived. It is shown that such a pulse experiences generic deformations. For any given linear medium, the pulse deformation is expressed as a generic differential operator, which characterizes the medium and which operates on the pulse at the singular points (the sharp boundaries). The theory is then applied to a Fabry-Perot etalon and to dispersive media with second order dispersion, third order dispersion, and a combination of both. Simple approximate expressions are also derived for a relatively short, i.e., low dispersive, medium and compared with exact numerical solutions.