Propagation of electromagnetic pulses with nonzero area in dissipative media

The propagation of ultrashort electromagnetic pulses with a nonzero electric area in dielectric and conducting media is studied in the frame of a unidirectional propagation model. General solutions for the electric pulse area are obtained for different types of media with a linear response to the external field. It is shown that the evolution of the electric area of the pulse is dramatically different for conducting and non-conducting media. In the case of dielectrics, where the current induced by an external field arises from the polarization of bound electrons, the electric pulse area is an invariant of pulse propagation in spite of the dissipation process. For media with free charge carriers (plasma or semiconductors), the electric pulse area decreases with time due to Joule heating of the media by the static component of the field.