Generalized time delay, velocity, and absorption in dispersive and absorbing media

The time delay and absorption of ultrashort electromagnetic pulses are defined from the local maximum of the wave's electric field and envelope. A time-domain framework is derived to obtain, in dispersive and absorbing linear media, the expressions of the phase and group time delays, and of the absorption undergone by the wave. These expressions are related to the dielectric properties of the medium but also to the local curvature of the wave's electric field. The result provides a unified and rational picture of the propagation, in dispersive and absorbing media, of ultrashort electromagnetic pulses in transmission and attenuated total reflection (ATR) geometries.