Group Delay Description for Broadband Pulses

The traditional concept of group delay usually arises in connection with an expansion of the phase delay for an electromagnetic pulse. In this context, the group delay function (evaluated at a single ‘carrier’ frequency) describes the time required for a pulse to traverse a given displacement. However, if the bandwidth of the pulse encompasses a substantial portion of a resonance structure the expansion fails to converge over the relevant range of frequencies. Because of this failure, traditional group delay suffers severe shortcomings when applied to broadband pulse propagation. We recently introduced a method for describing pulse delay in which the group delay function naturally arises. In contrast to the traditional formulation of group delay, this method retains validity for pulses of arbitrary bandwidth propagating in linear dielectrics (including cases where the spectrum overlaps resonances in the medium). In this work we give an overview of this method of description and demonstrate how it may be applied to gain insight into the behavior of broadband electromagnetic pulses. As an illustration we show how the method may be applied to the well-known precursor problem, where the traditional formulation of group delay fails.