On the accuracy of asymptotic approximations in ultrawideband signal, ultrashort-pulse, time-domain electromagnetics

After an ultrashort pulse (or an ultrawideband signal) has propagated a sufficiently large distance into a dispersive, attenuative material its spatiotemporal dynamics settle into a relatively simple (or mature) behavior for the remainder of the propagation. In this so-called mature dispersion regime the field becomes locally quasimonochromatic with fixed local frequency, wavelength, and attenuation in small regions of space that propagate with their own characteristic constant velocity (Sherman and Oughstun 1995). The modern asymptotic description of the dynamical evolution of an ultrashort electromagnetic pulse (or an ultrawideband electromagnetic signal) as it propagates through a homogeneous, isotropic, locally linear, temporally dispersive medium provides a detailed characterization of the entire temporal field evolution for all propagation distances that are in the mature dispersion regime (Oughstun and Sherman 1994). The accuracy of this asymptotic approximation is discussed.