Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium)

Abstract

The uniform asymptotic description of electromagnetic pulse propagation in a single-resonance Lorentz medium is presented. The modern asymptotic theory used here relies on Olver’s saddle-point method [ Stud. Appl. Math. Rev.12, 228 ( 1970)] together with the uniform asymptotic theory of Handelsman and Bleistein [ Arch. Ration. Mech. Anal.35, 267 ( 1969)] when two saddle points are at infinity (for the Sommerfeld precursor), the uniform asymptotic theory of Chester et al. [ Proc. Cambridge Philos. Soc.53, 599 ( 1957)] for two neighboring saddle points (for the Brillouin precursor), and the uniform asymptotic theory of Bleistein [ Commun. Pure Appl. Math.19, 353 ( 1966)] for a saddle point and nearby pole singularity (for the signal arrival). Together with the recently derived approximations for the dynamical saddle-point evolution, which are accurate over the entire space–time domain of interest, the resultant asymptotic expressions provide a complete, uniformly valid description of the entire dynamic field evolution in the mature dispersion limit. Specific examples of the delta-function pulse and the unit-step-function-modulated signal are considered.