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

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-functionmodulated signal are considered.