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.
© 1989 Optical Society of America
Original Manuscript: January 9, 1989
Manuscript Accepted: May 19, 1989
Published: September 1, 1989
Kurt Edmund Oughstun and George C. Sherman, "Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium)," J. Opt. Soc. Am. A 6, 1394-1420 (1989)