Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium)

Abstract

The classical theory of Sommerfeld and Brillouin of pulse propagation in a Lorentz medium is reexamined. We show by numerical techniques that Brillouin’s approximations for the saddle-point locations break down in certain space–time regions. Analytic approximations that describe the correct saddle-point behavior are derived and applied to obtain improved asymptotic expressions. Qualitatively, the resulting pulse behavior is similar to that predicted by Brillouin. The quantitative improvements are significant, however, and have led to a simple mathematical procedure for determining the pulse dynamics in addition to a clear physical interpretation.