Pulse propagation in a linear, causally dispersive medium

The uniform asymptotic description of optical pulse propagation in a linear, causally dispersive, absorptive dielectric, as described by the classical Lorentz model, is presented. The resultant pulse distortion in a single resonance Lorentz medium is shown to be primarily due to the Sommerfeld and Brillouin precursor fields. The mathematical approach does not rely upon any quasimonochromatic or slowly varying envelope approximation and consequently provides a canonical description of linear pulse dispersion dynamics that is completely valid for rapid risetime pulses of arbitrary time duration. The results do not depend upon any nth-order dispersion approximation so that the causality relations that are critical to the physically proper analysis of linear dispersive pulse propagation phenomena are maintained