Introduction

Abstract

The dynamic evolution of an electromagnetic pulse as it propagates through a linear, temporally dispersive medium is a classical problem of electromagnetism. If the medium was nondispersive, an arbitrary pulse would propagate unaltered at the phase velocity of the wave field in the medium. In a dispersive medium, however, the pulse is modified as it propagates due to two fundamentally interconnected effects. First of all, each monochromatic spectral component of the initial pulse propagates through the dispersive medium with its own phase velocity so that the phasal relationship between the various spectral components of the pulse changes with the propagation distance. Secondly, each monochromatic spectral component is absorbed at its own rate so that the relative amplitudes between the spectral components of the pulse change with the propagation distance. These two simple effects then result in a complicated change in the dynamical structure of the propagated field. The rigorous analysis of the dispersive pulse propagation phenomena is complicated by the simple fact that the dispersive and absoptive parts of the medium response are connected through the physical requirement of casuality [1.1]. For an initial pulse with a sufficiently rapid rise-time these effects manifest themselve through the formation of well defined precursor fields [1.2–4] whose evolution has been shown [1.5–11] to be completely determined by the dispersive and absoptive properties of the medium.