Theory of Electromagnetic Transients in Spatially Dispersive Media and a New Approach to Precursor Theory
The theoretical investigation of electromagnetic transients in media has been an ongoing topic of interest since (at least) the classic work of Sommerfeld and Brillouin  on precursor theory. The prototypical problem is the analysis of the amplitude f(z, t) of the electromagnetic field at point z, time t in a material dielectric when a wave with sharp front (for example, a sharply truncated laser) impinges on the surface of a bounded medium. Coming into play in this analysis are: the model of the medium, (which in the classical theory is taken as a “Lorentz model” dielectric); the coupling of field and medium via some dielectric response function; and the propagation of the field, described by Maxwell equations. All these aspects of radiation and matter theory can be explored by analysing the time evolution of the amplitude f(z, t), which in effect samples the dynamics of the system in a time-resolved succession of stages, each such stage referring to a different frequency regime.
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