Abstract
We consider the propagation of arbitrary electromagnetic pulses in anomalously dispersive dielectrics characterized by M relaxation processes. A partial differential equation for the electric field in the dielectric is derived and analyzed. This single equation describes a hierarchy of M + 1 wave types, each type characterized by an attenuation coefficient and a wave speed. Our analysis identifies a “skin-depth” where the pulse response is described by a telegrapher's equation with smoothing terms, travels with the wavefront speed, and decays exponentially. Past this shallow depth we show that the pulse response is described by a weakly dispersive advection-diffusion equation, travels with the sub-characteristic advection speed equal to the zero-frequency phase velocity in the dielectric, and decays algebraically. The analysis is verified with a numerical simulation. The relevance of our results to the development of numerical methods for such problems is discussed.
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