ASYMPTOTICS AND ENERGY ESTIMATES FOR ELECTROMAGNETIC PULSES IN DISPERSIVE MEDIA

We examine electromagnetic pulse propagation in anomalously dispersive media, using the Debye model as an example. Short-pulse, long-pulse, short-time, and long-time approximations and amplitude rate-of-decay e stimates are derived with asymptotic methods. We also study the follow ing problem: If we know only the peak amplitude and the energy density of an incident pulse, what can be said about the amplitude of the pro pagated pulse? We provide tight upper and lower bounds for the propaga ted amplitude, which may be useful in controlling the electromagnetic interference or the damage produced in dispersive media. We explain a factor-of-nine effect in the speed of pulses in a Debye model for wate r, which seems to have been previously unnoticed, and we also explain some observations from experimental studies of pulse propagation in bi ological materials. Finally, we propose some guidelines for sample siz e in transmission time-domain spectroscopy studies of dielectrics. Mos t of our results are easily extended to multiple space dimensions. (C) 1996 Optical Society of America