Low frequencies and peak amplitude in UWB pulse propagation

Previous studies of ultra-wideband electromagnetic pulses that propagate through causal, dispersive and attenuative dielectric material have shown the existence of a Brillouin precursor, a component of the propagated field that decays algebraically with propagation distance rather than exponentially. Because each nonzero frequency component of the pulse decays exponentially with distance, in accordance with the Beer-Lambert law, the Brillouin precursor is commonly attributed to the dc or low frequency content of the initial pulse. Here, the effect of low frequency components on the formation and peak amplitude of the Brillouin precursor is studied. A cascade of single-pole high-pass filters, each with cutoff angular frequency ω_H, is applied to a step modulated sine wave and a closed-form asymptotic approximation to the propagated field is given. Our results show that the Brillouin precursor exists even with the low frequency content suppressed. However, the decay rate of the Brillouin precursor does decrease with increasing ω_H.