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When an ultrawide-band electromagnetic pulse penetrates into a causally dispersive dielectric, the interrelated effects of phase dispersion and frequency dependent attenuation alter the pulse in a fundamental way that results in the appearance of so-called precursor fields. For a Debye-type dielectric, the dynamical field evolution is dominated by the Brillouin precursor as the propagation depth typically exceeds a single penetration depth at the carrier frequency of the input pulse. This is because the peak amplitude in the Brillouin precursor decays only as the square root of the inverse of the propagation distance. This nonexponential decay of the Brillouin precursor makes it ideally suited for remote sensing. Of equal importance is the frequency structure of the Brillouin precursor. Although the instantaneous oscillation frequency is zero at the peak amplitude point of the Brillouin precursor, the actual oscillation frequency of this field structure is quite different, exhibiting a complicated dependence on both the material dispersion and the input pulse characteristics. Finally, a Brillouin pulse is defined and is shown to possess near optimal (if not optimal) penetration into a given Debye-type dielectric.