  We point out inconsistencies in the recent paper by Oughstun et al. on
Sommerfeld and Brillouin precursors [J. Opt. Soc. Am. B 27, 1664-1670 (2010)].
Their study is essentially numerical and, for the parameters used in their
simulations, the difference between the two limits considered is not as
clear-cut as they state. The steep rise of the Brillouin precursor obtained in
the singular limit and analyzed as a distinguishing feature of this limit
simply results from an unsuitable time scale. In fact, the rise of the
precursor is progressive and is perfectly described by a Airy function. In the
weak dispersion limit, the equivalence relation, established at great length in
Section 3 of the paper, appears as an immediate result in the retarded-time
picture. Last but not least, we show that, contrary to the authors claim, the
precursors are catastrophically affected by the rise-time of the incident
optical field, even when the latter is considerably faster than the medium
relaxation time.
