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 an Airy function. In the weak dispersion limit, the equivalence relation, established at great length in Section 3 of that 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.
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