Comment on "Optical precursors in the singular and weak dispersion limits"

TL;DR

This paper critiques a recent study on optical precursors, clarifying misconceptions about the limits and emphasizing the importance of proper time scale analysis and the impact of incident field rise-time.

Contribution

It provides a critical analysis of previous numerical results, clarifies the behavior of optical precursors in different dispersion limits, and highlights the effect of incident field rise-time.

Findings

The steep rise in the singular limit is due to an unsuitable time scale.

The precursor rise is accurately described by an Airy function.

Precursors are significantly affected by the incident field's rise-time.

Abstract

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.