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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 28, Iss. 3 — Mar. 1, 2011
  • pp: 450–452

Comment on “Optical precursors in the singular and weak dispersion limits”

Bruno Macke and Bernard Ségard  »View Author Affiliations


JOSA B, Vol. 28, Issue 3, pp. 450-452 (2011)
http://dx.doi.org/10.1364/JOSAB.28.000450


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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 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.

© 2011 Optical Society of America

OCIS Codes
(260.2030) Physical optics : Dispersion
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5550) Ultrafast optics : Pulses

ToC Category:
Ultrafast Optics

History
Original Manuscript: September 16, 2010
Manuscript Accepted: October 12, 2010
Published: February 18, 2011

Citation
Bruno Macke and Bernard Ségard, "Comment on “Optical precursors in the singular and weak dispersion limits”," J. Opt. Soc. Am. B 28, 450-452 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-3-450


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References

  1. K. E. Oughstun, N. A. Cartwright, D. J. Gauthier, and H. Jeong, “Optical precursor in the singular and weak dispersion limits,” J. Opt. Soc. Am. B 27, 1664–1670 (2010). [CrossRef]
  2. Contrary to what is stated in , this (circular) frequency ω0 is not equal to the frequency of the resonance involved in the experiment on cold potassium atoms, but is 2π times smaller.
  3. L. Brillouin, “Propagation des ondes électromagnétiques dans les milieux matériels,” in Comptes Rendus du Congrès International d’Electricité (Gauthier-Villars, 1933), Vol.  2, pp 739–788. An English adaptation of this paper can be found in L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960), Ch. IV and Ch. V.
  4. Note that the Airy function A(x) used by Brillouin in differs from the standard one Ai(x) used in the present comment, with 2πAi(−x)=31/3A(31/3x). Peak amplitudes of A(x) and Ai(−x) are, respectively, 2.33 and 0.536.

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