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

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This article mainly deals with the propagation of step-modulated light pulses in a dense Lorentz-medium at distances such that the medium is opaque in a broad spectral region including the carrier frequency. The transmitted field is then reduced to the celebrated precursors of Sommerfeld and Brillouin, far apart from each other. We obtain simple analytical expressions of the first (Sommerfeld) precursor whose shape only depends on the order of the initial discontinuity of the incident field and whose amplitude rapidly decreases with this order (rise-time effects). We show that, in a strictly speaking asymptotic limit, the second (Brillouin) precursor is entirely determined by the frequency-dependence of the medium attenuation and has a Gaussian or Gaussian-derivative shape. We point out that this result applies to the precursor directly observed in a Debye medium at decimetric wavelengths. When attenuation and group-delay dispersion both contribute to its formation, we establish a more general expression of the Brillouin precursor, containing the previous one (dominant-attenuation limit) and that obtained by Brillouin (dominant-dispersion limit) as particular cases. We finally study the propagation of square or Gaussian pulses and we determine the pulse parameters optimizing the Brillouin precursor. Obtained by standard Laplace-Fourier procedures, our results are explicit and contrast by their simplicity from those derived by the uniform saddle point methods, from which it is very difficult to retrieve our asymptotic forms

Section: Discussionmentioning

confidence: 99%

“…An abundant bibliography can be found in the recent work by Oughstun [13]. Complementary studies on the effects of a finite turn-on time of the incident field on the precursors are reported in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Simple asymptotic forms for Sommerfeld and Brillouin precursors

Macke

Ségard

2012

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“…(8) it is usually reduced with the help of the convolution theorem to (see, for example, Refs. [9][10][11])…”

Section: Light Beam In a Thick Resonant Mediummentioning

confidence: 99%

Transformation of subradiant states to superradiant states in a thick resonant medium

Shakhmuratov

2014

The propagation of a step pulse through a thick resonant absorber with homogeneously broadened absorption line is considered. It is shown that a specific subradiant state is naturally developed in the absorber due to the formation of the spatial domains of the atomic coherence with opposite phases. It is proposed to divide the absorber into slices in accord with these domains and place the phase shifters in front of the first slice and between the other slices. If the phase shifters are switched on simultaneously at a particular moment of time, elapsed from the beginning of the step pulse, a strong sharp pulse is generated at the output of the last slice of the absorber. The effect is explained by the phasing of the atomic coherence along all slices of the absorber, which transforms subradiant state of atom-field system to superradiant state.

“…More than a century after their discovery, these transients, currently named Sommerfeld and Brillouin precursors, continue to raise considerable interest, due in particular to their sub-exponential attenuation with the propagation distance. An abundant bibliography on the subject is given in Ref [5] and more recent related studies are reported in Refs [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…In fact the simultaneous observation of welldistinguishable Sommerfeld and Brillouin precursors, as considered by their discoverers, requires experimental conditions that seem unrealizable in optics [8]. A qualitative demonstration of separated Sommerfeld and Brillouin precursors has only been performed in microwaves by using guiding structures with dispersion characteristics similar to those of a Lorentz medium [11].…”

Section: Introductionmentioning

confidence: 99%

Brillouin precursors in Debye media

Macke

Ségard

2015

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We theoretically study the formation of Brillouin precursors in Debye media. We point out that the precursors are visible only at propagation distances such that the impulse response of the medium is essentially determined by the frequency dependence of its absorption and is practically Gaussian. By simple convolution, we then obtain explicit analytical expressions of the transmitted waves generated by reference incident waves, distinguishing precursor and main signal by a simple examination of the long-time behavior of the overall signal. These expressions are in good agreement with the signals obtained in numerical or real experiments performed on water in the radio-frequency domain and explain in particular some observed shapes of the precursor. Results are obtained for other remarkable incident waves. In addition, we show quite generally that the shape of the Brillouin precursor appearing alone at sufficiently large propagation distance and the law giving its amplitude as a function of this distance do not depend on the precise form of the incident wave but only on its integral properties. The incidence of a static conductivity of the medium is also examined and explicit analytical results are again given in the limit of weak and strong conductivities.