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Communications in Theoretical Physics

Propagation of a Rectangular Pulse in an Anomalous Dispersive Medium

Chao-Guang Huang, Yuan‐Zhong Zhang

Published Aug 15, 2002• 3 citations
Publisher

Abstract

The pulse with a rectangular envelop propagating through the caesium vapour with two gain lines used in the Wang, Kuzmich, and Dogariu [Nature (London) 406 (2000) 277] experiment is studied. It is shown that there exists an obvious distortion for the pulse.
DOI
10.1088/0253-6102/38/2/224

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Physical Review A•Nov 17, 2009•1 citation
Analysis of an infinitely long train of sine-squared pulses—as a toy model—propagating in a medium exhibiting anomalous dispersion shows that although the shape of the light pulses seems to be almost preserved on a small scale, the pulses are severely distorted on a large scale. The frequency of the sine-squared pulses is doubled before they propagate a tenth of the width (FWHM) of a pulse in the medium. The analysis and a numerical calculation show that the front of a wave with a step-function envelope propagates at the speed of light, c , through a medium with two gain lines. Finally, the propagation of a Gaussian pulse—a more realistic pulse—in a medium exhibiting anomalous dispersion is studied. The distortion of the pulse in a Wang–Kuzmich–Dogariu (WKD) experiment (Wang L J, Kuzmich A and Dogariu A 2000 Nature 406 277) should be observable at a precision of ±1 ns. If a Gaussian pulse travels in the medium for 1/50 of a width (FWHM), it will collapse. 'Snapshots' of a Gaussian pulse show that the shape of the pulse in space will have more than one peak at certain times. A possible picture of light propagation in WKD-like experiments is proposed on the basis on these findings.
The mechanisms leading to a seemingly superluminal propagation of light in dispersive media are examined. The anomalous dispersion near an absorption line, involved in the first experiments displaying negative group velocity propagation, is shown to be not only simpler but also more efficient than the so-called transparent dispersion used in the later experiments of Wang et al. (Nature (London) 406, 277 (2000)) and of Dogariu et al. (Phys.Rev.A 63, 053806 (2001)). The modest pulse advances observed by these authors can in particular be reproduced with a better overall transmittance of the medium and the significant advances attained with a single-line arrangement would probably be unattainable with their gain-doublet arrangement.