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Physical Review A

Propagation of light pulses in a fast-light medium: Interplay between gain and dispersion

Thomas Crouzil, M. A. Bouchène

Published Nov 17, 2009• 1 citation
Publisher

Abstract

We consider here the situation of a Gaussian pulse that probes a medium exhibiting two close resonance lines. We study the spatial behavior of the light pulse and emphasize some overlooked features. Moreover, for long pulses and a fast-light medium, we show that the spatial distortion of the pulse due to residual gain at the central laser wavelength cannot be reduced without enhancing another distortion effect due to spectral wing amplification.

DOI
10.1103/physreva.80.055802

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We consider here the situation of a Gaussian pulse that probes a medium exhibiting two close resonance lines. We study the spatial behavior of the light pulse and emphasize some overlooked features. Moreover, for long pulses and a fast-light medium, we show that the spatial distortion of the pulse due to residual gain at the central laser wavelength cannot be reduced without enhancing another distortion effect due to spectral wing amplification.
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.