Negative group velocity and distortion of a pulse in an anomalous dispersion medium

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 1150 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.