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Physical Review A

Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor

Hirokazu Tanaka, H. Niwa, K. Hayami, Shingo Furue, K. Nakayama, T. Kohmoto, Masakazu Kunitomo, Yukio Fukuda

Published Nov 3, 2003• 65 citations
Publisher

Abstract

Propagation of optical pulses in a resonantly absorbing medium is studied. Propagation time of nanosecond pulses was measured for the Rb ${D}_{1}$ transition. At the center of two absorption lines, delay of the pulse peak which is about ten times as large as the pulse width was observed, where zero delay is defined for the propagation with the light velocity in vacuum. On the other hand, at the peak of an absorption line, negative delay was observed for large absorption, where the advance time is as large as 25% of the pulse width. Simulation including the effect of absorption and phase shift reproduced well the experimental results.

DOI
10.1103/physreva.68.053801

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Propagation of optical pulses in a resonantly absorbing medium is studied. Propagation time of nanosecond pulses was measured for the Rb D1{D}_{1}D1​ transition. At the center of two absorption lines, delay of the pulse peak which is about ten times as large as the pulse width was observed, where zero delay is defined for the propagation with the light velocity in vacuum. On the other hand, at the peak of an absorption line, negative delay was observed for large absorption, where the advance time is as large as 25% of the pulse width. Simulation including the effect of absorption and phase shift reproduced well the experimental results.
For a pulse with carrier frequency detuned less than an atomic plasma frequency but outside a narrow Lorentzian gain line, the group velocity will be negative. Unlike propagation at the center of an absorption line, the energy velocity is approximately equal to the group velocity, and is also negative. We show that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape. The peak of the transmitted pulse leaves the gain medium before the peak of the incident pulse enters, i.e., the pulse is transmitted superluminally. For a sufficiently long medium the exit pulse is well resolved from a comparison pulse traveling through an equal distance of vacuum. There is no conflict with causality, as numerical simulations with a switched-on Gaussian demonstrate. We propose an experiment to observe this kind of propagation by sending a pulsed probe beam through a Xe gas cell pumped to achieve inversion.
Propagation of femtosecond light pulses in a resonant absorption medium is studied. The propagation time of the light pulses was measured in a dye solution by the optical-Kerr-gate method. Nonadherence to the conventional group velocity domega/dk , which is defined in weak absorption region, was found. The observed wavelength dependences of the group delay and the spectral change in the anomalous dispersion region are qualitatively in good agreement with the theoretical prediction obtained from the new definitions of group velocity, which can be clearly defined even in strong absorption region.
We have examined the propagation of femtosecond laser pulses in an absorbing dye solution through a short to a long range of propagation distance. The transmitted pulses show strong spectral shift and a superluminal to subluminal transition in the propagation velocity keeping its initial shape almost intact. It is verified that the peak velocity is well described by a modified group velocity v(S) defined within the framework of the saddle-point method as well as by a recent prediction of the net group delay of surviving frequency.
We experimentally study the group time delay for a light pulse propagating through hot 87Rb^{87}\mathrm{Rb}87Rb vapor in the presence of a strong coupling field in a $\ensuremath{\Lambda}$ configuration. We demonstrate that the ultraslow pulse propagation is transformed into superluminal propagation as the one-photon detuning of the light increases due to the change in the transmission resonance line shape. Negative group velocity as low as $\ensuremath{-}c∕{10}^{6}=\ensuremath{-}80\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$ is recorded. We also find that the advance time in the regime of the superluminal propagation grows linearly with increasing laser field power.