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Physical Review A

Modulational instability in atomic vapors

P. Gauthier, O. Gobert, Michel Comte, Daniel L’Hermite, Jacques de Lamare, Didier Bénisti

Published Mar 1, 2002• 3 citations
Publisher

Abstract

We report an experimental, numerical, and analytical study of the near resonant propagation of a laser pulse through an atomic vapor. In the nonlinear regime probed, the light pulse develops frequency sidebands whose positions are, in first approximation, solely dependent on the maximum Rabi frequency of the system, in a fashion very similar to that observed in optical fibers. This modulational instability dictates the temporal reshaping of the laser field and finally results in pulse splitting.

DOI
10.1103/physreva.65.033834

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We report an experimental, numerical, and analytical study of the near resonant propagation of a laser pulse through an atomic vapor. In the nonlinear regime probed, the light pulse develops frequency sidebands whose positions are, in first approximation, solely dependent on the maximum Rabi frequency of the system, in a fashion very similar to that observed in optical fibers. This modulational instability dictates the temporal reshaping of the laser field and finally results in pulse splitting.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of pulse breakup into temporal-spatial (2-D) solitary waves. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum. Because the process of pulse breakup depends on the pulse area, the 2-D solitary waves are curved in the time-radius plane due to the transverse profile of the pulse. The curvature of the solitary waves in the time-radius plane results in a transverse spatial oscillation and a corresponding transverse wave vector that leads to conical emission in the far field.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of the breakup of the pulse into solitary waves. For an incident pulse with a transverse as well as a temporal profile, the crests and troughs of the 2-D solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation, resulting in conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. The cone opening angle depends on the initial transverse profile of the pulse and the process of beam breakup as well as self-focusing.
Summary form only given. A recent technique for creating "fast" light pulses (i.e. pulses of light having group velocity greater than c or less than zero) uses a continuous-wave bichromatic Raman pump laser beam to tailor the dispersion properties of an atomic vapor. We have discovered a number of effects that impose limits on fast-light propagation as the gain increases. Most important is the modulation instability, a nonlinear effect that can lead to temporal modulation of intense continuous-wave laser fields. We discuss the induced modulation instability in the context of high-gain bichromatically driven atomic systems, specifically in the context of fast-light pulse propagation. We further discuss the practical limitations that the induced modulation instability imposes on this method for creating faster-than-c pulses.
We study the one-dimensional propagation of a laser pulse through an atomic vapor of finite length L. Both the temporal and the time-dependent spectral profiles of the exiting laser pulse are calculated. It is shown that, when the pulse duration is comparable with or shorter than the effective relaxation time of the atomic density matrix, the spectrum of the final pulse exhibits frequency sidebands located in the vicinity of the time-varying generalized Rabi frequency, which can contain up to a few percent of the total laser power. The possible connection between this result and cone emission in the pulsed regime is addressed.