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Physical Review A

Multiconical emission at light counterpropagation in a resonant medium

Anatolii A Afanas'ev, B. A. Samson

Published Jan 1, 1996• 8 citations
Publisher

Abstract

We describe one of the possible ways of development of a spatial instability of counterpropagating strong light beams in resonant media. The interplay between self-focusing and saturation effects results in a formation of counterpropagating stable filaments. The nondegenerate four-photon scattering in these waveguiding structures leads to a far-field multiconical emission with the cones' frequencies shifted to both red and blue sides of the resonant transition. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.591

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We describe one of the possible ways of development of a spatial instability of counterpropagating strong light beams in resonant media. The interplay between self-focusing and saturation effects results in a formation of counterpropagating stable filaments. The nondegenerate four-photon scattering in these waveguiding structures leads to a far-field multiconical emission with the cones' frequencies shifted to both red and blue sides of the resonant transition. \textcopyright{} 1996 The American Physical Society.
A nonlinear medium interacting with two counterpropagating pump beams is potentially unstable. This instability is related to a mirrorless four-wave mixing oscillation.1 Recent experiments done in vapors2 show that the behavior is strongly different according to the sign of the frequency detuning from resonance. When the laser frequency ω is larger than the atomic resonance frequency ω0, the oscillation appears as a sharp conical emission, the oscillation frequency being ω. In some cases the cone is fragmented into a hexagon. When ω < ω0, the oscillation is more difficult to achieve and appears as a very broad cone.
This is the first of a series of papers on the theory of cone emission from a laser-pumped two-level atomic medium. Starting from microscopic quantum theory for both the active medium and the field, equations for the slowly varying macroscopic quantities are derived. In the steady-state limit, which experimentally corresponds to cw excitation, we find that the sources for the paraxial fields of interest have a long coherence length despite the random nature of spontaneous emission. These radiation sources enter into the equations for the fields in the same form as the source generated by four-wave mixing and therefore may be considered as a ``spontaneous four-wave mixing,'' since the photons emitted in the Rabi sidebands are correlated. This has far-reaching consequences on the physics of cone emission and also sheds some new light on the fluoresence from strongly driven atomic systems.
Two types of conical emission in sodium have appeared in the past. In the first, a single tightly focused laser beam is tuned to the blue side of the D1 line in conditions compatible with self-trapping. The emission is specular, has a cone half-angle of a degree, and occurs on the red side of line center. In the second type, two weakly focused counterpropagating laser beams are tuned to the red side of line center. The emission consists of radial filaments, has a cone half-angle of 8°, and is the same wavelength as the pumps. We report on yet a third type of conical emission which is distinct from the first two types by virtue of its spatial and spectral characteristics. Like the first type, the pumps are tuned to the blue side of line center, the emission has a cone half-angle of a degree and is specular. However, this phenomenon also resembles the second type of conical emission in that two counterpropagating pumps are required, the pumps are weakly focused, and the emission wavelength is the same as the pumps.
The propagation of a strong coherent "pump" wave traveling through a resonant medium is discussed. The medium is assumed to consist of identical stationary atoms, and the pump-wave frequency is assumed to coincide exactly with the resonance frequency for transitions between a particular pair of atomic states. A previously developed theory of the response of a strongly driven atom to a weak nearly resonant "signal" field is used to deduce the existence of a coupling between any two waves travelling parallel to the pump wave whose (nearly equal) frequencies sum to twice the pump-wave frequency. In the limit of very intense (highly saturating) pump fields, the coupling between the two waves of nearby frequencies leads to amplification of both waves if their frequencies lie within an interval about the pump-wave frequency equal to the Rabi frequency of population inversion. The basic process, which is roughly described by travelling-wave parametric-amplifier equations of motion, consists of the absorption of two pump-field photons followed by their emission at different nearby frequencies, and thus implies a frequency instability of the initially coherent pump wave.