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Physical Review A

Conical emission as cooperative fluorescence

Witold Chal upczak, Wojciech Gawlik, Jerzy Zachorowski

Published Apr 1, 1994• 25 citations
Publisher

Abstract

We have observed conical emission from a dense, strongly driven ensemble of two-level atoms without noticeable self-focusing. We present the arguments that conical emission, unaffected by autocollimation, is due to cooperative, \ifmmode \check{C}\else \v{C}\fi{}erenkov-like, spontaneous emission of collisionally perturbed, optically dressed atoms rather than to parametric wave mixing. Our results indicate the importance of many-atom correlations which must be taken into account when strong light interacts with dense media.

DOI
10.1103/physreva.49.r2227

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We have observed conical emission from a dense, strongly driven ensemble of two-level atoms without noticeable self-focusing. We present the arguments that conical emission, unaffected by autocollimation, is due to cooperative, \ifmmode \check{C}\else \v{C}\fi{}erenkov-like, spontaneous emission of collisionally perturbed, optically dressed atoms rather than to parametric wave mixing. Our results indicate the importance of many-atom correlations which must be taken into account when strong light interacts with dense media.
The cone emission obtained from pumped two-level atoms is related, by a perturbation theory, to time-dependent terms in the macroscopic Bloch equations. It is described as a cooperative superfluorescence radiation from collections of spatially distributed atoms, including in the theory the far-zone dipole-dipole interactions, in the presence of the strong monochromatic field. The distribution of the cone emission as a function of frequencies and cone angles is analyzed. A phase-matching condition is obtained for the wave vectors of the pump and conical beams that is similar to the Cherenkov condition. The frequency shift for the maximum of the cone light is found to be equal to the generalized Rabi frequency. The broadening of the cone emission is related to inhomogeneity in Rabi frequencies and decoherence effects. An approximate result is obtained for the ratio of intensities of the blue-shifted cone relative to the red-shifted cone so that the blue-shifted cone can appear only for extremely strong laser intensities.
We report computational results that show that the conical emission observed when a nearly resonant laser pulse propagates through an atomic vapor is the result of the breakup of the pulse into solitary waves. For an incident pulse with a radial as well as a temporal profile, the crests and troughs of the two-dimensional 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 that leads to 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 under the rotating-wave and slowly-varying-envelope approximations in the limit of no collisional damping or Doppler broadening. 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. We find that self-focusing is not required for the generation of conical emission, although it would be difficult to separate these effects experimentally.
We present experimental results of ac-Stark-effect-enhanced four-wave mixing in a dense sample of two-level atoms. The mixing efficiency exhibits strong maxima when the beams fulfill resonance and phase-matching conditions for the transitions in a dressed atom. The experimental arrangement enabled the verification of recent theories of parametric interactions in strongly driven systems. Good agreement of these theories with the experimental results allows one to use the wave mixing in the studies of properties and dynamics of strongly driven, dense, two-level systems. In particular, the possible role of parametric interaction in the phenomenon of conical emission has been analyzed in this manner.
Conical light emission is observed when an intense quasiresonant laser beam propagates in an atomic vapor.1-4 A parametric four-wave mixing process was suggested to explain this effect.1 However, this model is inconsistent with experiments both quantitatively in the value of the predicted cone angle and qualitatively due to the absence of the obligatory blue counterpart to the red-shifted cone photon.2-4 A model of Cherenkov radiation by a laser-induced moving polarization was proposed to account for the origin and angular/spectral dependencies of the conical emission.3
A detailed study on yellow conical emission observed in dense sodium vapor following near-resonant one-photon excitation of the Na 42P levels was performed. The origins of conical emission are suggested to be due to Raman resonant four-wave parametric mixing processes. In order to describe spectral and spatial features of off-axis emission, we introduce self-phase modulation and induced-phase modulation as important additional nonlinear processes, explaining the nonmonotonic detuning of the wavelength of the conical radiation with the exiting laser wavelength in the vicinity of resonance transitions. The spatial evolution of emission generated via four-wave mixing is modeled by solving the two-dimensional nonlinear Schrödinger equation describing the spatial evolution of light beams in a nonlinear media. Experimental and theoretical results are presented and discussed.