Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Degenerate conical emissions in atomic-sodium vapor

John Pender, Lambertus Hesselink

Published Jul 1, 1990• 64 citations
Publisher

Abstract

Degenerate conical emissions that appear in laser-pumped atomic sodium have been reported. The cones appear for both single- and double-pump geometries. The nonlinear medium is a small, high-density sodium-seeded flame. Earlier work that relates the cones to the process of degenerate phase conjugation is extended. The analysis for the single-pump phenomenon is formally related to amplified spontaneous emission. The double-pump case is analogous to a distributed-feedback laser. Theory and experiment are presented and discussed.

DOI
10.1364/josab.7.001361

Related papers

Conical emissions and phase conjugation in atomic sodium

John Pender, Lambertus Hesselink

Conical emissions in atomic sodium in which the cone wavelength is the same as the pump wavelength have been reported. These emissions appear about a single pump when the laser is tuned to the blue side of the D2 line but do not appear for red detunings. If two counterpropagating pumps are used, conical emissions appear for both blue and red detunings.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Conical emission in a small high-density sodium environment

John Pender, Lambertus Hesselink

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.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Conical emissions and phase conjugation in atomic sodium vapor

John Pender, Lambertus Hesselink

Observations of a new type of conical emission in atomic sodium provide the motivation for a series of phase conjugation experiments. These experiments show large variations in the reflectivity as a function of probe angle, which are not explained by existing theory. Analysis which includes self-induced refractive index changes leads to numerical calculations, which agree well with the observations.>

IEEE Journal of Quantum Electronics•Mar 1, 1989•25 citations

Degenerate four-wave mixing in sodium vapor in the Rabi regime

B. Kleinmann, F. Tréhin, M. Pinard +1 more

Degenerate four-wave mixing in sodium vapor is investigated using a flashlamp-pumped dye laser synchronized on a cw dye laser. At low atomic density, the reflectivity versus the pump intensity and the line shapes are in good agreement with theoretical predictions in the case of both plane waves and Gaussian beams. At high atomic density, reflectivities much higher than unity have been observed. The influence of the pump imbalance has been studied as well as the deformation of the wave front of the conjugated beam introduced by the pump beams. In the high-atomic-density case, the theoretical problem is more complex, and our experimental results exhibit only qualitative agreement with theory.

Journal of the Optical Society of America B•May 1, 1985•27 citations

Theory of optical near-resonant cone emission in atomic vapor

B. D. Paul, J. Cooper, Alan Gallagher +1 more

A time-dependent theory for conical emission during near-resonant propagation of laser light in an atomic vapor, which includes full propagation for the laser and frequency sidebands in a nonlinear two-level medium is presented. The density-matrix equations for the dipole moment and population are solved in the dressed atomic frame. The polarization source terms are accurate to order \ensuremath{\gamma}/R, where \ensuremath{\gamma} is a damping constant and R is the generalized Rabi frequency. Analytical plane-wave solutions and numerical, cylindrically symmetric propagation simulations including diffraction are presented. It is shown that the calculations with cylindrically symmetric fields and atomic excitation profiles are incapable of accounting for the high levels of optical gain that are responsible for the intense conical emission observed in experiments. This result is at first surprising, since the model accounts rigorously for all of the physical phenomena that have been previously proposed as being responsible for generating large gains, and the calculation matches the symmetry of the observations. The lack of large calculated gain seems to imply the existence of higher-order $(m>0)$ radial modes in the field for the experimental conditions that give rise to cone emission. In the simulations, however, the cylindrically symmetric fields do produce weak red-detuned cones with angular-frequency distributions similar to those seen in experiments.

Physical Review A•Dec 31, 2002•8 citations

Multiple conical emissions from a strongly driven atomic system

Yaakov Shevy, M. Rosenbluh

Two distinct forms of conical emission are observed when a strong near-resonant laser pulse propagates through sodium vapor. One of the cones originates in a resonantly enhanced parametric four-wave mixing process. A spatially and spectrally distinct cone is produced by the radiative decay of the coherently prepared population of the excited state at a frequency close to that of the unperturbed atomic resonance.

Journal of the Optical Society of America B•Jan 1, 1988•34 citations
Degenerate conical emissions that appear in laser-pumped atomic sodium have been reported. The cones appear for both single- and double-pump geometries. The nonlinear medium is a small, high-density sodium-seeded flame. Earlier work that relates the cones to the process of degenerate phase conjugation is extended. The analysis for the single-pump phenomenon is formally related to amplified spontaneous emission. The double-pump case is analogous to a distributed-feedback laser. Theory and experiment are presented and discussed.
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.
Degenerate four-wave mixing in sodium vapor is investigated using a flashlamp-pumped dye laser synchronized on a cw dye laser. At low atomic density, the reflectivity versus the pump intensity and the line shapes are in good agreement with theoretical predictions in the case of both plane waves and Gaussian beams. At high atomic density, reflectivities much higher than unity have been observed. The influence of the pump imbalance has been studied as well as the deformation of the wave front of the conjugated beam introduced by the pump beams. In the high-atomic-density case, the theoretical problem is more complex, and our experimental results exhibit only qualitative agreement with theory.
A time-dependent theory for conical emission during near-resonant propagation of laser light in an atomic vapor, which includes full propagation for the laser and frequency sidebands in a nonlinear two-level medium is presented. The density-matrix equations for the dipole moment and population are solved in the dressed atomic frame. The polarization source terms are accurate to order \ensuremath{\gamma}/R, where \ensuremath{\gamma} is a damping constant and R is the generalized Rabi frequency. Analytical plane-wave solutions and numerical, cylindrically symmetric propagation simulations including diffraction are presented. It is shown that the calculations with cylindrically symmetric fields and atomic excitation profiles are incapable of accounting for the high levels of optical gain that are responsible for the intense conical emission observed in experiments. This result is at first surprising, since the model accounts rigorously for all of the physical phenomena that have been previously proposed as being responsible for generating large gains, and the calculation matches the symmetry of the observations. The lack of large calculated gain seems to imply the existence of higher-order (m>0)(m>0)(m>0) radial modes in the field for the experimental conditions that give rise to cone emission. In the simulations, however, the cylindrically symmetric fields do produce weak red-detuned cones with angular-frequency distributions similar to those seen in experiments.