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 four-wave mixing in sodium vapor in the Rabi regime

B. Kleinmann, F. Tréhin, M. Pinard, G. Grynberg

Published May 1, 1985• 27 citations
Publisher

Abstract

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.

DOI
10.1364/josab.2.000704

Related papers

Detailed velocity-dependent line shapes for degenerate four-wave mixing spectra in a two-level atomic system

Binh Do, Daniel S. Elliott

We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the ${3s}^{2}{S}_{1/2},$ $F=2,$ ${m}_{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2},$ $F=3,$ ${m}_{\mathrm{F}}=3$ transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.

Physical Review A•Jun 19, 2003•3 citations

Four Wave Mixing Characteristics Of Sodium Vapor Under High Reflectivity Conditions

J. Brock, Joseph M. Fukumoto, Frank G. Patterson +3 more

Four wave mixing (FWM) performance of sodium vapor was investigated in the strong pump regime (I»I at) necessary to achieve good phase conjugate reflectivity, R. Reflectivities >230% were observed using narrowband CW pump powers less than 1 W. Degenerate FWM spectral response was measured with R as a parameter, and shown to depend on self-focusing effects at higher R. The field of view of the sodium FWM was determined under narrowband high R conditions and found to behave as expected, except for nearly collinear geometries. Faith-ful imaging through a severe optical aberration was demonstrated at moderate R, but experimental observations and analysis indicate potential fidelity problems at large R. Reflect-ivity and field of view were also measured for wideband (2 GHz) laser pumping.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 22, 1988•0 citations

Backward saturation in four-wave mixing in neon: Case of cross-polarized pumps

M. Pinard, Philippe Verkerk, G. Grynberg

The effect of an intense pump beam on the intensity of the phase-conjugated emission is studied in the case of a three-level atom. We first extend to the case of cross-polarized pump beams the dressed-atom model that we have presented previously [Phys. Rev. A 34, 4008 (1986)] for the case of two-level atoms. The range of validity of our theory is \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width). We have studied the line shape in degenerate four-wave mixing, the influence of a static magnetic field, and the resonances that appear in nondegenerate four-wave mixing. Experiments are done in a neon discharge using cw dye lasers. The experimental results are in good agreement with the theoretical predictions. In degenerate four-wave mixing, we have shown that the saturating dip disappears when the weak beams have orthogonal polarizations. In the presence of a static magnetic field and in the nearly degenerate case, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed. The intensity and the width of these resonances are in very good agreement with the predictions of the theoretical model.

Physical Review A•Jun 1, 1987•32 citations

Degenerate four-wave mixing line shapes in sodium vapor under pulsed excitation

Prem Kumar

Degenerate four-wave mixing (DFWM) line shapes are investigated in sodium vapor near the D(2) resonance line using nearly Fourier-transform-limited pulses. At low pump intensities sub-Doppler resolution is obtained. When the Rabi frequency associated with the pump intensity becomes comparable with the ground-state hyperfine frequency separation of sodium, each component of the double-peaked DFWM spectrum splits further into two components. An adiabatic-following model explains the near-resonant intensity dependence of the DFWM signal. A qualitative explanation of the observed splitting is also given.

Optics Letters•Feb 1, 1985•13 citations

Backward saturation in four-wave mixing in neon: Case of parallel pump polarizations

Philippe Verkerk, M. Pinard, G. Grynberg

We present in this paper a theoretical and experimental study of the effect of an intense pump beam on four-wave-mixing emission in the geometry of phase conjugation. The theoretical model is developed for \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width) and uses the dressed-atom approach. We have analyzed degenerate and nearly degenerate four-wave mixing. In this latter case, we have studied three situations according to which beam (intense pump, weak pump, or probe) has a different frequency. The experimental study has been done in a neon cell using cw lasers. Our experimental results are in excellent agreement with theory. This study shows the need to take into account the atomic motion in the theory. However a quantitative analysis cannot be done assuming an infinite Doppler width and we show the importance of the Boltzmann factor. In the case of nearly degenerate four-wave mixing, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed.

Physical Review A•Nov 1, 1986•23 citations

Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor

D. M. Bloom, P. F. Liao, Nicholas P. Economou

This Letter is the first report of the observation of amplified reflection and self-oscillation produced by degenerate optical four-wave mixing by using a resonantly enhanced Kerr nonlinearity in atomic sodium vapor. Phase-conjugated reflected waves with intensities 100 times greater than input-signal intensities were achieved with only 40-kW/cm2 pump intensity.

Optics Letters•Mar 1, 1978•199 citations
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.
We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the 3s2S1/2,{3s}^{2}{S}_{1/2},3s2S1/2​, F=2,F=2,F=2, ${m}_{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2},$ F=3,F=3,F=3, mF=3{m}_{\mathrm{F}}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.
Four wave mixing (FWM) performance of sodium vapor was investigated in the strong pump regime (I»I at) necessary to achieve good phase conjugate reflectivity, R. Reflectivities >230% were observed using narrowband CW pump powers less than 1 W. Degenerate FWM spectral response was measured with R as a parameter, and shown to depend on self-focusing effects at higher R. The field of view of the sodium FWM was determined under narrowband high R conditions and found to behave as expected, except for nearly collinear geometries. Faith-ful imaging through a severe optical aberration was demonstrated at moderate R, but experimental observations and analysis indicate potential fidelity problems at large R. Reflect-ivity and field of view were also measured for wideband (2 GHz) laser pumping.
The effect of an intense pump beam on the intensity of the phase-conjugated emission is studied in the case of a three-level atom. We first extend to the case of cross-polarized pump beams the dressed-atom model that we have presented previously [Phys. Rev. A 34, 4008 (1986)] for the case of two-level atoms. The range of validity of our theory is \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width). We have studied the line shape in degenerate four-wave mixing, the influence of a static magnetic field, and the resonances that appear in nondegenerate four-wave mixing. Experiments are done in a neon discharge using cw dye lasers. The experimental results are in good agreement with the theoretical predictions. In degenerate four-wave mixing, we have shown that the saturating dip disappears when the weak beams have orthogonal polarizations. In the presence of a static magnetic field and in the nearly degenerate case, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed. The intensity and the width of these resonances are in very good agreement with the predictions of the theoretical model.
Degenerate four-wave mixing (DFWM) line shapes are investigated in sodium vapor near the D(2) resonance line using nearly Fourier-transform-limited pulses. At low pump intensities sub-Doppler resolution is obtained. When the Rabi frequency associated with the pump intensity becomes comparable with the ground-state hyperfine frequency separation of sodium, each component of the double-peaked DFWM spectrum splits further into two components. An adiabatic-following model explains the near-resonant intensity dependence of the DFWM signal. A qualitative explanation of the observed splitting is also given.
We present in this paper a theoretical and experimental study of the effect of an intense pump beam on four-wave-mixing emission in the geometry of phase conjugation. The theoretical model is developed for \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width) and uses the dressed-atom approach. We have analyzed degenerate and nearly degenerate four-wave mixing. In this latter case, we have studied three situations according to which beam (intense pump, weak pump, or probe) has a different frequency. The experimental study has been done in a neon cell using cw lasers. Our experimental results are in excellent agreement with theory. This study shows the need to take into account the atomic motion in the theory. However a quantitative analysis cannot be done assuming an infinite Doppler width and we show the importance of the Boltzmann factor. In the case of nearly degenerate four-wave mixing, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed.