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

Physical Review A

Forward degenerate four-wave-mixing spectra of NO in the strong-field regime including polarization, line coupling, and multipole effects. II. Experiments

Véronique Krüger, M. Dumont, S. Le Boiteux, Y. J. Picard, Frédéric Chaussard, Brigitte Attal‐Trétout

Published Jun 13, 2001• 10 citations
Publisher

Abstract

The behavior of forward degenerate four-wave-mixing spectra of NO $\~A\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}(0,0)$ in the presence of strong optical fields is observed for two crossed-polarization arrangements. The NO features in terms of coupled and isolated lines are interpreted with the complete model described in the preceding paper [V. Kr\"uger et al., paper I, Phys. Rev. 63, 012716 (2001)]. In the intermediate regime of saturation, the variation of relative line intensities with input energy is properly reproduced for NO. Thanks to these fits, we have been able to determine saturation threshold with a good accuracy. Important properties of the different polarization schemes are observed and discussed.

DOI
10.1103/physreva.64.012717

Related papers

Forward degenerate four-wave-mixing spectra of NO in the strong-field regime including polarization, line coupling, and multipole effects. I. Theory

V. Krüger, M. Dumont, S. Le Boiteux +3 more

In the present paper, we investigate the saturation mechanism of FDFWM (forward degenerate four-wave-mixing) spectra, observed with different polarizations of the input beams, line coupling, and Doppler effect. Our theoretical approach uses a nonperturbative resolution of the density matrix equations, decomposed on the irreducible tensor basis. This formalism greatly simplifies analytical expressions and allows for a correct treatment of magnetic sublevels structure in a three-J level system. Systematic calculations of the FDFWM signal for specific NO lines are performed to characterize intensities and line shapes as a function of saturation. Relative intensities exhibit strong changes in the intermediate regime of saturation further supporting the necessity for using such a complete model. Under saturating conditions, line coupling is shown to distort the spectra, according to the type of transition and the polarization configuration. This effect is observed in the following paper [V. Kr\"uger et al., paper II, Phys. Rev. A 2001 (to be published)], where saturated experimental spectra of NO are presented and interpreted for two polarization configurations of interest for diagnostic purposes.

Physical Review A•Jun 13, 2001•10 citations

Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

Thomas A. Reichardt, Robert P. Lucht

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

The Journal of Chemical Physics•Dec 8, 1999•22 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

Level-crossing spectroscopy of atoms dressed by optical photons in degenerate four-wave mixing

M. Pinard, Philippe Verkerk, G. Grynberg

We investigate degenerate four-wave mixing on the 607.4-nm line of neon using crossed-polarized beams. We show that the line shape changes dramatically in the presence of a magnetic field. Narrow resonances are observed, which are interpreted as level-crossing resonances in the energy diagram of the dressed atom.

Optics Letters•Sep 1, 1984•16 citations

Saturation behavior of resonant degenerate four-wave and multiwave mixing in the Doppler-broadened regime: Experimental analysis on a low-pressure Ne discharge

S. Le Boiteux, Pierre Simoneau, Daniel Bloch +2 more

In this paper, we present a detailed analysis of saturation effects in resonant degenerate four-wave mixing (phase conjugation) or multiwave mixing (high-order diffraction on an optically induced grating). The experiments are performed in a low-pressure Ne discharge in the Doppler-broadened regime, both on an "ideal" two- or three-level system (1s_{4}(J = 1) - 2p_{3}(J = 0)) or on a degenerate multi-level system (1s_{5}(J = 2) - 2p_{9}(J = 3)). The saturation effects appearing when both pump beams are intense are studied, and a very good agreement is found with the previously developed theory [8]. It is demonstrated that there is an absolute maximum to the phase-conjugate reflectivity, and various effects on the lineshape (splitting, linewidth, etc.) are investigated. The effects produced by the Gaussian nature of the incident beams are analyzed in order to interpret some of the discrepancies between theory and experiment. Several new theoretical results for high-order diffraction are also presented, and compared with the experiments. The possibility of dealing with the saturation effects in four-wave mixing when all three incident fields are saturating appears as a consequence of these studies on multiwave mixing. Notably discussed are the case of an intense diffracting field, and of intense grating fields, whose intensity may be unbalanced. Finally, the polarization selection rules for high-order diffraction experiments are established.

IEEE Journal of Quantum Electronics•Aug 1, 1986•34 citations

Degenerate four-wave-mixing line shapes of hydroxyl at high pump intensities

Michael S. Brown, Larry A. Rahn, Robert P. Lucht

The degenerate four-wave-mixing spectral profile of the R(1)(9) transition in the A(2)Σ(+) ? X(2)∏(0, 0) band of OH has been measured for various combinations of saturating pump beams. With increasing pumpbeam intensity the degenerate four-wave-mixing line shape changes dramatically near line center. In phase-conjugate geometry, three distinct spectral line shapes were observed for the cases of (1) equally intense pump beams, (2) a strong forward pump and a weak backward pump, and (3) a weak forward pump and an intense backward pump. A significant saturation dip appears in the spectrum near line center for case (3). The measured spectra have been modeled by the use of nonperturbative numerical solutions of the density matrix equations, and agreement between the calculations and the experimental results is excellent. The differences in the saturated line shapes for cases (2) and (3) are explored theoretically, and the calculated results are compared with previous theoretical work [Bloch and Ducloy, J. Opt. Soc.Am. 73, 635 (1985)] in which the line shapes were calculated in the limit of infinite Doppler broadening.

Applied Optics•Jun 20, 1995•18 citations
The behavior of forward degenerate four-wave-mixing spectra of NO A˜\ensuremath−X\ifmmode~\else˜\fi(0,0)\~A\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}(0,0)A˜\ensuremath−X\ifmmode~\else˜\fi​(0,0) in the presence of strong optical fields is observed for two crossed-polarization arrangements. The NO features in terms of coupled and isolated lines are interpreted with the complete model described in the preceding paper [V. Kr"uger et al., paper I, Phys. Rev. 63, 012716 (2001)]. In the intermediate regime of saturation, the variation of relative line intensities with input energy is properly reproduced for NO. Thanks to these fits, we have been able to determine saturation threshold with a good accuracy. Important properties of the different polarization schemes are observed and discussed.
In the present paper, we investigate the saturation mechanism of FDFWM (forward degenerate four-wave-mixing) spectra, observed with different polarizations of the input beams, line coupling, and Doppler effect. Our theoretical approach uses a nonperturbative resolution of the density matrix equations, decomposed on the irreducible tensor basis. This formalism greatly simplifies analytical expressions and allows for a correct treatment of magnetic sublevels structure in a three-J level system. Systematic calculations of the FDFWM signal for specific NO lines are performed to characterize intensities and line shapes as a function of saturation. Relative intensities exhibit strong changes in the intermediate regime of saturation further supporting the necessity for using such a complete model. Under saturating conditions, line coupling is shown to distort the spectra, according to the type of transition and the polarization configuration. This effect is observed in the following paper [V. Kr\"uger et al., paper II, Phys. Rev. A 2001 (to be published)], where saturated experimental spectra of NO are presented and interpreted for two polarization configurations of interest for diagnostic purposes.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
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.
In this paper, we present a detailed analysis of saturation effects in resonant degenerate four-wave mixing (phase conjugation) or multiwave mixing (high-order diffraction on an optically induced grating). The experiments are performed in a low-pressure Ne discharge in the Doppler-broadened regime, both on an "ideal" two- or three-level system (1s_{4}(J = 1) - 2p_{3}(J = 0)) or on a degenerate multi-level system (1s_{5}(J = 2) - 2p_{9}(J = 3)). The saturation effects appearing when both pump beams are intense are studied, and a very good agreement is found with the previously developed theory [8]. It is demonstrated that there is an absolute maximum to the phase-conjugate reflectivity, and various effects on the lineshape (splitting, linewidth, etc.) are investigated. The effects produced by the Gaussian nature of the incident beams are analyzed in order to interpret some of the discrepancies between theory and experiment. Several new theoretical results for high-order diffraction are also presented, and compared with the experiments. The possibility of dealing with the saturation effects in four-wave mixing when all three incident fields are saturating appears as a consequence of these studies on multiwave mixing. Notably discussed are the case of an intense diffracting field, and of intense grating fields, whose intensity may be unbalanced. Finally, the polarization selection rules for high-order diffraction experiments are established.
The degenerate four-wave-mixing spectral profile of the R(1)(9) transition in the A(2)Σ(+) ? X(2)∏(0, 0) band of OH has been measured for various combinations of saturating pump beams. With increasing pumpbeam intensity the degenerate four-wave-mixing line shape changes dramatically near line center. In phase-conjugate geometry, three distinct spectral line shapes were observed for the cases of (1) equally intense pump beams, (2) a strong forward pump and a weak backward pump, and (3) a weak forward pump and an intense backward pump. A significant saturation dip appears in the spectrum near line center for case (3). The measured spectra have been modeled by the use of nonperturbative numerical solutions of the density matrix equations, and agreement between the calculations and the experimental results is excellent. The differences in the saturated line shapes for cases (2) and (3) are explored theoretically, and the calculated results are compared with previous theoretical work [Bloch and Ducloy, J. Opt. Soc.Am. 73, 635 (1985)] in which the line shapes were calculated in the limit of infinite Doppler broadening.