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

Optics Letters

Four-wave mixing with dynamic Stark effects in flames

Bruce K. Winker, John Curtis Wright

Published Jan 1, 1989• 5 citations
Publisher

Abstract

Four-wave mixing is studied in a Na-seeded flame in the regime of strong saturation of the Na D-line transitions. The output frequency differs from that of the input lasers so that spectral discrimination can distinguish the mixing signal. Scans of the D2 resonance with another laser set at the D1-line resonance reveals two resonances corresponding to the D2 resonance and the frequency difference of the D levels. The mixing efficiency at the D2 resonance increases with the detuning of the D1 resonance. The frequency difference resonance is weak because of interference between multiple coherent pathways.

DOI
10.1364/ol.14.000054

Related papers

Study of two-photon near resonant four-wave difference mixing in atomic sodium in a CH4/air flame

J. SINGH, Fang Yu Yueh

Study of a two-photon near resonant four wave difference mixing (FWDM) in Na in a CH4/air flame has been performed to understand the FWDM process reported by Singh and Yueh (1992). The FWDM signal was measured with reduced flame length and with the focal point at the center and also at one end of the flame to pinpoint the region in which the signal is generated. A partial contribution in the third peak was from the nonresonant background. A FWDM signal is generated slightly away from the focal point and nonresonant background, at the focal point in the present experimental conditions. An absorption spectrum of the Na D-lines at different dye laser energy was recorded to study the depletion of Na ground state at higher dye laser intensity. Comparative study of the FWDM signal with a narrow and broad bandwidth dye laser shows that a lower Na concentration detection limit could be achieved with a narrow linewidth probe laser tuned to about 9/cm lower frequency from the center of the D1 line. The two minima in the FWDM spectrum corresponding to Na D lines have been explained, qualitatively, with the saturation effect in the Na D-lines transition. 27 refs.

AIAA Plasmadynamics and Lasers Conference•Jul 6, 1992•0 citations

Four-wave difference mixing in Na in a CH_4–air flame

J. P. Singh, Fang Yu Yueh

A four-wave difference mixing signal has been observed for what is, to our knowledge, the first time, in sodium in a methane-air flame. The experimental conditions used to observe the signal in the flame are reported. An explanation of the observed signal in terms of near two photon resonant difference four-wave mixing is proposed.

Applied Optics•Aug 20, 1992•2 citations

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Mark J. Fernée, P. F. Barker, Alan E. W. Knight +1 more

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of $5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ atoms/${\mathrm{cm}}^{3}$. Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to ``seed'' the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.

Physical Review A•Apr 1, 1998•0 citations

Four-wave mixing in strongly driven four-level systems

F. A. M. de Oliveira, Cid Bartolomeu de Araujo, J. R. Rios Leite

A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.

Physical Review A•Dec 1, 1988•17 citations

Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations

Robert P. Lucht, Roger L. Farrow, David J. Rakestraw

Saturation effects in gas-phase degenerate four-wave mixing (DFWM) are investigated for conditions of interest for diagnostic applications in flames and plasmas. In particular, the case in which Doppler and collisional broadening are comparable, as is often the case for flame species such as NO and OH, is investigated. DFWM line shapes and signal intensities are calculated nonperturbatively and compared with high-resolution laser measurements. In the nonperturbative calculations the time-dependent density-matrix equations for a two-level system interacting with three laser fields are integrated directly on a grid of spatial locations along the phase-matching axis. The electric-field amplitude for the DFWM signal is determined by multiplying the time-varying, laser-induced polarization at each grid point by the appropriate phase factor and then by summing over all grid points. The calculations are in excellent agreement with measurements of DFWM line shapes and signal intensities for NO in a buffer gas of He over a wide range of He pressure. Under saturation conditions the pressure dependence of the DFWM signal is reduced greatly compared with the unsaturated case. The signal level is still dependent on the ratio of pure dephasing to quenching collisions, even for saturation conditions. From the standpoint of minimal dependence on collisional processes it appears that operation with pump-laser intensities approximately equal to the saturation intensity is optimal. The dependence of the DFWM line shape and signal intensity on the ratio of probe to pump-laser intensity is also investigated.

Journal of the Optical Society of America B•Sep 1, 1993•75 citations

Degenerate four-wave mixing spectroscopy with short-pulse lasers: theoretical analysis

Thomas A. Reichardt, Robert P. Lucht

The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.

Journal of the Optical Society of America B•Dec 1, 1996•17 citations
Four-wave mixing is studied in a Na-seeded flame in the regime of strong saturation of the Na D-line transitions. The output frequency differs from that of the input lasers so that spectral discrimination can distinguish the mixing signal. Scans of the D2 resonance with another laser set at the D1-line resonance reveals two resonances corresponding to the D2 resonance and the frequency difference of the D levels. The mixing efficiency at the D2 resonance increases with the detuning of the D1 resonance. The frequency difference resonance is weak because of interference between multiple coherent pathways.
Study of a two-photon near resonant four wave difference mixing (FWDM) in Na in a CH4/air flame has been performed to understand the FWDM process reported by Singh and Yueh (1992). The FWDM signal was measured with reduced flame length and with the focal point at the center and also at one end of the flame to pinpoint the region in which the signal is generated. A partial contribution in the third peak was from the nonresonant background. A FWDM signal is generated slightly away from the focal point and nonresonant background, at the focal point in the present experimental conditions. An absorption spectrum of the Na D-lines at different dye laser energy was recorded to study the depletion of Na ground state at higher dye laser intensity. Comparative study of the FWDM signal with a narrow and broad bandwidth dye laser shows that a lower Na concentration detection limit could be achieved with a narrow linewidth probe laser tuned to about 9/cm lower frequency from the center of the D1 line. The two minima in the FWDM spectrum corresponding to Na D lines have been explained, qualitatively, with the saturation effect in the Na D-lines transition. 27 refs.
Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of $5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ atoms/cm3{\mathrm{cm}}^{3}cm3. Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to ``seed'' the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.
A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.
Saturation effects in gas-phase degenerate four-wave mixing (DFWM) are investigated for conditions of interest for diagnostic applications in flames and plasmas. In particular, the case in which Doppler and collisional broadening are comparable, as is often the case for flame species such as NO and OH, is investigated. DFWM line shapes and signal intensities are calculated nonperturbatively and compared with high-resolution laser measurements. In the nonperturbative calculations the time-dependent density-matrix equations for a two-level system interacting with three laser fields are integrated directly on a grid of spatial locations along the phase-matching axis. The electric-field amplitude for the DFWM signal is determined by multiplying the time-varying, laser-induced polarization at each grid point by the appropriate phase factor and then by summing over all grid points. The calculations are in excellent agreement with measurements of DFWM line shapes and signal intensities for NO in a buffer gas of He over a wide range of He pressure. Under saturation conditions the pressure dependence of the DFWM signal is reduced greatly compared with the unsaturated case. The signal level is still dependent on the ratio of pure dephasing to quenching collisions, even for saturation conditions. From the standpoint of minimal dependence on collisional processes it appears that operation with pump-laser intensities approximately equal to the saturation intensity is optimal. The dependence of the DFWM line shape and signal intensity on the ratio of probe to pump-laser intensity is also investigated.
The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.