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Journal of Physics B Atomic and Molecular Physics

Absorption and saturation effects on degenerate four-wave mixing in excited states formed during collisions

P. Ewart, S.V. O’Leary

Published Nov 28, 1984• 18 citations
Publisher

Abstract

Degenerate four-wave mixing (DFWM) in excited atoms is investigated as a probe of the excited-state density produced by collision-assisted transitions. Sodium atoms are excited to the 3P state by absorption of light in the extreme blue wing of the D lines in the presence of He, Ne and Ar perturbers. The rare-gas pressure dependence of the DFWM signals, resonantly enhanced by the 3P-4D transition, is studied to determine the regime where the signals give an unambiguous measure of the excited-state (3P) density. The observed behaviour is compared with a simple model of DFWM in absorbing media. Good qualitative agreement is obtained and the results illustrate the role of absorption, saturation and finite laser bandwidth. The technique allows small excited-state densities ( approximately 10 9 cm -3 ) to be detected with good temporal and spatial resolution.

DOI
10.1088/0022-3700/17/22/019

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We have investigated degenerate four-wave mixing (DFWM) in a strongly absorbing molecular gas. A theory taking into account saturable absorption of the interacting beams is used to explain the dependence of the DFWM reflectivity on laser intensity and on the molecular number density. These parameters have a great influence on the observed spectra, owing to linear absorption that suppresses the DFWM signal in the line center of the molecular transitions. The great sensitivity of the spectra to the experimental conditions limits the applicability of DFWM for spectroscopic studies in absorbing media.

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Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in S${\mathrm{F}}_{6}$ using a pulsed C${\mathrm{O}}_{2}$ laser operated on the 10.4-\ensuremath{\mu} m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (\ensuremath{\sim}0.1 J/${\mathrm{cm}}^{2}$) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the S${\mathrm{F}}_{6}$ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.

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High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems

Jing Liu, Duncan G. Steel

We report a series of measurements of the nearly degenerate four-wave-mixing response in atomic sodium in the presence of a helium buffer gas. The results show the line shape associated with both the ground-state and excited-state dynamics. The line shape evolves as a function of pressure from a dip at a pressure of 0 Torr to a spike at a few Torr due to the presence of collisions. The width of the spike is determined by residual Doppler broadening. At higher pressure (\ensuremath{\ge}10 Torr), the width of the spike is further narrowed below the residual Doppler width. The additional reduction is due to a form of Dicke narrowing associated with the dynamics of the lower- and upper-level excitations. The results are in qualitative agreement with a perturbation solution of the density-matrix equations which include the effects of velocity-changing collisions and state-changing collisions.

Physical Review A•Nov 1, 1988•5 citations
Degenerate four-wave mixing (DFWM) in excited atoms is investigated as a probe of the excited-state density produced by collision-assisted transitions. Sodium atoms are excited to the 3P state by absorption of light in the extreme blue wing of the D lines in the presence of He, Ne and Ar perturbers. The rare-gas pressure dependence of the DFWM signals, resonantly enhanced by the 3P-4D transition, is studied to determine the regime where the signals give an unambiguous measure of the excited-state (3P) density. The observed behaviour is compared with a simple model of DFWM in absorbing media. Good qualitative agreement is obtained and the results illustrate the role of absorption, saturation and finite laser bandwidth. The technique allows small excited-state densities ( approximately 10 9 cm -3 ) to be detected with good temporal and spatial resolution.
The population of the 3P state in atomic sodium produced by absorption in the extreme blue wing of the D lines is measured by excited-state degenerate four-wave mixing (ESDFWM). The strength of this ESDFWM signal is shown to give a measure of the pressure-broadened extreme-wing absorption coefficient alpha ( omega ). Relative values of alpha ( omega ) for the rare gases He, Ne and Ar are measured and compared with values calculated from theoretical interatomic potentials and from extreme-wing emission data. Very good agreement is found demonstrating the ability of this nonlinear technique to make accurate measurements of small excited-state densities with excellent spatial and temporal resolution. Advantages of the method for other applications are briefly discussed.
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.
We have investigated degenerate four-wave mixing (DFWM) in a strongly absorbing molecular gas. A theory taking into account saturable absorption of the interacting beams is used to explain the dependence of the DFWM reflectivity on laser intensity and on the molecular number density. These parameters have a great influence on the observed spectra, owing to linear absorption that suppresses the DFWM signal in the line center of the molecular transitions. The great sensitivity of the spectra to the experimental conditions limits the applicability of DFWM for spectroscopic studies in absorbing media.
Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in SF6{\mathrm{F}}_{6}F6​ using a pulsed CO2{\mathrm{O}}_{2}O2​ laser operated on the 10.4-\ensuremath{\mu} m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (\ensuremath{\sim}0.1 J/cm2{\mathrm{cm}}^{2}cm2) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the SF6{\mathrm{F}}_{6}F6​ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.
We report a series of measurements of the nearly degenerate four-wave-mixing response in atomic sodium in the presence of a helium buffer gas. The results show the line shape associated with both the ground-state and excited-state dynamics. The line shape evolves as a function of pressure from a dip at a pressure of 0 Torr to a spike at a few Torr due to the presence of collisions. The width of the spike is determined by residual Doppler broadening. At higher pressure (\ensuremath{\ge}10 Torr), the width of the spike is further narrowed below the residual Doppler width. The additional reduction is due to a form of Dicke narrowing associated with the dynamics of the lower- and upper-level excitations. The results are in qualitative agreement with a perturbation solution of the density-matrix equations which include the effects of velocity-changing collisions and state-changing collisions.