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Journal of Physics B Atomic and Molecular Physics

Comparisons of sodium: rare-gas potentials by measurements of excited-state degenerate four-wave mixing

P Eward, S.V. O’Leary

Published Oct 28, 1982• 30 citations
Publisher

Abstract

The technique of excited-state degenerate four-wave mixing, ESDFWM, has been used to monitor the absorption of light at two wavelengths in the extreme wings of the pressure broadened Na D lines. The relative slopes of the ESDFWM signals as a function of pressure of rare gases He, Ne and Ar are compared with predictions of the quasistatic theory of line broadening using theoretical interatomic potentials.

DOI
10.1088/0022-3700/15/20/014

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Optics Letters•Jul 1, 1981•54 citations
The technique of excited-state degenerate four-wave mixing, ESDFWM, has been used to monitor the absorption of light at two wavelengths in the extreme wings of the pressure broadened Na D lines. The relative slopes of the ESDFWM signals as a function of pressure of rare gases He, Ne and Ar are compared with predictions of the quasistatic theory of line broadening using theoretical interatomic potentials.
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.
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.
Degenerate four-wave mixing in sodium vapor in the presence of a noble gas is measured and calculated for large detunings from resonance, where the collisional impact approximation is no longer applicable. The measurement thus probes the non-impact collisional potential of the Na-noble gas system. When the noble gas is Xe, and the detuning is to the red of the Na D 1 resonance, an avoided crossing between the quasi-molecular potentials results in a satellite in the absorption lineshape, which can be detected in the four wave mixing signal. We calculate collisional lineshapes with several available sets of Na-Xe interaction potentials using the quasi-static and semi-classic line broadening theories, and find that the available potentials do not yield line shapes which agree with the measurements. The lineshape derived from the measured degenerate four wave mixing signal shows good agreement with theoretical calculations, only if the non-adiabatic nature of the level crossing is considered. Based on our experimental lineshape and a non-adiabatic level crossing theory, we derive corrections to the Na-Xe potentials, near the level crossing, that is for interatomic separations in the range of 0.55–0.75 nm.
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 present paper deals with a three-level model of interaction with three cross-polarized and co-propagating fields having the same frequency. The two pump waves have arbitrary intensities and the third one (the probe wave) is assumed to be non-saturating. Using the radiative renormalization method, density matrix equations are solved analytically. The forward degenerate four-wave mixing (FDFWM) signal is calculated under thermodynamic conditions where collisional and Doppler broadenings are comparable. The calculation also takes into account crossed-polarization effects. The FDFWM intensity is computed as a function of power densities and pressure. FDFWM experimental spectra of the - (0 - 0) band of OH obtained in a welding torch flame are compared to theoretical profiles. For incident laser intensities in the range of a few , a good agreement is obtained between calculated and experimental profiles. Discrepancies arise under stronger conditions of saturation, showing the limits of application of our model. However, because there is little virtue in using higher laser powers, the model should be extremely useful in practical applications. In particular, we demonstrate that the signal intensity is optimal and the pressure dependence is minimized when the saturation parameter is unity.