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Journal of Physics B Atomic and Molecular Physics

Measurement of relative extreme-wing absorption coefficients by excited-state degenerate four-wave mixing

P. Ewart, S.V. O’Leary

Published Nov 28, 1984• 8 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/17/22/020

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Quantitative nonlinear spectroscopy: a direct comparison of degenerate four-wave mixing with cavity ring-down spectroscopy applied to NaH

Lucia Lehr, P. Hering

Cavity ring-down spectroscopy and degenerate four-wave mixing have been applied for spectroscopic studies, temperature determination, and measurement of relative dipole transition moments of photochemically produced sodium hydride. In our experiment, NaH was formed within a heat-pipe oven after 3p excitation of sodium in a hydrogen atmosphere with a second dye laser. The reaction product NaH was probed in the near ultraviolet part of the spectrum at 382 nm with 1-4-/spl mu/s delay to the excitation pulse using both a linear and nonlinear spectroscopic technique with a pulsed dye laser source (pulsewidth 15-ns full-width half-maximum). The strengths and limitations of these two spectroscopic techniques are discussed. Since the two processes depend on different parameters and the image-forming beams have different properties, it is difficult to define a single criterion for comparison. But our measurements indicate that cavity ring-down spectroscopy is a powerful tool with a sensitivity better than 10/sup 9/ particles per cm/sup 3/ and quantum state which is comparable to degenerate four-wave mixing in our case.

IEEE Journal of Quantum Electronics•Jan 1, 1997•21 citations
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.
We present a method for measuring the diffusion coefficients for excited atoms in buffer gases that uses degenerate four-wave mixing. We show that, for low beam intensities and atomic densities, the relative angular response of the degenerate four-wave mixing signal is dependent on the excited state diffusion and decay rate only, and that it is independent of the ground state diffusion. We have experimentally measured the diffusion of potassium atoms in the 4P4P4P state in xenon and found that the diffusion coefficient DDD at 155 \ifmmode^\circ\else\textdegree\fi{}C and 760 torr is 0.084(4) cm2{\mathrm{m}}^{2}m2 s−−1{\mathrm{s}}^{--1}s−−1.
The effect of Doppler broadening on degenerate four-wave mixing (DFWM) signal intensities in the regime of high pump and probe laser intensities is investigated theoretically. DFWM reflectivities are calculated by solving the time-dependent density-matrix equations for a two-level system interacting with three laser fields. The density-matrix equations are integrated directly in the time domain on a grid of spatial locations along the phase-matching axis; the DFWM signal level is then calculated by summation of the polarization contribution (with the appropriate phase factor) from each of the spatial grid points. For the case in which the Doppler and the collisional linewidths are comparable, the DFWM reflectivity is found to be inversely proportional to the factor 1 + (bΔωD/ΔωC)2, where ΔωD is the Doppler width, ΔωC is the collisional width, and b is weakly dependent on the pump and the probe laser powers. We developed an analytical expression for the reflectivity of a line that is both collision and Doppler broadened by dividing the widely used Abrams and Lind expression for homogeneous reflectivity Rhom by the factor 1 + (bΔωD/ΔωC)2. This modified reflectivity expression is found to give accurate results for the DFWM reflectivity over a wide range of values for the ratio of Doppler to collisional width. With this modified Abrams–Lind expression, strategies for quantitative DFWM concentration measurements in flames and plasmas are proposed and analyzed. We conclude that, by selection of the appropriate rotational transition, a DFWM reflectivity that is directly proportional to the square of the total species number density can be obtained over a wide range of temperature for constant-laser-intensity spatial profile mapping in flames.
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.
Cavity ring-down spectroscopy and degenerate four-wave mixing have been applied for spectroscopic studies, temperature determination, and measurement of relative dipole transition moments of photochemically produced sodium hydride. In our experiment, NaH was formed within a heat-pipe oven after 3p excitation of sodium in a hydrogen atmosphere with a second dye laser. The reaction product NaH was probed in the near ultraviolet part of the spectrum at 382 nm with 1-4-/spl mu/s delay to the excitation pulse using both a linear and nonlinear spectroscopic technique with a pulsed dye laser source (pulsewidth 15-ns full-width half-maximum). The strengths and limitations of these two spectroscopic techniques are discussed. Since the two processes depend on different parameters and the image-forming beams have different properties, it is difficult to define a single criterion for comparison. But our measurements indicate that cavity ring-down spectroscopy is a powerful tool with a sensitivity better than 10/sup 9/ particles per cm/sup 3/ and quantum state which is comparable to degenerate four-wave mixing in our case.