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Journal of the Optical Society of America B

Effects of absorption on degenerate four-wave mixing in iodine vapor

Jörg Gumbel, W. Kiefer

Published Dec 1, 1992• 6 citations
Publisher

Abstract

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.

DOI
10.1364/josab.9.002206

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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.
We have investigated the dependence of degenerate four-wave mixing (DFWM) spectra of gas-phase I2I_{2}I2​ on laser intensity, molecular transition moments and molecular concentration. The experimental results are interpreted by using a weak-field theory of DFWM derived with a density-matrix method. For comparison, the direct absorption spectra of I2I_{2}I2​ are also presented. We have demonstrated, in our observed DFWM spectra of I2I_{2}I2​, that the spectral resolution in DFWM can be better than that of linear optical spectroscopy. The outcome has also been elucidated by the theoretical result.
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.
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 object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (I2{\mathrm{I}}_{2}I2​) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211--284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/Ilaser{\mathrm{I}}_{\mathrm{laser}}Ilaser​, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.
Degenerate four-wave mixing (DFWM) spectroscopy is a potentially powerful technique for quantitative measurement of minor species in gas-phase media [1-3]. In this paper we compare the DFWM signal levels and lineshapes obtained using two different phase-matching geometries: the phase-conjugate geometry and the forward phase-matched geometry. DFWM signal levels are calculated by solving the time-dependent density matrix equations using direct numerical integration (DNI) [4, 5] for a two-level system interacting with three laser beams. This numerical analysis includes the effects of molecular motion, intermolecular collisions, and high laser intensities, all of which have been shown to affect the DFWM signal level.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.