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The Journal of Chemical Physics

Effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing

Skip Williams, Larry A. Rahn, Richard N. Zare

Published Mar 15, 1996• 46 citations
Publisher

Abstract

We present a combined theoretical and experimental study on the effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing (RFWM). Signal generation in RFWM can be viewed as the formation of and scattering from laser-induced population, orientation, and alignment gratings. We show that the relative contributions from the upper-state and lower-state population, orientation, and alignment gratings to the observed output signal can be changed by varying the polarizations of the three input fields. A theory is developed to account for these changes in collisional environments where the three multipole moments of the total angular momentum distribution, i.e., the population, the orientation, and the alignment, relax unequally. This theory is applied to the OH radical in an atmospheric-pressure H2/O2/He flame for which we have measured the line profiles using high-resolution degenerate and nearly degenerate four-wave mixing. We find that orientation and alignment gratings relax more rapidly than population gratings for low rotational levels of OH in the presence of He but at essentially the same rate for high rotational levels. A discussion is presented of the importance of this effect in the interpretation of RFWM experiments.

DOI
10.1063/1.471250

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Journal of the Optical Society of America B•Sep 1, 1993•75 citations
We present a combined theoretical and experimental study on the effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing (RFWM). Signal generation in RFWM can be viewed as the formation of and scattering from laser-induced population, orientation, and alignment gratings. We show that the relative contributions from the upper-state and lower-state population, orientation, and alignment gratings to the observed output signal can be changed by varying the polarizations of the three input fields. A theory is developed to account for these changes in collisional environments where the three multipole moments of the total angular momentum distribution, i.e., the population, the orientation, and the alignment, relax unequally. This theory is applied to the OH radical in an atmospheric-pressure H2/O2/He flame for which we have measured the line profiles using high-resolution degenerate and nearly degenerate four-wave mixing. We find that orientation and alignment gratings relax more rapidly than population gratings for low rotational levels of OH in the presence of He but at essentially the same rate for high rotational levels. A discussion is presented of the importance of this effect in the interpretation of RFWM experiments.
Applying a recently developed ns Two-Colour Resonant Four-Wave Mixing (TC-RFWM) technique, a number of resonance lines forbidden by conventional three-level schemes are observed. A theoretical frequency-domain picture is developed with the help of exact (off-diagonal) relaxation matrices and general four-level schemes. The newly observed extra resonances are induced by collisional transfer of rotational energy. The role of the population, orientation and alignment gratings that are formed in both electronic states coupled by laser fields is elucidated. Relaxation models using the fast-collision approximation are elaborated for Hund's cases a and b giving quantitative arguments for the proposed interpretation. The potential of the TC-RFWM technique to study state-to-state transfer rates is emphasized.
The polarization properties of backward-box, degenerate four-wave mixing from OH molecules are measured in a flame and compared with theory. Ratios of signal intensities for different laser polarizations are shown to exceed perturbation-theory predictions for a closed two-level system when optical intensity gratings are formed in the interaction volume. These results are shown to be inconsistent with population-nonconserving effects and are attributed to scattering from quenching-induced thermal density gratings.
A stimulated photon echo technique with specially selected linear polarizations of the coherent resonant driver pulses is used to study depolarizing collisions in the molecular gas SF 6 and in mixtures of it with buffer He and Xe. The collisional decay rates of the population, orientation, and alignment in an ensemble of gas particles are determined for the first time in a single experiment. These relaxation rates are measured as a function of the longitudinal translational velocities of the resonant particles. To within the experimental accuracy, no significant dependence of the collisional decay rates on the translational velocities of the particles was observed. This result confirms the conventional theoretical approach to depolarizing collisions. In pure SF 6 the decay rates for the orientation and alignment were lower than the relaxation constant for collisions involving a change in the longitudinal velocity (elastic collisions) that is known from experimental observations of the ordinary photon echo. This means that only some of the elastic collisions participate in destroying the multipole moments of the levels. Evidence is found that the relaxation of the multipole moments created by polarized radiation in a resonant medium of molecular SF 6 gas depends on j , the total angular momentum of the level.
The method of a stimulated photon echo with specially selected linear polarizations of pumping pulses of a coherent resonant radiation is applied to a research of depolarizing collisions in molecular gas SF6 and its mixtures with buffer gases He and Xe. For the first time in one experiment the rates of a collisional decay of three lowest moments of polarization (population, orientation and alignment) are defined in an ensemble of gas particles. These rates of a relaxation are measured as functions on longitudinal velocities of resonant particles. In the frames of an experimental accuracy any noticeable dependence on velocities of particles was not detected both for orientation and alignment neither in pure resonant gas SF6 nor in mixtures. This result confirms the standard theoretical approach to depolarizing collisions. In pure SF6 decay rates of orientation and alignment have proved lesser than relaxation rate constant due to velocity changing (elastic) collisions. It means, that only the part of elastic collisions participates in destruction of multipole polarization moments of resonant levels. In comparison with our previous work the evidence is obtained that the relaxation of multipole moments seems to be j-dependent one in a medium of molecular gas SF6.
We present a combined theoretical and experimental study of the effects of laser polarization on optical coherences produced in two-color, resonant four-wave mixing (TC-RFWM). A time-dependent model incorporating diagrammatic perturbation theory and spherical tensor formalism is used to interpret observations of quantum beats due to molecular hyperfine structure in time-resolved TC-RFWM in nitric oxide. Good agreement is found between the model and the observed time-resolved signals for two distinct excitation schemes and a variety of polarization configurations including both polarization and population gratings. Measured hyperfine energy intervals are reported for the $X{}^{2}{\ensuremath{\Pi}}_{1/2},$ v=0v=0v=0 ground state and the $A{}^{2}{\ensuremath{\Sigma}}^{+},$ v=0v=0v=0 excited state of NO. The experimental results demonstrate that TC-RFWM can be used to perform state-selective, quantum beat spectroscopy in three-level systems by suitably designing three experimental features: the excitation scheme for the matter-field interaction, the time ordering of the laser pulses, and the polarization of the incident laser beams.
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.