ALBERT

Notes: The collisional dependence of polarization spectroscopy (PS) with a picosecond-pulse laser is investigated theoretically with a perturbative treatment and experimentally by probing hydroxyl (OH) in a flow cell with a buffer gas of argon. Using a frequency-doubled distributed-feedback dye laser (DFDL), the PS signal strength is monitored as a function of pressure using a nonsaturating pump beam and a saturating pump beam. The collisional dependence of the PS signal is found to decrease significantly with a saturating pump beam. Increasing the flow-cell pressure by a factor of 50 (from 10 torr to 500 torr), the PS signal strength produced with a nonsaturating pump beam decreases by a factor of 18 while that produced with a saturating pump decreases by only a factor of 3. A third-order perturbative (weak-field) approach is used to develop an analytical expression for the PS signal generated by single-mode, exponentially decaying laser pulses. This expression correctly predicts the experimental results acquired with the nonsaturating pump beam. The analytical solution is used to examine the effects of pulse length on the collisional dependence of the weak-field PS signal strength. Results are also presented for a numerical simulation of the time-dependent density matrix equations for the high intensity case. © 2000 American Institute of Physics.

Notes: The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening. © 1999 American Institute of Physics.

Notes: The physics of polarization spectroscopy (PS) is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The numerical solution of the time-dependent density matrix equations enables us to investigate the effects of strong saturation on PS signal levels and line shapes. Bath levels not directly coupled by the laser radiation are included in the numerical modeling to investigate the effects of collisional rates and different types of collisions on signal levels and line shapes. The effects of Doppler broadening are included by solving the density matrix equations for numerous velocity groups. At low laser power we find that the homogeneously broadened PS line shape is Lorentzian-cubed, as compared to the Lorentzian predicted in several previous low-power analytical solutions. In the low laser power regime, the line-center PS signal is proportional to (collision rate)−6, obviously greatly complicating the application of unsaturated PS for quantitative concentration measurements in flames and plasmas. As the transition begins to saturate at higher laser intensities, the dependences of the signal strength on the laser intensity and on the collision rate decrease drastically, although the line-center PS signal is still approximately proportional to (collision rate)−2. The dependence of the PS signal intensity on the ratio of the population-transfer collision rate to the dephasing collision rate is minimized for saturating pump beam intensities. For resonances that are both Doppler- and collision-broadened, the low-power PS line shape is Lorentzian with a linewidth equal to the collisional width for the case where the Doppler width is much greater than the collisional width. At low pump laser intensities, the PS signal is very dependent on the ratio of Doppler broadening to collisional broadening when the Doppler width is greater than the collisional width. However, at high intensity, the line-center PS signal intensity becomes nearly independent of collision rate when the collisional linewidth is less than the Doppler linewidth. Quantitative application of polarization spectroscopy for concentration measurements in flames and plasmas will almost certainly require resolution of the PS line shape and/or accurate measurement of the saturation curve. © 1998 American Institute of Physics.