- and Thermal-Grating Contributions to Degenerate Four-Wave Mixing.

Degenerate four-wave mixing (DFWM) is a nonlinear optical-measurement technique that has recently received attention for its potential as a quantitative probe of gaseous media, including plasma and combustion environments. DFWM can be used to measure temperature, species concentration, velocity, and other properties non-intrusively. DFWM measurements in the gas phase have traditionally been attributed to population gratings (spatial perturbations in the level populations of absorbing species). Recently, contributions from thermal gratings (spatial perturbations in the overall density) have been observed in the gas phase. We report investigations of DFWM line intensities in the A ^2Sigma^{+}arrow X^2Pi electronic transitions of nitric oxide (NO). Using several experimental and analytical techniques, we distinguished and compared contributions from population and thermal gratings. For small quantities of NO in a strongly quenching buffer gas (CO_2 ), thermal-grating contributions dominated at room temperature for gas pressures of ~0.5 atm and higher. In a nearly non-quenching buffer (N _2), population gratings dominated at pressures of ~1.0 atm and lower. Population gratings of NO also dominated at higher temperatures in an atmospheric-pressure methane/air flame. To interpret these results, we propose a simple model for the ratio of thermal- to population-grating scattering intensities that varies as P^4T^{-4cdot4 }. Preliminary investigations of the temperature dependence and detailed studies of the pressure dependence are in agreement with this model. Measurements of the temporal evolution and peak intensity of isolated thermal -grating signals are in detailed agreement with calculations based on a linearized hydrodynamic model from the literature. In a further investigation, we used high-resolution lasers to perform detailed measurements of the shapes of DFWM spectral lines for conditions dominated by both population and thermal gratings. The observed thermal-grating spectra had larger linewidths and weaker line strength dependences than population-grating spectra. The spectra are in excellent agreement with calculations based on perturbation theory for contributions from population gratings and a Voigt -squared profile for contributions from thermal gratings. Based on this work, we discuss the relative merits of various DFWM schemes for measuring temperature and concentration in practical high-temperature environments.