A simple model to describe thermal grating effects in degenerate four wave mixingspectroscopy

Abstract

The pressure dependence of the resonant degenerate four wave mixing (D4WM) spectra of NO₂ recorded between 0 and 900 Torr of N₂, Ar and He are reported. The results are interpreted in terms of a transient grating model that incorporates the effects of thermalising collisions between the optically pumped molecule and the bath gas. The observed pressure dependence demonstrates that two transient gratings contribute to the total signal. The signal observed at low pressure is that due to a laser induced population grating. After an initial saturation region where the D4WM signal is essentially pressure-independent, a sharp fall-off due to the collisional removal of energy from the population grating is observed. At pressures above about 100 Torr, depending on the buffer gas, a second mechanism, with a near-quadratic pressure dependence, becomes important. This contribution is attributed to a thermal grating with local heating caused by thermal relaxation of the population grating. A simple model that includes both of these contributions is developed. This model is able to reproduce the observed behaviour. Confidence in the model is reinforced by its ability to predict the behaviour of argon from the results obtained for nitrogen with no additional assumptions or free parameters. The experiments were repeated under identical conditions with an optical arrangement involving cross-polarised laser beams. The secondary rise in D4WM signal is not observed in this experiment. A decay of D4WM signal with pressure was however still observed and can be accounted for by the re-orientation and re-alignment of molecules within a polarisation grating by collisions with other gas phase species.