Measurement and theoretical modeling of quantum beats in picosecond time-resolved degenerate four-wave mixing and polarization spectroscopy of OH in atmospheric pressure flames

Abstract

Using tunable ultraviolet picosecond laser pulses pump-probe degenerate four-wave mixing (DFWM) and polarization spectroscopy experiments were conducted in atmospheric pressure flames to investigate the temporal signal behavior in selected rotational transitions of the OH $A{}^{2}\ensuremath{\Sigma}--X{}^{2}\ensuremath{\Pi} (0,0)$ electronic band. The relaxation behavior of simultaneously excited main and satellite transitions in the Q and P branches was studied in premixed stoichiometric methane-air and hydrogen-oxygen flames. Experimental signal traces are compared with expressions from a detailed theoretical treatment of the signal generation process using perturbation calculations. The theoretical approach consists in calculating the energy density in the signal field mode taking into account the frequency spread of the pump and probe beam radiation, collisional relaxation effects, and the polarization configuration of the incident beams. Relaxation times for population and orientation deduced from the fitting algorithm are in good agreement with DFWM line-shape studies [S. Williams et al., J. Chem. Phys. 104, 3947 (1996)]. It is shown that quantitative agreement with experimental data obtained for different polarization configurations of pump, probe, and signal photons can be achieved when appropriate time correlated interactions of pump and probe photons are taken into account. In addition, it is shown that due to the frequency spread of the employed laser pulses the different frequency components in the signal beam contribute with different amplitude to the oscillating and nonoscillating parts in the temporal development of the signal intensity depending on the relative strength of the simultaneously excited transitions.