Balanced cross-rate model for saturated molecular fluorescence in flames using a nanosecond pulse length laser

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Abstract
The balanced cross-rate model is proposed to analyze laser-induced molecular fluorescence signals when the laser pulse length is of the order of nanoseconds. Nanosecond pulse length lasers, specifically Q-switched Nd:YAG-pumped dye lasers, are attractive for saturated molecular fluorescence spectroscopy because of their high peak power and because their short pulse length minimizes the risk of laser-induced chemistry. In the balanced cross-rate model, single upper and lower rotational levels are assumed to be directly coupled by the laser radiation. Because the laser-induced processes which couple these levels are so fast at saturation intensities, a steady state is established between the two levels within picoseconds. Provided that the total population of the two laser-coupled rotational levels is constant during the laser pulse, the total molecular population can be calculated from the observed upper rotational level population using a two-level saturation model and Boltzmann statistics. Numerical simulation of the laser excitation dynamics of OH in an atmospheric pressure H2/O2/N2 flame indicates that the balanced cross-rate model will give accurate results provided that the rotational relaxation rates in the upper and lower sets of rotational levels are approximately equal.