Use of rate equations to describe laser excitation in flames
The region of validity of conventional rate equation formulations used to describe the excitation of flame gases for spectroscopic diagnostic purposes is examined by direct comparison with the density matrix formulation. The density matrix equations are formulated for an ensemble of atoms or molecules in the gas state. These equations are reduced to the steady-state limit for a two-level system under the effect of single-mode and multimode optical fields. The steady-state equations are shown to be valid only when the laser pulse rises slowly with respect to the collisional dephasing rate for single-mode excitation, and for certain special cases under multimode excitation.