Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption

We present the results of analysis of rate equations for reverse saturable absorption (RSA) process to understand the applicability and probable errors in using only time dependence of the excitation pulse as against both space and time dependence in numerical simulations of rate equations. We have considered a three-level approximation of the five-level rate equations under nano-second laser pulse excitations. The population density, nonlinear absorption and transmission have been calculated and compared for different approximations and for different excitation pulse spatial shapes. We show that the neglect of spatial characteristics of the excitation pulses in the rate equation analysis can lead to considerable errors in the numerical simulations of RSA in case of excitation fluences below the fluence for saturation of transmission.