Estimating the Optically Pumped Threshold Fluence of Thin-Film Gain Media Using Arbitrary Excitation Beams

Optically pumped threshold fluences are a widely reported metric to benchmark the performance of thin-film gain media and lasers. Estimating the threshold fluence for nonhomogeneous beams, such as a circular Gaussian excitation, is not trivial since the average fluence depends on the estimated spot diameter. Using an exemplary lead halide perovskite film, the inversion volume at different pump energies is mapped. It is shown that the peak fluence of an arbitrary spatial beam profile is more relevant at the threshold, as it provides an upper bound to the threshold fluence. Also, simple conversion factors to estimate the peak fluence using Gaussian excitation beams are provided and the methodology to arbitrary profiles is extrapolated. Furthermore, it is advocated for using flat-top or uniform stripe excitations to unambiguously extract the threshold fluence, since these excitations display minor discrepancies between the average and peak fluence, and keep the inversion volume relatively constant during the measurement.