Upconversion assisted decay of population inversion in Er-doped silica after delta-pulse excitation

We investigate homogeneous upconversion (HUC) assisted decay of the population inversion in Er-doped silica after delta-pulse excitations by means of Monte Carlo simulations. We derive an analytic expression for this decay when energy migration among Er is negligible and show that it is essentially an extension of the Förster-type donor-acceptor quenching decay for the case when donor and acceptor ions are the same species. We compare HUC during the decay to HUC while pumping CW and show that they considerably differ at the low and moderate Er concentrations. Based on Monte Carlo (MC) simulations, we construct a heuristic approximation to the HUC assisted decay, which makes our MC results readily available for the future experimental and theoretical studies and provides simple means for determination of HUC parameters by fitting to experimental data.