Monte Carlo simulations of homogeneous upconversion in erbium-doped silica glasses

Quenching of Er³⁺ ions by homogeneous energy-transfer upconversion in high-concentration erbium-doped silica glasses has been theoretically investigated, The results indicate that at Er³⁺ concentrations of 1.0-2.0·10²⁶ m^-3 or below, the kinetic limit of strong migration is not reached, and hence the widely accepted quadratic upconversion model is not generally valid. Nevertheless, the results offer an explanation of the experimental observations of quadratic upconversion. Furthermore, it has been shown that at a given population inversion, the quenching rate depends on the rate of exchange of the excited Er³⁺ ions by emission and absorption