Modeling time-dependent upconversion in Er-Yb doped sol-gel silicate glass

Examining pulsed IR to visible upconversion in Er$^{3+}$-Yb$^{3+}$ doped sol-gel silicate glass may lead to applications in fiber optic communication due to the similar time scale of its GHz bandwidth. Excited state absorption of Er$^{3+}$ accompanying energy transfer from neighboring Er$^{3+}$ and Yb$^{3+}$ is responsible for the upconversion process. The dynamics of Yb$^{3+}$ to Er$^{3+}$ energy transfer are studied by observing green emission from the $^{4}$F$_{7/2}$ and $^{4}$S$_{3/2}$ levels of Er$^{3+}$ after a 6-ns pulsed laser excitation of the $^{2}$F$_{5/2}$ level of Yb$^{3+}$ at 978nm. This study examines the time-dependence of the fluorescence emission by varying the Yb$^{3+}$ concentrations and the annealing temperature. Our previous work has shown that the rare earth ions reside on the pore surface, and so the nanoporous nature of the sol-gel glass creates a finite reservoir of energy donors in each pore. These finite energy reservoirs foil the application of standard rate equation models and instead necessitate Monte Carlo simulations which can be used to determine the physical parameters of each energy transfer step in the upconversion chain.