Stochastic Model of Energy-Transfer Processes Among Rare-Earth Ions. Example of Al2O3:Tm3+

Abstract

Energy-transfer processes strongly affect the performance of lanthanide-doped photonic devices. In this work, we introduce a simple stochastic model of energy-transfer processes and successfully apply it to the example of cross-relaxation (CR) and energy-transfer upconversion (ETU) in amorphous Al2O3:Tm3+ waveguides on silicon intended for lasers operating at ∼2 μm. The stochastic model is based on the rate-equation formalism and considers two spectroscopically distinct ion classes, namely single ions and ions with neighbors (pairs and clusters), with the corresponding ion fractions being dependent on the doping concentration. We prove that a more accurate description of the luminescence properties of amorphous Al2O3:Tm3+ is obtained when accounting for the presence of these distinct ion classes. Based on the developed model, we derive microscopic CR and ETU parameters of CCR = 5.83 × 10–38 cm6 s–1, CETU1 = 0.93 × 10–40 cm6 s–1, and CETU2 = 7.81 × 10–40 cm6 s–1, and determine the laser quantum efficiency ...