Modelling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides

Effects of high concentration and clustering on the performance of erbium-doped silica waveguide amplifiers are numerically investigated. The model, based on propagation-rate equations of a laser system containing isolated ions and ion-pairs, is numerically solved by combining Runge-Kutta and full-vectorial finite-element methods; it allows the description of both uniform and pair-induced upconversion mechanisms. Numerical results show that cooperative upconversion processes seriously deteriorate amplifier performance at high erbium concentration. Moreover, we show that only the detrimental effect due to uniform upconversion can be reduced by a careful design of waveguide geometry and refractive index profile; performance degradation due to clustering may only be overcome by reducing the fraction of ions in pair using suitable codopants. The proposed model is validated with published experimental results