Abstract

Our recently developed statistical model [1] for migration enhanced homogeneous upconversion in Er doped glasses well explains strongly non linear dependence of the upconversion rate on the population inversion and the increase of upconversion rate with increasing pump and signal powers at a given population inversion which we have experimentally observed [2] However, since the model considered continuous wave (cw) and a delta pulse excitation it could non be directly applied to the studied [2] decay characteristics. Here we present an extension of the model to the case of Continuous Wave Excitation Switch-off (CWES). The starting point of the theory are microscopic rate equations for an Er ion in a silica matrix for the cw excitation (CWE) and the (CWES) regimes. We average the solutions to those equations with respect to the probability distributions for the migration and the upconversion [1], which leads to a non-linear algebraic equation for the CWE regime and to a non-linear weakly singular Volterra integral equation for the (CWES) regime. In the figure we show the numerically calculated upconversion rate for the two different regimes as a function of the population inversion for erbium concentration 9 10^–19 ions/cm³.

© 2001 EPS