Quadrature frequency resolved spectroscopy of upconversion photoluminescence in GeGaS:Er3+: I. Determination of energy transfer upconversion parameter

Abstract

The article presents the formulas of quadrature frequency resolved spectroscopy (QFRS) on the upconversion photoluminescence (UCPL) of rare-earth (RE) doped materials on the general M-level model. The formulas are derived in matrix-equation form with the first-order perturbation on the rate equations at the M energy-levels of RE ion. The QFRS spectra for three different UCPL processes, i.e., the excited state absorption (ESA), energy transfer upconversion (ETU) and photon avalanche (PA) via cross relaxation process (CRP) in a particular case of M = 3 are demonstrated with the respective salient features of the excitation power dependence. We have measured the QFRS on the UCPL (4S3/2 → 4I15/2) by systematically varying Er-doping in Ge28.1Ga6.3S65.6 chalcogenide glass from 0.01 to 0.5 at.% as well as 975 nm excitation power. Thereby the relaxation rates k1 at the intermediate level 4I11/2, k2 at the top level 4S3/2 and ETU parameter w are determined as a function of Er concentration. The UCPL dynamics on the basis of the formulas for the 3-level model is interpreted in terms of the determined parameters.