Energy transfer rates and population inversion of I 4 11 / 2 excited state of Er 3 + investigated by means of numerical solutions of the rate equations system in Er : LiYF 4 crystal

In this work, we present the spectroscopic properties of LiYF 4 (YLF) single crystals activated by high doping of erbium ions. The most important processes that lead to the up-conversion erbium emissions in the infrared region were identified. A time-resolved luminescence spectroscopy technique was employed to measure the luminescence decays and to determine the most important mechanisms involved in the up-conversion processes that populate the S 4 3 / 2 excited state. A study of the energy transfer up-conversion (ETU) processes in Er:YLF showed that an ETU rate can be obtained from the I 4 11 / 2 (ETU1) and S 4 3 / 2 (ETU2) up-conversion luminescence transient analysis, i.e., from best fittings of the acceptor state luminescence. An analysis of the ETU rate dependence on the wavelength and intensity of pulsed laser excitations allowed us to obtain the ETU rate constants from the lower ( I 4 13 / 2 ) and upper ( I 4 11 / 2 ) laser levels to use them in the numerical solutions of the rate equation system for the Er-doped YLF crystal (15 mol%) pumped [continuous wave (cw)] at 972 nm. As a result, we found that the I 4 11 / 2 → I 4 13 / 2 laser emission (or small signal gain) shows a temporal profile intensity, which passes through a maximum at around 820 μ s before getting the steady state regime. It was demonstrated that the ETU2 process (from the I 4 11 / 2 level) is the mechanism responsible for the laser gain profile observed. The results of the numerical simulation of the rate equation system showed that the highest population inversion density of 8.5 × 10 19 cm − 3 for Er 3 + (or a small signal gain of 2.54 cm − 1 ) is obtained for 15 mol% of erbium in the YLF crystal when it is pumped by a cw laser at 972 nm using a pump intensity of 5.4 kW cm − 2 (or a pumping rate of 300 s − 1 ) for the laser transition near 2.75 μ m . It was seen also that a pumping rate of 300 s − 1 maximizes the population inversion in the cw pump regime. A simulation using a square wave pump with a pumping time of 1 ms showed a population inversion increasing by a factor of 1.31 with respect to the population inversion obtained in the continuous pump simulation.