Comparison between the calculated and measured energy transfer rates of the ⁴S_3/2 state in Er³⁺-doped fluorozirconate glasses

The dependence of the fluorescence lifetime of the ⁴S_3/2 state of the Er³⁺ ion on the ErF₃ concentration was measured in fluorozirconate glasses at room temperature. Energy transfer rates were calculated from optical parameters assuming that the Er³⁺ ions in fluorozirconate glasses were dispersed as the cubic, bcc, or fcc structure, and were inserted into the rate equation. The dependence of the total transition rate of the ⁴S_3/2 state of the Er³⁺ ion on the ErF₃ concentration was calculated by using the rate equation and compared with the total transition rate measured by the lifetime experiment. Although many studies have reported the energy transfer rates in various rare-earth ions, the reliability of the calculated energy transfer rates has been hardly discussed. The energy transfer rate can be derived from the total transition rate. The energy transfer rate estimated from the rate equation calculation was compared with the energy transfer rate obtained from the lifetime measurement. It could be shown that the calculated energy transfer rate assuming that the Er³⁺ ions were dispersed as the cubic structure was closer to the measured energy transfer rate than that as the bcc and fcc structures. With increasing the ErF₃ concentration, the calculated energy transfer rate when the Er³⁺ ions were dispersed as the cubic structure was comparable to the measured energy transfer rate. It was suggested that at the lower concentration of ErF₃ (≤2 mol %), we needed to use the distance between Er³⁺ ions which was shorter than that as the cubic structure in the calculation of the energy transfer rate.