Radiative and non-radiative transitions of excited Ti³⁺ cations in sapphire

We have measured the fluorescence quantum efficiency in Ti³⁺:sapphire single crystals between 150 K and 550 K. Using literature-given effective fluorescence lifetime temperature dependence, we show that the zero temperature radiative lifetime is (4.44 ± 0.04) μs, compared to the 3.85 μs of the fluorescence lifetime. Fluorescence lifetime thermal shortening resolves into two parallel effects: radiative lifetime shortening, and non-radiative transition rate enhancement. The first is due to thermally enhanced occupation of a ΔE = 1,700 cm⁻¹ higher (top) electronic state of the upper multiplet, exhibiting a transition oscillator strength of f = 0.62, compared to only 0.013 of the bottom electronic state of the same multiplet. The non-radiative rate relates to multi-phonon decay transitions stimulated by the thermal phonon occupation. Thermal enhancement of the configuration potential anharmonicity is also observed. An empiric expression for the figure-of-anharmonicity temperature dependence is given as Hˆ (T) = Hˆ (0)(1 + β exp(−ℏω_co /k_BT)), where Hˆ (0) = 0.276, β = 5.2, ℏω_co = 908 cm⁻¹, and k_B is the Boltzmann constant.