Upconversion-pumped population kinetics for4I13/2 and4I11/2 laser states of Er3+ ion in several host crystals

Population kinetics of the upper⁴I_11/2 and lower⁴I_13/2 laser states of the Er³⁺ ion were studied experimentally and theoretically in (Er)BaY₂F₈, (Er)YLF, (Er)YSGG, (Er)CaF₂ and (Er)YALO. Fluorescence from these states to the⁴I_15/2 ground state was excited through upconversion simultaneously with the⁴I_11/2 →⁴I_13/2 lasing using 1.53 µm radiation from an erbium : glass laser for optical pumping. Lifetimes of both states are altered during lasing by co-operative energy transfer processes: the lifetime of the lower state τ₁ is shortened and that of the upper state τ₂ increased with the resultant ratio τ₂/τ₁>1. After lasing the lifetime ratio returns to the ‘normal’ value τ₂/τ₁ <1; that is, one obtained under weak ultraviolet excitation. Kinetic rate equations for the population density functions for both laser states were set up and solved by approximation in three time domains. It was assumed that only one co-operative energy transfer process operates in the laser crystals and determines the population inversion kinetics. Consistency relationships for comparison of the theoretical results with the experiment were developed. Only (Er)BaY₂F₈ spectral features showed close agreement with theory, resulting in a high score of 94% for the overall correlation in the consistency test, whereas all other crystals scored <50%. As a result of this high correlation, a close match between theoretical and experimental population decay curves was shown for (Er)BaY₂F₈. Most probably, more than one energy transfer process shapes the decay curves and determines the population inversion kinetics for the other laser crystals. (Er)YALO showed little lifetime change for the laser states, apparently due to inefficient co-operative energy transfer processes. As a result it probably lased in a self-terminating short-pulse mode.