Population dynamics of the three-micron emitting level of Er³⁺ in YAlO₃

An analysis of the nonexponential behavior of the kinetics of the initial laser level for three-micron generation (⁴I_11/2) in an Er³⁺(45 at. %):YAlO₃ crystal under intense pump in the ⁴S_3/2 level is performed. The observed nonexponential ⁴I_11/2 decay can be satisfactorily described by the rate equation model which includes energy transfer processes inside the system of erbium ions, such as up-conversion from ⁴I_13/2 and ⁴I_11/2 and cross-relaxation from ⁴S_3/2 and ⁴I_9/2 provided only a small fraction (β₂₁≈0.11) of the excitation from ⁴I_11/2 level reaches the terminal laser level, ⁴I_13/2. The low value of β₂₁ and the observed reduction of the fluorescent lifetime of ⁴I_11/2 with the increasing erbium doping could be related to the presence of accidental impurities.