A simple analytical expression for threshold pump power in an end-pumped quasi-three-level solid-state laser, which takes into account the influence of energy-transfer-upconversion (ETU), is derived. This expression indicates that threshold pump power can be increased dramatically by ETU, especially in low gain lasers and lasers with pronounced three-level character due to the need for high excitation densities in the upper manifold to reach threshold. The analysis has been applied to an Er:YAG laser operating at 1645 nm in-band pumped by an Er,Yb fiber laser at 1532 nm. Predicted values for threshold pump power as a function of erbium doping concentration are in very good agreement with measured values. The results indicate that very low erbium doping levels (~0.25 at.% or less) are required to avoid degradation in performance due to ETU even under continuous-wave lasing conditions in Er:YA
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