Precise determination of energy transfer upconversion coefficient for the erbium and ytterbium codoped laser crystals

Energy transfer upconversion (ETU) coefficient plays a crucial role in investigating complex laser systems as it greatly influences both the laser output behavior and heat generation. For some quasi-three-energy-level lasers based on Er³⁺ doped, Ho³⁺ doped and codoped gain media, the available theoretical studies relied on some unreasonable approximations due to the lack of spectroscopic data, notably the ETU coefficient. We put forward what we believe is a novel approach to overcome the difficulties caused by wavelength jump occurred in aforementioned laser systems. Based on net gain cross-section analysis and rate equations modelling, the functional relationship between the ETU coefficient, the laser power and pump power at the jumping wavelength are established. ETU coefficients and their temperature dependences of Er,Yb:YAB crystals with different crystal doped concentrations are experimentally determined for the first time. The results reveal that the ETU process in Er,Yb:YAB laser system is 5∼35 times stronger than that in Er³⁺ and Yb³⁺ codoped phosphate glass. The determination of these spectroscopic data paves the way for precise modelling of laser system based on Er,Yb:YAB or similar gain media.