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• The electronic structures and optical properties of Tm:YAG, Tm:LuYAG, and Tm:LuAG crystals are calculated based on first principles. • The reasons for the variation of the output wavelength of three crystals are analyzed by dielectric function. • The output wavelength of the Tm:LuYAG crystal can be effectively changed by adjusting the content of Lu element in the mixed crystal. Thulium-doped mixed yttrium aluminum garnet Tm:(Lu x Y 1-x) 3 AG crystals are popular laser crystals, with the Tm:YAG terminal compound being widely applied. However, it is unclear how the content of Lu3+ affects the properties of Tm:YAG. Based on the first principles of density functional theory, we have studied the electronic structure and optical properties of Tm:(Lu x Y 1-x) 3 AG crystals. The two terminal compounds Tm:YAG and Tm:LuAG have the same crystal structure as Tm:LuYAG and the band gap values change to 4.50 eV, 4.57 eV, and 4.95 eV with Lu3+ doping concentration of 0, 50 %, and 100 %. The calculation of optical properties shows that with the increase of Lu3+ doping concentration, the overall dielectric function peak occurs redshift, which is effectively proved by the output wavelength Tm:YAG (2013.84 nm) Tm:LuYAG (2018.95 nm) Tm:LuAG (2025.23 nm) of the three crystals in the experiment. In the ultraviolet, visible and infrared bands (0–6 eV), the optical properties of the three crystals, such as reflectivity, refractive index, and transmittance, are the same. This theoretical analysis can provide insights for studying the variation of the output wavelength of other laser crystals. [ABSTRACT FROM AUTHOR]