A model of the active medium in YAG:Tm<sup>3+</sup> and CNGG:Tm<sup>3+</sup> laser crystals is presented here and is used as the basis for studying the dynamics of the population and population relaxation of the energy levels of the Tm<sup>3+</sup> ions under various intensities of steady-state pumping by a semiconductor laser diode to the <sup>3</sup>H<sub>4</sub> level. The minimum (threshold) pumping levels are determined for which lasing is possible.
F. A. Bol'shchikov, P. A. Ryabochkina, A. V. Popov, and S. N. Ushakov, "Modelling the population processes of the energy levels of Tm3+ ions in yttrium-aluminum garnet and calcium-niobium-gallium garnet crystals doped with Tm3+ ions under steady-state pumping," J. Opt. Technol. 73, 51-54 (2006)