Role of the stimulated radiation of Yb$^{3+}$ ions in the formation of luminescence of the Y$_{0.8}$Yb$_{0.2}$F$_3$:Tm$^{3+}$ solid solution

A new mechanism has been proposed for the transfer of the energy of exciting laser radiation through the donor subsystem (Yb$^{3+}$) to acceptors (Tm$^{3+}$), which induces multiphoton transitions in the acceptor subsystem. The coherence of the induced radiation of donors is of key importance in this mechanism. An analytical dependence of the intensity of the up-conversion luminescence of Tm$^{3+}$($^1$G$_4\to ^3$H$^6$) ions in the Y$_{0.8}$Yb$_{0.2}$F$_3$:Tm$^{3+}$ system on the pump power at the steady-state excitation by $934$-nm infrared radiation of a laser diode has been obtained using the mathematical technique of the theory of Poisson processes. In contrast to known mechanisms, this dependence approximates the experimental dependence well in a wide power range ($200$–$1200$ mW). The proposed model is applicable for any system where the energy of pump radiation is transferred to acceptors through the subsystem of donor ions.