Mechanisms of energy transfer to $2\mu$ lasing channel in a BaYb$_2$F$_8$:Ho$^{3+}$ crystal

It was found that when the energy of neodymium laser radiation absorbed in a $BaYb_2F_8:Ho^{3+}$ (0.5%), crystal reached 1 J/cm$^3$, the obvious mechanism of population of the ${}^5I_7$ state of the activator involving nonradiative energy transfer from the sensitizer ions $|^2F_{5/2}(Yb),{}^5I_8(Ho)>\!\to|^2F_{7/2}(Yb),{}^5I_6(Ho)>$ followed by the relaxation process $|{}^5I_6(Ho)>\sim\to|{}^5I_7(Ho)>)$ changed to a cooperative process consisting of three successive stages of step-like sensitization $|^2F_{5/2}(Yb),{}^5I_8(Ho)>\!\to|^2F_{7/2}(Yb),{}^5I_6(Ho)>$; $|^2F_{5/2}(Yb),{}^5I_6(Ho)>\!\to|^2F_{7/2}(Yb),{}^5S_2(Ho)$; $|^2F_{5/2}(Yb),{}^5S_2(Ho)>\!\to|^2F_{7/2}(Yb),{}^3H_6(Ho)>$, and two successive stages of intercenter cross relaxation $|^5G_4(Ho),{}^2F_{7/2}(Yb)>\!\to|^5F_5(Ho),{}^2F_{5/2}(Yb)>$; $|^5F_5(Ho),{}^2F_{7/2}(Yb)>\!\to|^5I_7(Ho),{}^2F_{5/2}(Yb)>$. Ways of optimizing the active medium of a laser converter to the $2\mu$ wavelength were determined for $BaYb_2F_8:Ho^{3+}$. The feasibility of constructing an anti-Stokes ($1.06\to0.75\mu$) laser frequency converter was analyzed.