Study on the threshold of Tm~(3+), Tb~(3+):LiYF_4 laser at ～1.5μm wavelength

摘要

The analytical formulas of laser threshold of the quasi-four-energy-level system for Tm~(3+), Tb~(3+):LiYF_4 are deduced from rate-equation of transition. The energy transfer between Tm~(3+) and Tb~(3+) is discussed. The optimal concentration of Tm~(3+) and Tb~(3+) and the optimal length of the crystal rod for the minimum threshold pump intensity are calculated. It shows that when Tm~(3+)-ion-doped concentration is comparatively high the threshold of the ～1.5μm laser corresponding to ~3H_4→~3F_4 transition of Tm~(3+) increases because of the cross-relaxation. When co-doped with Tb~(3+) ion, on one hand, the threshold tends to decreases by contribution of Tm-Tb energy transfer which effectively reducing the population on the terminal laser level, on the other hand, it results in an increase in threshold due to Tm-Tb energy transfer which also reduces the lifetime of the initial laser level. In this paper the theoretical analysis for optimal Tb~(3+) concentration is furnished. Calculation shows that for LiYF_4 crystal with the Tm~(3+) concentration being latm% the optimal concentration of Tb~(3+) is 0.2atm%. In addition, the dependence of optimal length of the crystal rod on the concentration of Tm~(3+) and Tb~(3+) and distributed rod loss were analyzed.