Analysis of the laser performance of Tm3+, Tb3+(Ho3+):YVO4 crystals at ～1.5μm wavelength

The absorption spectra of Tb,Tm:YVO_4 and Ho,Tm:YVO_4 are measured. The radiant and non-radiant transition probabilities from higher level to lower level, A_{i,j} and ω_{i,j}, and the cross-elaxation probability are calculated in virtue of Judd－Ofelt and Dexter theories. The fluorescence lifetime of Tm^{3+} in the Tb^{3+} (or Ho^{3+}) co-doped crystal is calculated. It indicates that the lifetime of initial level {}^3H_4 of the laser transition can be shorter than that of terminal level {}^3F_4 of the transition if the atomic percentage of Tb^{3+} (or Ho^{3+}) ions is bigger than about 1 at%: namely, by means of the co-doping Tb^{3+} (or Ho^{3+}) ions the self-termination phenomenon of laser light can be eliminated. Inserting the optic parameters to the formula deduced here on the laser threshold power P^{(4)}_{th} and the slope efficiency η^{(4)}_s of the four-energy-level system, we obtain the relationship of threshold power P^{(4)}_{th} to the concentration of Tm^{3+} ions and discuss the effect of Tb^{3+} (or Ho^{3+}) ion concentration on the laser threshold power P^{(4)}_{th} around 1.5μm wavelength. The result shows that Tb,Tm:YVO_4 crystal is a better choice to make the laser at ～1.5μm wavelength than Ho,Tm:YVO_4 crystal. We give the appropriate composition of (1－2) at% Tb, (1－2) at% Tm:YVO_4, just for reference.     

Tb，Tm：YVO4晶体的激光性能分析

Tm：YVO4和Tb，Tm：YVO4晶体中激活离子之间或激活离子与敏化离子间的交叉弛豫、与无辐射跃迁及激光上能级的辐射跃迁的几率是相近的，对这种双掺离子晶体的激光阈值理论估算式中必须同时考虑离子间交叉弛豫。从激活离子能级跃迁速率方程和激光、抽运光传输方程推导出端面抽运的包含交叉弛豫几率等光学参量的激光阈值的理论估算式。用这些方程讨论了Tm：YVO4和Tb，Tm：YVO4的1．5μm和1．9μm波长的激光性能，并论述了Tb3 离子的作用。结果表明。Tb3 离子的的掺入，增加1．5μm波段激光的强度，降低阈值能量，但对1.9μm波长激光有负面作用。     

Tb,Tm∶YVO4晶体的激光性能分析

Tm∶YVO4 和Tb ,Tm∶YVO4 晶体中激活离子之间或激活离子与敏化离子间的交叉弛豫、与无辐射跃迁及激光上能级的辐射跃迁的几率是相近的 ,对这种双掺离子晶体的激光阈值理论估算式中必须同时考虑离子间交叉弛豫。从激活离子能级跃迁速率方程和激光、抽运光传输方程推导出端面抽运的包含交叉弛豫几率等光学参量的激光阈值的理论估算式。用这些方程讨论了Tm∶YVO4 和Tb ,Tm∶YVO4 的 1 .5μm和 1 .9μm波长的激光性能 ,并论述了Tb3+ 离子的作用。结果表明Tb3+ 离子的的掺入 ,增加 1 .5μm波段激光的强度 ,降低阈值能量 ,但对1 .9μm波长激光有负面作用     

Study on energy up-conversion in Yb, Ho:YAG crystal

Optic parameters, such as the probabilities of radiative and non-radiative transition and the cross-relaxation probability between Yb3+ and Ho3+ ions in Yb,Ho:YAG crystal, are calculated on the basis of Judd-Ofelt and Dexter theories. The energy up-conversion process is analyzed by solving the transition rate-equations. The results show that (1) the intensity of the green fluorescence relates to the square of the concentration of the active ions; (2) the intensity increases with the concentration of sensitive ions as well, but the increasing rate goes rather too slow; (3) the efficiency of the energy up-conversion relates with the speed of the energy up-conversion and the quantum efficiency of the transiting from upper level to lower level.