双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。

Theoretical Analysis of the Threshold in (Tm3+ , Tb3+ ) :LiYF4 Laser at 1.5 μm Wavelength

The analytical formulas of laser threshold of the quasi-four-energy-level system for (Tm3+ ,Tb3+ ) :LiYF4 are deduced from rate-equation of transition. The energy transfer between Tm3+ and Tb3+ is discussed. The optimal concentration of Tm3+ and Tb3+ and the optimal length of the crystal for the minimum threshold pump intensity are calculated. It shows the threshold of the about 1.5 ?m laser corresponding to 3H4?3F4 transition of Tm increases because of the Tm-Tm cross-relaxation. When codoping with Tb3+ ion, on one hand the threshold decreases by contribution of Tm-Tb energy transfer which reduces effectively the population on the terminal laser level while on the other hand it increases because of Tm-Tb energy transfer which also reduces the lifetime of the initial laser level. Calculation shows the optimal doped atom fraction of Tb3+ is y = 0.002 for y = 0.01 Tm3+ in LiYF4 crystal, and it also shows the optimal length of the crystal depends on the concentration of Tm 3+ and Tb 3+ and the distributed rod loss.