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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~3H_4→~3F_4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:LiYF_4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。
The laser thresholding formulas of quasi - quaternary systems of double doped (Tm 3+ and Tb 3+) ions are derived from the rate equations. The effects of Tm 3+ and Tb 3+ ions are discussed. interaction between. The relationship between the laser threshold near the 1.5μm wavelength and the doping number and crystal length of Tm ~ (3 +) and Tb ~ (3 +) ions was analyzed. The results show that for a laser beam of about 1.5μm wavelength corresponding to ~ 3H_4 → ~ 3F_4 transition of Tm ~ (3+) ion, the cross-relaxation effect will make the activation energy of Tm ~ (3+) System threshold increases rapidly. The addition of Tb ~ (3+) ions can not only lower the energy level of the laser beam but also reduce the threshold value. On the other hand, the lifetime of the laser energy level is reduced and the threshold value is increased. So Tb ~ (3+) ions have the best doping atomic number fraction. For the Tm: LiYF_4 crystal with Tm atomic number of y = 0.01, the optimal doping atomic number of Tb 3+ ions is about 0.002. At the same time, the laser threshold is related to the crystal length. The optimum crystal length is related to the fraction of doping atoms of Tm ~ (3 +) and Tb ~ (3+) and the diffraction and absorption loss of the crystal.