脉冲Ti^（3＋）：Al_2O_3激光器的增益长度

Gain Medium Length of the Ti:Sapphire Pulse Laser

脉冲激光束纵向泵浦Ｔｉ￣（３＋）：Ａｌ＿２Ｏ＿３晶体，根据晶体中增益区的分布情况和脉冲运转的特点，从获取高转换效率考虑，可用“损耗平衡”确定晶体长度。单纵向泵浦时晶体的长度１由式选取。式中α＿ｐ是晶体对泵浦光的吸收系数，β是ＦＯＭ值。双纵向泵浦时，“损耗平衡”表示为：是晶体长度。根据实际光路的调整状态，设双纵向泵浦参数基本对称，对高α＿ｐ晶体取Ｌ＝１．５ｌ。若α＿ｐ较低，且泵浦参数并不对称，则Ｌ在ｌ＜Ｌ＜１．５ｌ范围内取值。这一方法与实验系统运转情况相符。

We present a“Loss Balance”criterion to estimate the proper gain medium length (GML)of the Ti:sapphire pulse laser.In the one-longitudinally-pumped Ti:sapphire laser,when the conditions of the cavity are in certain,and in high pump level,the criterion can be written as follows :exp (-α_pl)=1-exp(-α_pl/β).Where α_p is the absorption coefficient to the pump beam,α_p/β=α_s is the absorption coefficient to the lasing beam,β is the figure of merit of the crystal,l is the GML of the crystal.When dual-longitudinally-pumped,the proper GML should be longer. That is L=l+△l.If one of the pump beam A_p is focused on the crystal ahead of the other pump beam B_p. We obtain the “Loss Bal-ance”equation:exp[-α_p(l+△l)]+exp(-α_p△l)· exp(-α′_pl)=1-exp[-α_p(l+△l)/β],(0≤α′_p≤α_p).Considering the gain region pattern in the crystal which is dual-longitudinally-pumped,we have obtained the result:L≤1. 5l. We use L=1.5l,if the crystal has a high α_p,but for a low α_p,we use l<L<1. 5l,according to the pump condition. This criterion has been tested by several examples in one-or dual-longitudinally-pumped Ti:sap-phire lasers.