Theoretical analysis on threshold of solar pumped solid state lasers
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摘要: 为了选择适合太阳光泵浦的激光材料,本文从四能级速率方程出发,综合考虑了太阳辐射带状光谱特性和激光材料对泵浦光吸收能力,建立了太阳光泵浦固体激光理论模型。利用该模型推导得到了单束光侧面泵浦和椭球腔侧面泵浦方式下的泵浦阈值表达式,并结合Nd3+:YAG、Nd3+:glass、Nd3+:Cr3+:GSGG (Nd3+:Cr3+:Gd3Sc2Ga3O12)、Cr3+:BeAl2O4和Cr3+:Nd3+:YAG等激光材料的光谱参数,计算了这些材料的泵浦阈值光强。结果表明:在单束光侧面泵浦和椭球腔侧面泵浦方式下,Nd3+:YAG的泵浦阈值光强分别为448个太阳常数和224个太阳常数,是比较适合用太阳光泵浦的激光材料。由于椭球腔的特殊结构,采用椭球腔侧面泵浦激光介质,阈值光强比较低。分析了泵浦阈值光强与材料直径的关系。该模型可用于从现有的激光材料中筛选出在太阳光泵浦下最易输出激光的工作物质。Abstract: In order to select suitable solar pumped laser materials, a theoretical model is established based on the four-level rate equation, taking the solar spectrum into account. By this model, the pump intensity thresholds of Nd3+:YAG, Nd3+:glass, Nd:Cr:GSGG (Nd3+:Cr3+:Gd3Sc2Ga3O12), Cr3+:BeAl2O4 and Cr3+:Nd3+:YAG for the different pump schemes are analyzed. The results show that the pump intensity threshold of Nd3+:YAG is 448 sun constant when it is side pumped by a single beam and is 224 sun constant when it is side pumped inside a ellipsoidal cavity, respectively, indicating that Nd3+:YAG is suitable for solar pumped laser material. Due to the special structure of the ellipsoidal cavity, the pump intensity threshold is relatively low when it is side pumped inside a ellipsoidal cavity. The relationship between the pump intensity threshold and the diameter of the material is also analyzed. The model could be applied to select suitable materials which are easier to achieve laser output from the existing laser materials.
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Key words:
- solid state lasers /
- solar pumped /
- rate equation /
- theoretical analysis /
- pump intensity threshold
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图 5 不同直径Nd3+∶YAG的阈值光强
Figure 5. Pump intensity thresholds versus different Nd3+∶YAG rod diameters
表 1 几种常用激光材料的光谱参数
Table 1. Spectral parameters of some laser materials
Active medium Nd3+∶YAG Cr3+∶BeAl2O4 Nd3+∶glass Nd3+∶Cr3+∶GSGG(Nd3+∶Cr3+∶Gd3Sc2Ga3O12) Cr3+∶Nd3+∶YAG DopingDensity/cm3 1.38×10201 at.%[ 10] 2.9×10190.1 at.%[ 12] 2.85×10203 at.%[ 18] Nd3+=2×1020Cr3+=1×1020 [10] Cr3+=1.39×10190.1 at.%Nd3+=1.39×10201 at.%[ 19] Absorptionband/nm 515~545565~595735~765795~825855~885[ 20] 360~460500~600[ 21] 515~545565~595735~765795~825855~885[ 18] 400~545565~700735~765795~825855~885[ 10] Nd3+:510~540560~630730~760790~825Cr3+:450~490510~540865~890[ 19] Absorption cross section/cm2 0.56×10-20(530~550)0.84×10-20(570~600)1.41×10-20(750~775)1.69×10-20(800~820)[ 14] 1.04×10-19(360~460)1.9×10-19(500~600)[ 21] 1.33×10-20 0.393 75×10-20(400~545)0.355×10-20(565~700)0.125×10-20(735~765)0.11×10-20(795~825)0.078×10-20(855~885)[ 22] 2.518×10-19 Fluorescence Lifetime/μs 230[ 12] 260[ 12] 350[ 23] Nd3+：280Cr3+：120 [ 24] 600[ 13] Emission cross section/cm2 6.5×10-19@1 064[ 13] 0.7×10-20@760[ 25] 3×10-20@1 064[ 26] 3.2×10-19@1 060[ 27] 2.35×10-19@1 064[ 28] 
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