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摘要:
针对近准直碟片多通放大器在高功率、高能量运行条件下面临的热致光焦度敏感、稳定工作区间受限等问题，本文开展了基于泵浦光强分布调控的热透镜效应抑制研究。首先，基于碟片光焦度实验测量结果，分析碟片光焦度变化与泵浦光强分布之间的关系；在此基础上，提出采用M形泵浦替代传统超高斯泵浦，并建立理论模型，对0~8.13 kW/cm2泵浦功率密度范围内两种泵浦方式下的碟片温度分布及光焦度变化规律进行对比分析。仿真结果表明，当M形泵浦中心凹陷区的超高斯阶数为8时，碟片光焦度变化量最小，水平和竖直方向分别为
0.00283 m−1和−0.00455 m−1；与超高斯阶数为10的传统泵浦相比，两个方向的光焦度变化量分别降低了0.05171 m−1和0.06355 m−1，降幅达94.7%和93.3%。M形泵浦能够显著抑制碟片热致光焦度变化，为全泵浦功率密度范围内的模场匹配提供更有利的条件，大幅降低泵浦功率变化引发的光学元件损伤风险。Abstract:To address the high sensitivity of thermally induced diopter and the limited stable operating range of near-collimated propagation thin-disk multi-pass amplifiers under high-power and high-energy conditions, this work investigates the suppression of the thermal lensing effect based on pump light intensity distribution control. First, the relationship between thin-disk diopter variation and the pump light intensity distribution is analyzed based on experimental measurements of the thin-disk diopter. On this basis, an M-shaped pumping is proposed to replace the conventional super-Gaussian pumping. A theoretical model is established to comparatively analyze the thin-disk temperature distribution and diopter variation under both pumping techniques within a pump power density range of 0−8.13 kW/cm2. The simulation results show that when the super-Gaussian order of the central depression region of the M-shaped pump is 8, the diopter variation of the thin-disk is minimized, with values of
0.00283 m−1 and −0.00455 m−1 in the horizontal and vertical directions, respectively. Compared with the traditional pump with a super-Gaussian order of 10, the diopter variations in the two directions are reduced by0.05171 m−1 and0.06355 m−1, corresponding to reductions of 94.7% and 93.3%, respectively. The M-shaped pumping can significantly reduce the thermally induced diopter variation of the thin-disk. This provides more favorable conditions for mode matching over the full pump power density range and substantially mitigates the risk of optical damage caused by pump power fluctuations.-
Key words:
- diopter /
- thermal lensing effect /
- m-shaped pumping /
- thin-disk laser
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图 1 光焦度测量实验光路图。(a)荧光模式；(b)激光模式
Figure 1. Optical path diagram for thin-disk diopter measurement experiment. (a) fluorescence mode; (b) laser mode
图 2 荧光模式下的实验测试结果。(a)碟片处最高温度变化情况；(b)碟片光焦度变化情况；(c)泵浦功率为620W时，碟片光斑图以及水平方向光强分布情况
Figure 2. Experimental results in the fluorescence mode. (a) variation of the maximum temperature at the thin-disk; (b) variation of the thin-disk diopter; (c) beam profile and horizontal light intensity distribution at the thin-disk with a pump power of 620 W
图 3 激光模式下，不同泵浦功率下的碟片实测结果。(a)碟片光斑图；(b)水平光强分布情况；(c)碟片最高温度
Figure 3. Thin-disk test results under different pump powers in the laser mode. (a) beam profile at the thin-disk; (b) horizontal light intensity distribution; (c) maximum temperature at the thin-disk
图 4 激光模式下的实验测试结果。(a)碟片处最高温度及输出功率变化情况；(b)碟片光焦度变化情况；(c)泵浦功率为620W时，碟片光斑图以及水平方向光强分布情况
Figure 4. Experimental results in the laser mode. (a) variation of the maximum temperature at the thin-disk; (b) variation of the thin-disk diopter; (c) beam profile and horizontal light intensity distribution at the thin-disk with a pump power of 620 W
图 5 荧光模式与激光模式实验结果对比图。(a)碟片处最高温度变化情况；(b)碟片光焦度变化情况
Figure 5. Comparison of experimental results in the fluorescence and laser modes. (a) variation of the maximum temperature at the thin-disk; (b) variation of the thin-disk diopter
图 6 三维有限元模型示意图，界面连接层在碟片晶体与热沉之间（以热沉下表面中心为坐标原点建立参考系）
Figure 6. Schematic diagram of the three-dimensional finite element model, with the interface bonding layer between the thin-disk crystal and the heat sink (a reference system is established with the center of the lower surface of the heat sink as the origin)
图 7 超高斯泵浦(n=10)的光强分布及其泵浦功率密度为8.13 kW/cm2时的碟片温度场分布。(a)光强的X轴一维截面分布；(b)光强的三维空间分布；(c)碟片径向上表面温度分布；(d)碟片轴向截面温度分布（以热沉下表面中心为z轴原点，碟片晶体下表面与上表面分别位于z=2.85 mm与z=2.98 mm处）
Figure 7. Light intensity distribution of the super-Gaussian pump (n=10) and the temperature field distribution of the thin-disk at a pump power density of 8.13 kW/cm2. (a) one-dimensional cross-sectional light intensity distribution along the x-axis; (b) three-dimensional spatial light intensity distribution; (c) temperature distribution of the upper radial surface of the thin-disk; (d) temperature distribution of the axial cross-section of the thin-disk (with the center of the lower surface of the heat sink as the origin of the z-axis, and the lower and upper surfaces of the thin-disk crystal are located at z = 2.85 mm and z = 2.98 mm, respectively)
图 8 阶数n为10的超高斯泵浦下，碟片光焦度随泵浦功率密度变化情况。
Figure 8. Variation of the thin-disk diopter as a function of pump power density under super-Gaussian pumping with an order of n=10
图 9 阶数n为10的超高斯泵浦下的仿真结果与荧光模式下的实验结果对比情况。(a)碟片处最高温度；(b)碟片光焦度变化
Figure 9. Comparison between the simulation results under super-Gaussian pumping with an order of n=10 and the experimental results obtained in the fluorescence mode. (a) maximum temperature at the thin-disk; (b) variation of the thin-disk diopter
图 10 不同中心凹陷区超高斯阶数（m=2、4、6、8、10、12）的M形泵浦光强分布及其泵浦功率密度为8.13 kW/cm2时的碟片温度场分布。(a)光强的X轴一维截面分布；(b)光强的三维空间分布；(c)碟片径向上表面温度分布；(d)碟片轴向截面温度分布（以热沉下表面中心为z轴原点，碟片晶体下表面与上表面分别位于z=2.85 mm与z=2.98 mm处）
Figure 10. Light intensity distributions of the M-shaped pump for different super-Gaussian orders of the central depression region (m=2, 4, 6, 8, 10, and 12) and the temperature field distribution of the thin-disk at a pump power density of 8.13 kW/cm2. (a) one-dimensional cross-sectional light intensity distribution along the x-axis; (b) three-dimensional spatial light intensity distribution; (c) temperature distribution of the upper radial surface of the thin-disk; (d) temperature distribution of the axial cross-section of the thin-disk (with the center of the lower surface of the heat sink as the origin of the z-axis, and the lower and upper surfaces of the thin-disk crystal are located at z=2.85 mm and z=2.98 mm, respectively)
图 11 不同中心凹陷区超高斯阶数（m=2、4、6、8、10、12）的M形泵浦下，碟片光焦度随泵浦功率密度变化情况。(a)水平方向；(b)竖直方向
Figure 11. Variation of the thin-disk diopter as a function of pump power density under M-shaped pumping with different super-Gaussian orders of the central depression region (m=2, 4, 6, 8, 10, and 12). (a) horizontal direction; (b) vertical direction
图 12 超高斯泵浦（超高斯阶数n=10）与M形泵浦（不同中心凹陷区超高斯阶数m=4、8、10）下，碟片光焦度随泵浦功率密度变化情况。
Figure 12. Variation of the thin-disk diopter as a function of pump power density under super-Gaussian pumping (order n=10) and M-shaped pumping with different super-Gaussian orders of the central depression region (m=4, 8, and 10).
表 1 热仿真模型基本参数
Table 1. Basic parameters of the thermal simulation model
物质 参数 符号 仿真数值 Yb:YAG碟片晶体 半径 $ {\textit{r}}_{TD} $ 6 mm 厚度 $ {\textit{d}}_{TD} $ 130 μm 掺杂浓度 $ {c}_{Yb} $ 0.07 密度 $ {\rho }_{TD} $ 4560 kg/m3比热容 $ {C}_{TD} $ 590 J/(kg·K) 热膨胀系数 $ {\alpha }_{TD} $ 7.5×10−6 1/K 杨氏模量 $ {E}_{TD} $ 310 GPa 泊松比 $ {\nu }_{TD} $ 0.3 产热率 $ {\eta }_{TD} $ 0.07 界面连接层 半径 $ {\textit{r}}_{bond} $ 6 mm 厚度 $ {d}_{bond} $ 50 μm 导热系数 $ {K}_{bond} $ 6.15 W/(m*K) 热膨胀系数 $ {\alpha }_{bond} $ 42×10−6 1/K 杨氏模量 $ {E}_{bond} $ 9 GPa 泊松比 $ {\nu }_{bond} $ 0.35 金刚石热沉 半径 $ {\textit{r}}_{Diamond} $ 8 mm 厚度 $ {\textit{d}}_{Diamond} $ 2.8 mm 导热系数 $ {\textit{K}}_{Diamond} $ 1900 W/(m·K) 热膨胀系数 $ {\alpha }_{Diamond} $ 9×10−7 1/K 杨氏模量 $ {E}_{Diamond} $ 1100 GPa泊松比 $ {\nu }_{Diamond} $ 0.1 空气环境 环境温度 $ {T}_{air} $ 20 °C 环境半径 $ {r}_{air} $ 18 mm 环境长度 $ {L}_{air} $ 20 mm 泵浦光 半径 $ {\omega }_{pump} $ 3 mm 超高斯阶数 $ n $ 10 
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