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以求解热传导方程为基础,研究了端面抽运圆截面激光晶体内部温度场和抽运端热形变。通过对端面抽运激光晶体工作特点的分析,建立了晶体端面与外界非绝热边界条件;提出了热传导方程新的求解方法,得出了圆截面激光晶体内部温度场和抽运端热形变的解析表达式;研究了σ(空气传热系数与晶体导热系数之比)取不同值时,晶体中的温度场和抽运端热变形分布。结果表明,常用的晶体端面绝热假设与晶体实际工作状态不符。当σ=0,0.6和∞时,计算出晶体中的最大温升分别为165.2,135.7和40.1℃,晶体抽运端的最大热变形分别是0.66,0.55和0.22μm。
Based on solving the heat conduction equation, the internal temperature field and the thermal deformation at the pumping end were studied. By analyzing the operating characteristics of the end-pumped laser crystal, the boundary condition between the crystal end face and the external non-adiabatic boundary is established. A new method of solving the thermal conduction equation is proposed, and the analysis of the internal temperature field and the thermal deformation at the pumping end is obtained. The temperature field and the thermal deformation distribution at the pumping end of the crystal were studied when σ (the ratio of air heat transfer coefficient to thermal conductivity of crystal) was different. The results show that the commonly used crystal face adiabatic assumption does not match the actual working condition of the crystal. When σ = 0, 0.6 and ∞, the maximum temperature rise in the crystal was calculated to be 165.2, 135.7 and 40.1 ° C, respectively. The maximum thermal deformations at the pumping end were 0.66, 0.55 and 0.22 μm, respectively.