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以解析热分析理论为基础,建立了平板Nd:GdVO4激光晶体在激光二极管阵列端面抽运时的导热微分方程。通过对方程的求解,得到了Nd:GdVO4晶体内部温度场解析式和热透镜焦距随抽运光半径和功率变化的分布关系。温度场的数值模拟表明:当泵浦光功率P=30W、泵浦区域为1mm×1 mm时,晶体在x,y,z方向的最高相对温升分别为104 K、31 K和31.8 K;若令z=0和x=0,则xy和xz面处的温度场分布类似于倒鼻型,这两个面上最高相对温升均为104 K;若令x=0,则yz面上的温度场分布类似于波包,此面处最高的温升为31 K左右;热透镜焦距的数值模拟给出了热透镜效应随抽运光功率和泵浦光半径变化的趋势。此方法也可以应用于其他激光晶体的热问题研究中,为有效解决激光系统热问题提供了理论依据。
Based on the analysis of thermal analysis theory, the differential thermal conduction equation of a flat Nd: GdVO4 laser crystal at the end face of a laser diode array is established. By solving the equations, the analytical solution of the internal temperature field of Nd: GdVO4 crystal and the distribution of the focal length of the thermal lens with the pumping light radius and power change are obtained. The numerical simulation of the temperature field shows that the maximum relative temperature rise of the crystal in the x, y and z directions is 104 K, 31 K and 31.8 K, respectively, when the pump power is P = 30W and the pump area is 1mm × 1mm. If z = 0 and x = 0, then the distribution of temperature field at xy and xz is similar to the inverted nose, with the maximum relative temperature rise of 104 K on both surfaces. If x = 0, The temperature distribution is similar to that of the wave packet. The highest temperature rise at this surface is about 31 K. The numerical simulation of the thermal lens focal length shows the trend of the thermal lens effect with the pump power and the pump light radius. This method can also be applied to other thermal problems of laser crystals, providing a theoretical basis for effectively solving the thermal problem of laser systems.