采用格林函数法,考虑径向边界条件和对流热损失,理论上求解了有限尺寸高反射光学元件在激光作用下的热传导方程,获得了样品内的温度场分布。为验证所求解,模拟计算了不同光斑形状和光斑尺寸激光束照射下样品的温升曲线,并与有限元数值计算结果进行了比较,获得了较好的一致性,讨论了此精确物理模型中不同热交换系数对激光束照射下光学薄膜样品温升的影响。结果表明:热交换系数越大,样品内的温度分布越趋于平衡。

By solving a thermal conduction equation with Green’s function method,a theoretical model is developed to describe the three-dimensional temperature distribution of a highly reflective optical coating sample with a finite radial size irradiated by a continuous-wave laser beam. The radial boundary conditions and heat losses from the sample to the environment are both considered in this model. To verify the theoretical model,temperature distributions are numerically calculated under different pump-beam profiles and beam radii and the results are in good agreement with those of the finite-element method. Furthermore,the influence of different thermal loss coefficients on the temperature distributions of the sample irradiated by laser beams is discussed.