端面抽运圆截面激光晶体热变形量的简便求解方法

Simplified Method for Thermal Distortion of End-Pumped Laser Crystal with Circular Cross-Section

激光二极管(LD)抽运的全固态激光器(DPSSL)应用广泛。抽运光在激光晶体中产生的热效应是影响全固态激光器工作特性的主要因素之一。通常先求解激光晶体中的温度场分布,再对热应变积分计算晶体的热变形量,这是一个既复杂又困难的过程。将求解晶体热传导微分方程与对热应变积分计算晶体热变形量相结合,在圆截面激光晶体侧面恒温、端而绝热的条件下,建立了晶体热变形量满足的微分方程和边界条件,把冗长的两步压缩为简单的一步,并使微分方程大为简化;得到了圆截面激光晶体热变形量的解析解;给出了一个算例。借助数值计算,分析了晶体抽运端热变形最及变形端面曲率半径与抽运光束半径之间的关系。提出的圆截面激光晶体热变形量简便求解方法有一定的通用性。

Laser diode pumped solid state laser （DPSSL） has many applications. The thermal effect of laser crystal produced by pumping light is one of the main factors affecting the characteristics of DPSSL. Usually, the temperature field distribution in laser crystal is found first, then the thermal distortion of laser crystal is calculated by integrating thermal strain along crystal. This process is complex and difficult. Under the condition that the side surface of laser crystal has constant temperature and its ends are adiabatic, the heat conduction equation and integrating thermal strain are combined, the differential equation and boundary conditions of laser crystal thermal distortion are set. The ordinarily used two-step method is simplified to one step and the new differential equation can be solved much more easily than the old one. The analytical solution of thermal distortion differential equation of laser crystal with circular cross-section has been got. A computation example is also given. By numerical calculating, the relations between thermal distortion and curvature radius of distorted pumped-end of crystal with pumping beam radius are analyzed. The proposed simplified method for thermal distortion of end-pumped laser crystal has some generalization.