Non-uniform (gradient) heating due to absorption of laser radiation in optical elements causes thermal lensing and paraxial focus shift and aberration leading to change in size and intensity profile of focused spot in optics operating with high-power lasers. Analysis of primary physical effects of geometrical deformation of optical surfaces in the form of aspheric bulges and transformation of the material into a gradient refractive medium makes it possible to estimate quantitatively the focus shift and aberrations for single-mode and multimode lasers, to formulate optimal relationships between the physical properties of optical materials for reduction of thermo-optical effects through compensating the effects from material thermal expansion by the effects due to change in the refractive index—condition of self-compensation or athermalization. Comparison of characteristics Temperature Coefficient of the Optical Pathlength and Thermo-Optical Ratio allows determining the optimal materials for the optics for high-power lasers: athermal crystalline quartz and specialty glasses, sapphire with extremely high thermal conductivity ensuring minimal temperature gradients. Optics made of these materials exhibit minimized thermal focus shift and aberration even when absorption of laser energy in bulk material and coatings, by contamination, scratches, and other surface defects. Weak birefringence of crystalline quartz and sapphire does not prevent their successive use in laser optics.

中文翻译：

---

基于热梯度引起的焦点偏移和像差分析的高功率激光光学材料选择

由于在光学元件中吸收激光辐射而导致的非均匀（梯度）加热会导致热透镜和近轴焦点偏移和像差，从而导致使用高功率激光器工作的光学器件中聚焦光斑的尺寸和强度分布发生变化。分析非球面凸起形式的光学表面几何变形的主要物理效应和材料向梯度折射介质的转变，可以定量估计单模和多模激光器的焦点偏移和像差，以制定最佳关系光学材料的物理特性之间的关系，通过补偿材料热膨胀的影响，由折射率变化引起的影响来减少热光效应——自补偿或非热化的条件。特性比较光程长度的温度系数和热光比允许确定高功率激光器光学元件的最佳材料：无热晶体石英和特种玻璃，具有极高导热性的蓝宝石，确保最小的温度梯度。即使在块状材料和涂层中吸收激光能量、污染、划痕和其他表面缺陷时，由这些材料制成的光学器件也能最大限度地减少热焦点偏移和像差。晶体石英和蓝宝石的弱双折射并不妨碍它们在激光光学中的连续使用。无热结晶石英和特种玻璃，蓝宝石具有极高的导热性，确保最小的温度梯度。即使在块状材料和涂层中吸收激光能量、污染、划痕和其他表面缺陷时，由这些材料制成的光学器件也能最大限度地减少热焦点偏移和像差。晶体石英和蓝宝石的弱双折射并不妨碍它们在激光光学中的连续使用。无热结晶石英和特种玻璃，蓝宝石具有极高的导热性，确保最小的温度梯度。即使在块状材料和涂层中吸收激光能量、污染、划痕和其他表面缺陷时，由这些材料制成的光学器件也能最大限度地减少热焦点偏移和像差。晶体石英和蓝宝石的弱双折射并不妨碍它们在激光光学中的连续使用。