Objective Fused silica has been used in a variety of applications, including high-power laser devices, owing to its excellent chemical stability and optical properties. However, the fused silica optical elements in high-power laser devices are easily damaged owing to various complex physical and chemical mechanisms, thereby the system stability is affected. Researchers have successively conducted a lot of basic and applied researches on laser induced damage. However, most of the existing researches focus only on the dynamic process of material surface damages caused by the interaction between optical materials and lasers, such as temperature distribution, material evaporation, and damaged pit morphological change. Many researches have been conducted on the thermal stress distribution on fused silica material surfaces. However, there are few studies on the stress field distributions inside materials along the direction of an incident laser. This study presents a detailed research and an analysis on temperature and damage morphological distributions of materials and clarifies the interaction mechanism between laser and matter from the three-dimensional stress viewpoint.

Methods To study the three-dimensional stress distribution of laser damaged optical components, this study establishes a finite element thermodynamic model describing the interaction between pulsed CO₂ laser and fused silica. This model can simulate temperature evolution inside fused silica during laser irradiation, and can be used to analyze the initial damage morphology of the specimen and three-dimensional stress distribution inside the material after cooling. To ensure the accuracy of the constructed thermodynamic model, this study considers classical heat conduction, heat radiation, and heat loss caused by heat convection on the specimen surface. Solving the heat conduction equation, one can get the internal temperature distribution when laser interacts with fused silica. Simultaneously, using the obtained surface temperature of the specimen, one can get the depth of damage pit. However, a single thermoelastic equation is not enough to completely describe the change in the material cooling process, and the viscoelasticity of materials is also needed to be included to investigate the variation of strain and stress with time. Therefore, a generalized Maxwell model with a single element is introduced to represent the viscoelastic materials, and the three-dimensional stress distribution of laser damaged fused silica can be calculated after the material is cooled. Further, a more in-depth analysis of laser damage can be conducted.

Results and Discussion Based on the model we established above, we obtained the three-dimensional radial stress and hoop stress in fused silica along the direction of the incident laser. As for the difference between the two stresses, the corresponding parameters in the numerical simulation are selected according to the experimental ones, and the comparison between the experimental and simulation results shows that the two stresses have a completely consistent trend, which proves the accuracy of the numerical model describing the interaction between the pulsed CO₂ laser and fused silica. Moreover, according to the interpretation of the obtained three-dimensional stress distribution, the radial stress within the depth of the damage pit appears as a compressive stress. The radial stress first increases to the maximum. After exceeding the damage depth, the radial stress gradually decreases until approaches zero. In addition, the internal radial stress of fused silica first reaches the maximum compressive stress value near the bottom of damage pit and then gradually transforms from the radial compressive stress to the tensile stress before gradually decreasing to zero along the axial direction. The hoop stress near damage pit appears as the compressive stress, similar to the radial stress. With the radius value decreasing, the hoop compressive stress is transformed into the tensile stress. The hoop stresses first increase along the z-axial direction until they reach the maximum value and then gradually decrease with the increase of depth until they become zero. In addition, the increase of laser pulse energy leads to the significant increase of the hoop and radial stresses and their influence ranges. These numerical calculation results, especially the three-dimensional hoop and radial stress distributions, are difficult to obtain with the traditional optical measurement technology.

Conclusion The traditional laser damage stress measurement experiment is complicated. It has a huge margin of error, and it is difficult to directly measure the radial and hoop stress distributions through this experiment; only the difference between these two stresses can be measured through this experiment. In this study, a finite element analysis method is used to establish a thermodynamic model describing the interaction between a pulsed CO₂ laser and fused silica. Based on the obtained temperature evolution inside fused silica and the initial damage morphology of specimen during the laser heating process, the three-dimensional stress distribution inside the material is calculated. The thermodynamic model considers the classical heat conduction, heat radiation, and heat loss caused by heat convection on the specimen surface. The three-dimensional distribution of the difference between the radial and hoop stresses calculated using this numerical model has the same changing trend as that from the experiment, which proves the accuracy of the numerical model. Based on the calculation of the three-dimensional stress distribution, the relationship between the radial and hoop stress distributions, the depth of damage pit, the distance from damage pit, and laser pulse energy are also analyzed in detail. These results are helpful to establish a three-dimensional stress field inside fused silica and provide a theoretical basis for the improvement of CO₂ laser repair process.