Lasers are widely used in laser processing, laser medical treatment, optical communication, inertial confinement, and nuclear fusion. With the continuous development of laser technology, the output power and single-pulse energy of lasers are increasing. Under high energy density conditions, the laser damage resistance of optical elements is one of the main factors affecting further development of high-power laser systems. Laser-induced damage shortens the working life of optical elements and considerably reduces the peak power output of high-power laser systems. Therefore, it is necessary to investigate the damage characteristics of optical materials under high-power laser irradiation. The mechanism of laser damage is very complicated and involves several physical processes, such as laser energy deposition, temperature and stress changes, and material phase transformation. During these processes, stress leads to damage of optical components, such as pits and cracks, and the residual stress in optical components increases the difficulty of laser repairing optical components. Therefore, it is crucial to investigate the thermal stress characteristics of laser-irradiated optical materials. However, current research on thermal stress properties is focused on optical materials with smooth surfaces, and the results are not applicable to uneven-surface optical elements with various defects and periodic structures. The thermal stress characteristics of complex surfaces under laser irradiation should be analyzed using thermodynamic models and related experiments.

Based on the theories of electromagnetic fields, heat conduction, and elastic-plastic mechanics, thermal stress numerical models of optical materials are established for different types of nanosecond pulse laser irradiation to investigate the uneven-surface thermal stress characteristics of optical materials under laser irradiation. This thermal stress numerical model can simulate the temperature and stress field distributions of optical materials with smooth and uneven surfaces under laser irradiation. Moreover, it can analyze the modulation effect of the surface structure on the incident laser and the relationship between light field modulation and the temperature and stress fields. During laser irradiation, the energy absorbed by the material is regarded as a heat source. It considers the classical heat conduction and heat loss induced by heat convection and radiation to improve the accuracy of the model. Moreover, the thermal stress model reflects the diffraction and interference of the incident laser near the material surface structure by introducing the relative light intensity factor. The temperature and stress field distributions in optical materials can be determined by solving heat conduction and thermoelastic equations.

The simulation results for fused silica with smooth surface irradiated by a single pulse indicate that when the laser energy distribution in the fused silica does not change, the temperature and stress distributions are consistent with the Gaussian distribution of laser energy (Fig. 2). The simulation results for fused silica with scratch surface under single-pulse irradiation show that owing to the light field modulation via surface scratching, the fused silica with scratch surface reaches the melting point at a low laser energy density, and the temperature and thermal stress fields in the scratch surface appear as streaking phenomena (Fig. 3). The simulation results for the stress induced by the smooth surface under laser irradiation are compared with the experimental results. The results demonstrate the accuracy of the proposed model for simulating the thermal stress characteristics of the fused silica with smooth surface induced by laser irradiation (Fig. 5). The experimental and simulation results for laser-irradiated fused silica with scratch surface also demonstrate the accuracy of the model for simulating the thermal stress characteristics of laser-irradiated scratch surfaces (Fig. 9). Under the same laser energy density irradiation, more significant stress is generated in the fused silica with scratch surface because of the modulation effect of the surface scratch on the incident laser, and the stress enhancement is related to the surface scratch size (Fig. 11).

In this study, a thermal stress model is established to show the interaction between laser and optical materials with uneven surface. The thermal stress characteristics of the fused silica materials with a smooth surface and a scratch surface irradiated by a 355 nm nanosecond pulse laser are evaluated using the proposed model, and a laser damage test and stress online-measurement system are built to verify the model. The experimental and simulation results show that the established numerical model for the laser-material interaction can precisely simulate the stress distribution generated via laser irradiation on fused silica with smooth surface. The computed results for the stress distribution generated by laser irradiation on the scratch surface are consistent with the experimental results. Compared to that generated by the fused silica with smooth surface, the light field modulation generated by the fused silica with uneven surface enhances the thermal stress inside the fused silica after laser irradiation, and the size of the surface structure significantly influences the stress. The thermal stress model is valuable for analyzing the laser damage mechanism and residual stress of optical elements with uneven surfaces and provides a theoretical basis for controlling thermal stress during laser processing.