## 1 Introduction
It is of great theoretical and practical significance to explore the underlying mechanisms involved in the laser-induced surface damage and develop new engineering techniques to remove the surface and subsurface defects for improving the laser damage resistance of fused silica. The primary source leading to the low surface LIDT of fused optics is the subsurface damage (SSD) caused in the chemical-mechanical polishing process. The SSD layer located beneath the polished surface generally consists of re-deposition layer (also named the Beilby layer), a defect layer with crack and scratch defects included, and a deformed layer [17; 18; 19]. During the polishing process, the highly absorptive impurities (e.g., Ce, Fe, etc.) coming from the polishing slurries are randomly distributed among the re-deposition layer. Some of the impurities are even embedded and hidden deeply inside the defect layer via entering the open subsurface cracks and scratches. Under the irradiation of intense laser, the impurity defects would make the natively transparent fused silica optics highly absorptive to incident laser, resulting in very high local temperature and stress, and eventually the breakdown of the optical parts [7; 20; 21]. Meanwhile, the absorptive impurity defects would change the initial band-gap structure of fused silica and also trigger new photon excitation under intense laser irradiation. These effects caused by the impurity defects would substantially affect the laser-induced nonlinear excitation of dielectric silica optics (e.g., multi-photon and avalanche ionizations), making the optical material more susceptible to laser damage [22; 23]. The absorptive impurities mainly originate from three kinds of sources in the optical processing stage: oxide polishing slurries (CeO\({}_{2}\), ZrO\({}_{2}\), etc. ), metal polishing tools (Fe, Cu, Cr, etc.) and Al ion from optical cleaning. [PERSON] et al. [24] demonstrated that besides subsurface scratch and dig defects, \(\sim\)35% of the laser damage sites were initiated at invisible defects, probably being absorptive impurities with submicrometer size. It was also experimentally proved by [PERSON] et al. [17; 25] that the laser-induced damage on fused silica was closely associated with the subsurface absorptive impurities and different types of impurity defects would incur different levels of optical damage. Hence, in this work, the heat conduction and thermo-elastic equations involved in the absorbing process of impurity defects under intense laser irradiation are firstly numerically resolved using the finite element method (FEM). Then, the temperature and thermal stress distributions inside fused silica caused by impurity defects are investigated to figure out the most dangerous species and size range of impurity defects in decreasing the laser damage resistance of silica optics. This part of work could provide further understanding of the laser-induced damage mechanisms on optical components, which are beneficial to the surface/subsurface quality evaluation and SSD removal of ultra-precision fabricated fused silica optics. To alleviate the effect of SSD defects on the laser damage resistance of fused silica optics, many engineering techniques (e.g., hydrofluoric HF acid etching [26; 27; 28], ultraviolet or CO\({}_{2}\) laser preprocessing [8; 29], plasma etching [30], and magneto-rheological finishing (MRF) [31], etc.) have been developed and applied in the actual preparation processes of high-quality silica surfaces. In the laser preprocessing process, lasers with energy lower than the LIDT are used to irradiate the fused silica surfaces. Due to the strong absorption of silica material to CO\({}_{2}\) lasers, the temperature on the optical surface would moderately rise, resulting in the recombination of surface micro-structure and the healing of subsurface cracks. At the same time, the lasers can bring about the electronic excitation of the impurity defects, which would finally lower the defect energy band to a steady state.