ear the front surface become dominant in the absorption process. Consequently, the ablation threshold is closely related to CB electrons generation and energy absorption by the CB electrons generated inside the medium.

\[sec:conclusion\] Conclusion
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Through first-principles simulations, we have investigated the changes in the optical response of bulk and thin-film $\alpha$-quartz when irradiated with an intense ultrashort laser pulse. The generation of CB electrons in the medium has also been investigated in detail. The change in the reflectance with laser intensity was mainly attributed to the generation and spatial distribution of the CB electrons in the medium. The simulation studies performed for laser intensities in the range $10^{10} \, \mathrm{W/cm^{2}}$ to $2 \times 10^{15} \, \mathrm{W/cm^{2}}$ successfully described the transition (from a dielectric to plasma) property of the medium as well as the laser intensity required for this change in the optical properties. At low laser intensities, the interference effect between the secondary waves from the front and rear surfaces was the dominant process in the reflectance behavior of thin films. However, at high laser intensities, the CB electrons generated on the front surface played a dominant role and interference a minor role in changing the reflectance.

The energy absorbed by the CB electrons in the medium was used to estimate the laser-induced ablation threshold of $\alpha$-quartz materials. The theoretical estimation showed a good agreement with the experimental value, despite some limitations in the simulations, particularly, underestimation of the band gap energy. This limitation can be easily overcome by using more elaborate functionals; these will be discussed in a further study. The results obtained in our study can provide fundamental information on the parameters required for designing a high-performance optical coating structure, such as a high-damage-threshold and broadband multilayer coated mirror.

This work w