Physics-based prediction of nanosecond laser-induced structural coloration of titanium through thermal history, oxidation kinetics, and thin film interference

Laser-induced coloration of titanium is widely exploited for marking and functional surface engineering; however, a quantitative understanding linking laser processing conditions, oxide layer formation, and resulting optical color remains limited. In this work, titanium surfaces processed by a nanosecond ytterbium fiber laser in air are investigated using combined experiments and physically based modeling. A transient heat transfer and oxidation model is used to predict the thicknesses of a transparent TiO2 surface layer and an underlying TiO/Ti2O3 suboxide layer; the predictions agree with cross-sectional scanning electron microscopy measurements. The optical response is calculated using a transfer-matrix thin-film model, treating TiO2 as the interference layer and the suboxides as an effective absorbing substrate. Simulated reflectance spectra are converted to CIELAB coordinates, reproducing the observed color evolution and establishing a quantitative relationship between the oxide thickness and color. The proposed coupled framework provides a model-based approach for selecting processing conditions to achieve targeted color palettes in nanosecond laser marking of titanium.