Abstract

This study develops a fractional Jeffreys heat conduction model to describe laser-induced thermoelastic distortions in thin optical materials under ultrafast surface heating. The framework employs three fractional parameters to characterize anomalous thermal transport modes: retarded conduction, accelerated conduction, and transitions between super- and sub-diffusive regimes. Thermo-optic effects are represented through a linear relation between temperature and refractive-index perturbation; however, a full optical-aberration decomposition is not claimed in this work. Numerical results demonstrate that anomalous heat transfer significantly affects temperature localization, heat-flux evolution, stress distributions, and OPD-based thermo-optic indicators in components subjected to ultrafast laser pulses. Quantitative optical indicators, including refractive-index variation, optical path difference, wavefront error, focal-length shift, and thermal-lens distortion, are derived from the computed temperature field to connect the thermal solution directly with thin-lens performance. Simulations combining Maple2024 and MATLAB R2023a quantify the coupled thermoelastic-optical response at picosecond time scales.

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