Time-fractional subdiffusion model for thin metal films under femtosecond laser pulses based on Caputo fractional derivative to examine anomalous diffusion process

Abstract

In this paper, the non-Fourier effects are examined in thin metal films exposed to femtosecond laser pulses. For the first time, the time-fractional subdiffusion model is presented based on the Caputo fractional derivative to examine the anomalous diffusion process in nano-scale metal films. The fractional heat conduction equation is solved numerically, using the finite difference method based on implicit scheme and the numerical results are compared to experimental data. The comparison implies that the numerical results well coincide with experimental data, proving the accuracy and suitability of fractional model to capture thermal behaviors of thin metal films heated by short-pulse laser. Furthermore, the results of time-fractional model are compared to other models including parabolic and hyperbolic two-step models. Having compared, one can be found is that the fractional model is more reliable than other models, because its results are well matched with experimental data. The use of Fourier's law in parabolic and hyperbolic two-step model leads to deviation from experimental data which can be addressed upon applying the proposed time-fractional model in this work. Moreover, the presented time-fractional model can be effectively utilized for studying the heat transport in thin metal films under laser pulses as well as the laser heating process and its applications in engineering. Ultimately, the effect of changes in various parameters such as order of fractional derivative, laser pulse duration, metal materials (gold and chromium), gold film thickness, relaxation time and absorption depth of laser pulses are investigated on temperature response of thin metal films.