Non-equilibrium transient thermal grating relaxation in metal

Abstract

Thermal grating relaxation in a metal with predominantly electronic heat transport is analyzed within the framework of the two-temperature model. Analytical solutions are obtained in the one-dimensional case, whereas the two-dimensional model simulating laser-induced transient grating experiment requires a numerical step to obtain time-domain solutions. When the grating period becomes comparable to (λ/G)1/2, where λ is the thermal conductivity and G the electron-phonon coupling constant, local thermal equilibrium between electrons and the lattice is not established even on a time scale much longer than the electron-phonon relaxation time. As a result, the thermal grating relaxation time is longer than predicted by the classical thermal diffusion model. For metals with high electron mobility such as gold, the effect is significant for thermal grating periods on the order of or under a micron and needs to be taken into account in the analysis of the laser-induced transient grating measurements.