Radiative contribution to thermal grating decay

The decay of a spatially sinusoidal temperature perturbation (thermal grating) via thermal transport by both conduction and radiation is analyzed theoretically. The intrinsic non-radiative conduction is described by the heat diffusion equation while radiative transport is described by the radiation transport equation for a non-scattering absorbing medium. We solve the coupled equations analytically and obtain the thermal grating decay rate, which leads to an explicit expression for the radiative contribution to the effective thermal conductivity measured with the laser-induced transient thermal grating technique. We find that at a given thermal grating period, the radiative contribution to thermal transport is maximized when the absorption length of thermal radiation is about 1/4 of the period. We present the expression for an upper bound for the radiative contribution and discuss the results for representative materials. We conclude that in a typical transient grating measurement with the grating period in the micrometer range, the radiative contribution is negligible, but it may be significant if the grating period is in the millimeter or centimeter range. Our analysis also provides a Fourier-domain Green's function that can be used to find the temperature field produced by an arbitrary spatiotemporal distribution of heat sources.