Multidimensional quasiballistic thermal transport in transient grating spectroscopy

Transient grating spectroscopy has emerged as a useful technique to study thermal phonon transport because of its ability to perform thermal measurements over length scales comparable to phonon mean free path (MFPs). Although several prior works have performed theoretical studies of quasiballistic heat conduction in transient grating, the analysis methods are either restricted to one spatial dimension or require phenomenological fitting parameters. Here, we analyze quasiballistic transport in a two-dimensional transient grating experiment in which heat conduction can occur both in and cross plane using an analytic Green’s function of the Boltzmann equation we recently reported that is free of fitting parameters. We demonstrate a method by which phonon MFPs can be extracted from these measurements, thereby extending the MFP spectroscopy technique using transient grating to opaque bulk materials.