  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 paths (MFPs). While 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.
