  It is challenging to characterize thermal conductivity of materials with
strong anisotropy. In this work, we extend the time-domain thermoreflectance
(TDTR) method with a variable spot size approach to simultaneously measure the
in-plane (Kr) and the through-plane (Kz) thermal conductivity of materials with
strong anisotropy. We first determine Kz from the measurement using a larger
spot size, when the heat flow is mainly one-dimensional along the through-plane
direction, and the measured signals are sensitive to only Kz. We then extract
the in-plane thermal conductivity Kr from a second measurement using the same
modulation frequency but with a smaller spot size, when the heat flow becomes
three-dimensional, and the signal is sensitive to both Kr and Kz. By choosing
the same modulation frequency for the two sets of measurements, we can avoid
potential artifacts introduced by the frequency-dependent Kz, which we have
found to be non-negligible, especially for some two-dimensional layered
materials like MoS2. After careful evaluation of the sensitivity of a series of
hypothetical samples, we provided a guideline on choosing the most appropriate
laser spot size and modulation frequency that yield the smallest uncertainty,
and established a criterion for the range of thermal conductivities that can be
measured reliably using our proposed variable spot size TDTR approach. We have
demonstrated this variable spot size TDTR approach on samples with a wide range
of in-plane thermal conductivity, including fused silica, rutile titania (TiO2
[001]), zinc oxide (ZnO [0001]), molybdenum disulfide (MoS2), hexagonal boron
nitride (h-BN), and highly ordered pyrolytic graphite (HOPG).
