  We developed a novel contactless frequency-domain approach to study thermal
transport, which is particularly convenient when thermally anisotropic
materials are considered. The method is based on a similar line-shaped heater
geometry as used in the 3-omega method, however, keeping all the technical
advantages offered by non-contact methodologies. The present method is
especially suitable to determine all the elements of the thermal conductivity
tensor, which is experimentally achieved by simply rotating the sample with
respect to the line-shaped optical heater. We provide the mathematical solution
of the heat equation for the cases of anisotropic substrates, multilayers, as
well as thin films. This methodology allows an accurate determination of the
thermal conductivity, and does not require complex modeling or intensive
computational efforts to process the experimental data, i.e., the thermal
conductivity is obtained through a simple linear fit ("slope method"), in a
similar fashion as in the 3-omega method. We demonstrate the potential of this
approach by studying isotropic and anisotropic materials in a wide range of
thermal conductivities. In particular, we have studied the following inorganic
and organic systems: (i) glass, Si, and Ge substrates (isotropic), (ii)
$\beta$-Ga$_2$O$_3$, and a Kapton substrate (anisotropic) and , (iii) a 285 nm
SiO$_2$/Si thin film. The accuracy in the determination of the thermal
conductivity is estimated at $\approx$ 5\%, whereas the best temperature
resolution is $\Delta$T $\approx$ 3 mK.
