Probing optical anisotropy of van der Waals materials with nano-infrared spectroscopy

Anisotropic dielectric tensors of uniaxial van der Waals (vdW) materials are notoriously difficult to investigate at infrared frequencies. The small dimensions of high-quality exfoliated crystals prevent the practical use of diffraction-limited spectroscopies. Near-field microscopes coupled to broadband lasers can function as Fourier transform infrared spectrometers with nanometric spatial resolution (nano-FTIR). While dielectric functions of isotropic materials can be readily extracted from nano-FTIR spectra, the in- and out-of-plane permittivities of anisotropic vdW crystals cannot be easily distinguished. We show how to separate the in- and out-of-plane contributions by exploiting the information in the screening of substrate resonances by vdW crystals. As an example, we determine the dielectric tensor of a bulk 2H-WSe2 microcrystal in the mid-IR and demonstrate how to quantify the uncertainty on the extracted permittivities using likelihood-based confidence intervals.