Hyperspectral imaging of complex dielectric functions in 2D materials

It remains a challenge to characterize inhomogeneities in two-dimensional (2D) layered materials associated with strain and defects. Spectroscopic ellipsometry and reflectance/transmittance measurement can be used to characterize complex dielectric functions. However, these techniques are not well suited for submicron spectroscopic imaging of inhomogeneities across a macroscale sample. Here, we report hyperspectral phase microscopy (HPM) to image spatially-resolved complex dielectric functions of refractive index and extinction coefficient of transition metal dichalcogenides. This was implemented by measuring wavelength-dependent phase shifts in optical interference, which were then analyzed by a simple Kramers-Kronig-consistent model. We successfully image not only the phase difference but also patterns of modulated carrier density and strain in mono-/bi-layer heterostructured transition metal dichalcogenides.