Giant optical anisotropy in the edge surfaces of layered crystals: unveiled by direct measurements of out-of-plane optical constants

Abstract

Large optical anisotropy is of paramount importance for efficient light manipulation in optoelectronic devices. Van der Waals layered materials, exhibiting large structural contrast between in-plane and out-of-plane directions, are inherently anisotropic in 3D space. The measurements of their optical constants were limited to the 2D planes. Here, the reflectance spectra of layered MoS₂, NbOCl₂, and WTe₂ crystals are measured directly from their edge and basal surfaces to compare their out-of-plane and in-plane optical constants in the range of 500–1000 nm. The results indicate that their out-of-plane refractive indices are smaller than the in-plane refractive indices. The out-of-plane extinction coefficients of MoS₂ and NbOCl₂ are zero but nonzero for WTe₂, as confirmed by the transient reflection spectroscopies. The nonzero extinction coefficient of WTe₂ arises from the symmetry of the transition dipole moment and density of states, which are determined by the crystal structure. Meanwhile, compared to their in-plane optical constants, the out-of-plane optical constants of MoS₂ and NbOCl₂ exhibit less dispersion, whereas WTe₂ exhibits enhanced out-of-plane dispersion around 2.14 eV. This enhancement is attributed to significant increases in optical transition probability resulting from a larger density of states. These optical parameters indicate giant birefringence (e.g., >1.8 for MoS₂, >0.6 for NbOCl₂, and >0.5 for WTe₂) and linear dichroism (e.g., up to 100% for MoS₂ and NbOCl₂, 40.7% for WTe₂) on the edge surface of layered materials. These results could be used to predict the optical response at arbitrary angles of incidence and are helpful for their application in polarization-related optoelectronic devices.