  Guided modes in anisotropic two-dimensional van der Waals materials are
experimentally investigated and their refractive indices in visible wavelengths
are extracted. Our method involves near-field scanning optical microscopy of
waveguide (transverse electric) and surface plasmon polariton (transverse
magnetic) modes in h-BN/SiO2/Si and Ag/h-BN stacks, respectively. We determine
the dispersion of these modes and use this relationship to extract anisotropic
refractive indices of h-BN flakes. In the wavelength interval 550-700 nm, the
in-plane and out-of-plane refractive indices are in the range 1.98-2.12 and
1.45-2.12, respectively. Our approach of using near-field scanning optical
microscopy allows for direct study of interaction between light and
two-dimensional van der Waals materials and heterostructures.
