  Numerous optical phenomena and applications have been enabled by nanophotonic
structures. Their current fabrication from high refractive index dielectrics,
such as silicon or gallium phosphide, pose restricting fabrication challenges,
while metals, relying on plasmons and thus exhibiting high ohmic losses, limit
the achievable applications. Here, we present an emerging class of layered
so-called van der Waals (vdW) crystals as a viable nanophotonics platform. We
extract the dielectric response of 11 mechanically exfoliated thin-film (20-200
nm) van der Waals crystals, revealing high refractive indices up to n = 5,
pronounced birefringence up to $\Delta$n = 3, sharp absorption resonances, and
a range of transparency windows from ultraviolet to near-infrared. We then
fabricate nanoantennas on SiO$_2$ and gold utilizing the compatibility of vdW
thin films with a variety of substrates. We observe pronounced Mie resonances
due to the high refractive index contrast on SiO$_2$ leading to a strong
exciton-photon coupling regime as well as largely unexplored
high-quality-factor, hybrid Mie-plasmon modes on gold. We demonstrate further
vdW-material-specific degrees of freedom in fabrication by realizing
nanoantennas from stacked twisted crystalline thin-films, enabling control of
nonlinear optical properties, and post-fabrication nanostructure transfer,
important for nano-optics with sensitive materials.
