In-plane anisotropic optical and mechanical properties of two-dimensional MoO$_3$

Molybdenum trioxide (MoO$_3$) in-plane anisotropy has increasingly attracted the attention of the scientific community in the last few years. Many of the observed in-plane anisotropic properties stem from the anisotropic refractive index and elastic constants of the material but a comprehensive analysis of these fundamental properties is still lacking. Here we employ Raman and micro-reflectance measurements, using polarized light, to determine the angular dependence of the refractive index of thin MoO$_3$ flakes and we study the directional dependence of the MoO$_3$ Young's modulus using the buckling metrology method. We found that MoO$_3$ displays one of the largest in-plane anisotropic mechanical properties reported for 2D materials so far.