Actively tuning anisotropic light-matter interaction in biaxial hyperbolic material $\alpha$-MoO$_3$ using phase change material VO$_2$ and graphene

Anisotropic hyperbolic phonon polaritons (PhPs) in natural biaxial hyperbolic material MoO$_3$ has opened up new avenues for mid-infrared nanophotonics, while active tunability of $\alpha$-MoO$_3$ PhPs is still an urgent problem needing to be solved.In this study, we present a theoretical demonstration of actively tuning $\alpha$-MoO$_3$ PhPs using phase change material VO$_2$ and graphene. It is observed that $\alpha$-MoO$_3$ PhPs are greatly depending on the propagation plane angle of PhPs. The metal-to-insulator phase transition of VO$_2$ has a significant effect on the hybridization PhPs of the $\alpha$-MoO$_3$/VO$_2$ structure and allows to obtain an actively tunable $\alpha$-MoO$_3$ PhPs, which is especially obvious when the propagation plane angle of PhPs is 90