Interfacing differently oriented biaxial van der Waals crystals for negative refraction.

Negative refraction has a wide range of applications in diverse fields such as imaging, sensing, and waveguides and typically entails the fabrication of intricate metamaterials endowed with hyperbolic features. In contrast to artificially engineered hyperbolic materials, natural van der Waals (vdW) materials are more accessible owing to their inherent strong in-plane covalent bonding and weak interlayer interactions. However, most vdW materials manifest uniaxial crystal properties, which restrict their behavior solely to out-of-plane hyperbolicity. This characteristic poses a considerable challenge to their seamless integration via planar fabrication techniques, unless a suitable pattern is employed. Recent advances have identified natural biaxial -MoO as a promising vdW material capable of exhibiting in-plane hyperbolicity. In this study, we performed numerical simulations demonstrating that negative refraction could be achieved by interfacing differently oriented -MoO slabs coated with tunable graphene on a gold substrate. Our comprehensive analysis yielded three notable outcomes: negative refraction, simultaneous positive and negative refractions, and diffractionless propagation. These outcomes could be operated in a broad range of frequencies and achieved at all angles to offer a superior platform for the flexible manipulation of mid-infrared polaritons. Our findings provide valuable insights into the potential application of other two-dimensional vdW materials for advances in nanoscale super-resolution imaging, molecular sensing, and on-chip photonic integrated circuits.