Two-dimensional negative refraction steering of hybrid polaritons in graphene/twisted bilayer <i>α</i>-MoO₃ heterostructures

Hyperbolic materials have emerged as a powerful medium for manipulating polaritons at deeply subwavelength scales. In the realm of polaritonic applications, <i>α</i>-MoO₃/graphene heterostructures have shown great promise, featuring low-loss, electrically tunable negative refraction, and enhanced focusing and steering capabilities. However, a significant challenge has been the manipulation of the focusing position of hybrid polaritons, which is limited to a line perpendicular to the interface or unable to be manipulated while steering. Stacking twisted bilayer <i>α</i>-MoO₃ with graphene could provide a potential way to manipulate the steering and focusing position with more flexibility. Here, we demonstrate tunable negative refraction steering of hybrid polaritons within a two-dimensional plane in graphene/twisted bilayer <i>α</i>-MoO₃ heterostructures. By modulating the Fermi energy of graphene and adjusting the twist angle of <i>α</i>-MoO₃ bilayers, we facilitate the modulation of the focusing position across a two-dimensional plane. This method enables precise tunable directional control of the energy flow within the heterostructures, facilitating a versatile approach to the nanoscale planar focusing of polaritons.