Hybrid surface plasmon polaritons in graphene coupled anisotropic van der Waals material waveguides

Polaritons in anisotropic van der Waals materials (AvdWMs), with either hyperbolic or elliptical topologies, have garnered significant attention due to their ability of field confinement and many useful applications in in-plane polariton nanophotonics, including directional guiding, canalization, and hyperlensing. Here, we obtain the dispersion relation of hybrid surface plasmon polaritons (SPPs) supported by a parallel-plate waveguide composed of an AvdWM, as an example tungsten ditelluride, that is coupled with a graphene layer. Through analytical calculations and numerical simulations, we first investigate the impact of losses on the modal characteristics of SPPs supported by the AvdWM. We then show that the coupling of the anisotropic layer to a graphene sheet in a parallel-plate waveguide heterostructure allows one to control the in-plane propagation and dispersion topology of the hybrid SPPs by changing the spacer thickness and the graphene chemical potential. Moreover, it is found that owing to the different coupling regimes, this anisotropic-isotropic SPPs hybridization can enhance the propagation length and spatial localization of the guided modes. We believe this approach can lead to the realization of vdW heterostructures with improved functionalities for in-plane and out-of-plane infrared nanophotonics.