Super-sensitive tunable planar lens based on graphene hyperbolic metamaterials

We theoretically study the topological transition of dispersion types and propose a tunable planar lens based on graphene hyperbolic metamaterials (HMMs). By tuning the chemical potential (μc) of graphene, the dispersion relation of the HMM is topologically switchable between ellipse (μc 0.6 eV) where positive and negative refractions occur respectively. Especially, for μc>0.6 eV, a Gaussian light beam is negatively refracted twice and focuses at a far-field point finally, acting well as a planar lens. Furthermore, its focal length l can be sensitively tuned by controlling μc, and Δl reaches 260 μm (from 528 to 268 μm) while μc varies with only 0.05 eV (from 0.65 to 0.7 eV). The physical reason is attributed to the different anisotropy degrees of EFCs for different μc. Such a compact, high-speed, and sensitively tunable planar lens holds great promise in photonic integration, photonic imaging, and directional coupling applications.