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 (μ_c) of graphene, the dispersion relation of the HMM is topologically switchable between ellipse (μ_c<0.6 eV) and hyperbola (μ_c>0.6 eV) where positive and negative refractions occur respectively. Especially, for μ_c>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 μ_c, and Δl reaches 260 μm (from 528 to 268 μm) while μ_c 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 μ_c. Such a compact, high-speed, and sensitively tunable planar lens holds great promise in photonic integration, photonic imaging, and directional coupling applications.