Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition

We investigated a multilayer graphene-dielectric composite material, comprising graphene sheets separated by subwavelength-thick dielectric spacer, and found it to exhibit hyperbolic isofrequency wavevector dispersion at far- and mid-infrared frequencies allowing propagation of waves that would be otherwise evanescent in a dielectric. Electrostatic biasing was considered for tunable and controllable transition from hyperbolic to elliptic dispersion. We explored the validity and limitation of the effective medium approximation (EMA) for modeling wave propagation and cutoff of the propagating spatial spectrum due to the Brillouin zone edge. We found that EMA is capable of predicting the transition of the isofrequency dispersion diagram under certain conditions. The graphene-based composite material allows propagation of backward waves under the hyperbolic dispersion regime and of forward waves under the elliptic regime. Transition from hyperbolic to elliptic dispersion regimes is governed by the transverse epsilon-near-zero (TENZ) condition, which implies a flatter and wider propagating spectrum with higher attenuation, when compared to the hyperbolic regime. We also investigate the tunable transparency of the multilayer at that condition in contrast to other materials exhibiting ENZ phenomena.