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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 beotherwise evanescent in a dielectric. Electrostatic biasing was considered fortunable and controllable transition from hyperbolic to elliptic dispersion. Weexplored the validity and limitation of the effective medium approximation(EMA) for modeling wave propagation and cutoff of the propagating spatialspectrum due to the Brillouin zone edge. We found that EMA is capable ofpredicting the transition of the isofrequency dispersion diagram under certainconditions. The graphene-based composite material allows propagation ofbackward waves under the hyperbolic dispersion regime and of forward wavesunder the elliptic regime. Transition from hyperbolic to elliptic dispersionregimes is governed by the transverse epsilon-near-zero (TENZ) condition, whichimplies a flatter and wider propagating spectrum with higher attenuation, whencompared to the hyperbolic regime. We also investigate the tunable transparencyof the multilayer at that condition in contrast to other materials exhibitingENZ phenomena.

journal of nanophotonics

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