Nonlocal quantum gain facilitates loss compensation and plasmon amplification in graphene hyperbolic metamaterials

Abstract

Graphene-based hyperbolic metamaterials have been predicted to transport evanescent fields with extraordinarily large vacuum wave vectors. It is particularly at much higher wave vector values that the commonly employed descriptional models involving structure homogenization and assumptions of an approximatively local graphene conductivity start breaking down. Here, we combine a nonlocal quantum conductivity model of graphene with an exact mathematical treatment of the periodic structure to develop a toolset for determining the hyperbolic behavior of these graphene-based hyperbolic metamaterials. The quantum conductivity model of graphene facilitates us to predict the plasmonic amplification in graphene sheets of the considered structures. This allows us to reverse the problem of Ohmic and temperature losses, making this simple yet powerful arrangement practically applicable. We analyze the electric field distribution inside the finite structures, concluding that Bloch boundary solutions can be used to predict their behavior. With the transfer-matrix method, we show that at finite temperature and collision loss, we can compensate for losses, restoring imaging qualities of the finite structure via an introduction of chemical imbalance.