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 in order to develop a tool-set for determining the hyperbolic behavior of these graphenebased 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 of 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.

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In particular, nanoplasmonics is seen as a pathway forward to produce noisy intermediate-scale quantum (NISQ) devices circa room-temperature by taking advantage of its ultrafast (pico-femto second) dynamics [3] and the relatively low decoherence rates of plasmonically-coupled quantum emitters. [4] Such characteristics are highly desired for the fabrication of quantum networks which include logic gates, memories, and repeaters for error correction. [5,6] Furthermore, nanoheating due to plasmonics has notably been used within the next generation of data storage devices, [7] cancer treatments, [8] photovoltaic and solar cell technology, [9] and pro-