# Non-local quantum gain facilitates loss compensation and plasmon amplification in graphene hyperbolic metamaterials

## TL;DR

This paper develops a quantum non-local conductivity model for graphene hyperbolic metamaterials, enabling loss compensation and plasmon amplification, which enhances their potential for subwavelength imaging and wave manipulation.

## Contribution

It introduces a non-local quantum conductivity model combined with exact structure analysis to accurately predict hyperbolic behavior and plasmonic amplification in graphene metamaterials.

## Key findings

- Quantum model predicts plasmonic amplification in graphene sheets.
- Loss compensation achieved through chemical imbalance at finite temperature.
- Bloch solutions effectively describe electric field distribution in finite structures.

## 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 non-local 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 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 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.