# Graphene and active metamaterials: theoretical methods and physical properties

## TL;DR

This paper explores the theoretical aspects of plasmons in metals, graphene, and metamaterials, highlighting quantum effects in graphene and proposing applications like lossless plasmon propagation and tunable wave control.

## Contribution

It provides a comprehensive theoretical analysis of plasmons in various materials, emphasizing the quantum nature of graphene plasmons and introducing novel metamaterial configurations.

## Key findings

- Graphene plasmons are purely quantum modes, unlike classical plasmons in metals.
- A gain medium can eliminate metallic losses, enabling lossless surface plasmon polaritons.
- Periodic graphene layers can form tunable plasmonic metamaterials with unique wave properties.

## Abstract

The interaction of light with matter has triggered the interest of scientists for long time. The area of plasmonics emerges in this context through the interaction of light with valence electrons in metals. The random phase approximation in the long wavelength limit is used for analytical investigation of plasmons in three-dimensional metals, in a two-dimensional electron gas and finally in the most famous two-dimensional semi-metal, namely graphene. We show that plasmons in bulk metals as well as in a two-dimensional electron gas originate from classical laws, whereas, quantum effects appear as non-local corrections. On the other hand, graphene plasmons are purely quantum modes and, thus, they would not exist in a "classical world". Furthermore, under certain circumstances, light is able to couple with plasmons on metallic surfaces, forming a surface plasmon polariton, which is very important in nanoplasmonics due to its subwavelength nature. In addition, we outline two applications that complete our theoretical investigation. Firstly, we examine how the presence of gain (active) dielectrics affects surface plasmon polariton properties and we find that there is a gain value for which the metallic losses are completely eliminated resulting to lossless plasmon propagation. Secondly, we combine monolayers of graphene in a periodic order and construct a plasmonic metamaterial that provides tunable wave propagation properties, such as epsilon-near-zero behavior, normal and negative refraction.