# Quantization of graphene plasmons

## TL;DR

This paper presents a comprehensive quantization of graphene plasmons using classical and quantum hydrodynamic models, accounting for dispersion and non-local effects, and analyzes their impact on emitter decay rates.

## Contribution

It introduces a novel quantization method for graphene plasmons considering dispersion and non-local effects, with applications to emitter decay rate calculations.

## Key findings

- Mode-functions depend on graphene's dispersive properties
- Non-local effects significantly influence decay rates at small Fermi energies
- Quantization methods accurately predict emitter decay near graphene

## Abstract

In this article we perform the quantization of graphene plasmons using both a macroscopic approach based on the classical average electromagnetic energy and a quantum hydrodynamic model, in which graphene charge carriers are modeled as a charged fluid. Both models allow to take into account the dispersion of graphenes optical response, with the hydrodynamic model also allowing for the inclusion of non-local effects. Using both methods, the electromagnetic field mode-functions, and the respective frequencies, are determined for two different graphene structures. we show how to quantize graphene plasmons, considering that graphene is a dispersive medium, and taking into account both local and nonlocal descriptions. It is found that the dispersion of graphene's optical response leads to a non-trivial normalization condition for the mode-functions. The obtained mode-functions are then used to calculate the decay of an emitter, represented by a dipole, via the excitation of graphene surface plasmon-polaritons. The obtained results are compared with the total spontaneous decay rate of the emitter and a near perfect match is found in the relevant spectral range. It is found that non-local effects in graphene's conductivity, become relevant for the emission rate for small Fermi energies and small distances between the dipole and the graphene sheet.