# Excitation of SPP's in graphene by a waveguide mode

## TL;DR

This paper develops a semi-analytical model to predict and analyze the excitation of surface-plasmon polaritons in graphene using a waveguide mode, revealing resonance behaviors linked to Fermi energy.

## Contribution

The work introduces a novel semi-analytical approach to model graphene SPP excitation and identifies unique resonance signatures related to Fermi energy variations.

## Key findings

- SPP excitation signatures are observable in transmission, reflection, and absorption.
- Resonance frequencies disperse with the square root of Fermi energy.
- The model provides a way to compute spatial probability densities of plasmonic resonances.

## Abstract

We present a semi-analytical model that predicts the excitation of surface-plasmon polaritons (SPP) on a graphene sheet located in front of a sub-wavelength slit drilled in thick metal screen. We identify the signature of the SPP in the transmission, reflection, and absorption curves. Following previous literature on noble-metal plasmonics, we characterize the efficiency of excitation of SPP's in graphene computing a spatial probability density. This quantity shows the presence of plasmonics resonances dispersing with the Fermi energy, $E_F$, as $\sqrt{E_F}$ an unambiguous signature of graphene plasmons.