# Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances

## Abstract

**:**

## 1. Introduction

## 2. Formulation and Solution of the Problem

_{n}) of the n-th harmonic of the surface current density [57],

_{n}is denoted by

## 3. Numerical Results and Discussion

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Normalized ACS and TSCS of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=1\mathrm{ps}$, ${\mu}_{c}=0.25\mathrm{eV},0.5\mathrm{eV},0.75\mathrm{eV},1\mathrm{eV}$, for varying values of the frequency (f) when a plane wave orthogonally impinges onto the disk. (

**a**) Normalized ACS; (

**b**) Normalized TSCS.

**Figure 3.**Normalized ACS and TSCS, when a plane wave orthogonally impinges onto the disk, and solutions of Equation (20) of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=0.5\mathrm{ps},1\mathrm{ps},1.5\mathrm{ps}$, ${\mu}_{c}=1\mathrm{eV}$, for varying values of the frequency (f). (

**a**) Normalized ACS; (

**b**) Normalized TSCS.

**Figure 4.**Near E-field behavior in the Cartesian coordinate planes of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=1\mathrm{ps}$, ${\mu}_{c}=1\mathrm{eV}$, at the resonance frequency $f=3.304433\mathrm{THz}$, when a plane wave orthogonally impinges onto the disk with ${\underset{\_}{E}}_{0}={E}_{0}\widehat{y}$. (

**a**) Near E-field in the xz plane; (

**b**) Near E-field in the yz plane; (

**c**) Near E-field in the xy plane.

**Figure 5.**Near E-field behavior in the Cartesian coordinate planes of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=1\mathrm{ps}$, ${\mu}_{c}=1\mathrm{eV}$ at the resonance frequency $f=4.637150\mathrm{THz}$, when a plane wave orthogonally impinges onto the disk with ${\underset{\_}{E}}_{0}={E}_{0}\widehat{y}$. (

**a**) Near E-field in the xz plane; (

**b**) Near E-field in the yz plane; (

**c**) Near E-field in the xy plane.

**Figure 6.**Near E-field behavior in the Cartesian coordinate planes of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=1\mathrm{ps}$, ${\mu}_{c}=1\mathrm{eV}$ at the resonance frequency $f=5.662107\mathrm{THz}$, when a plane wave orthogonally impinges onto the disk with ${\underset{\_}{E}}_{0}={E}_{0}\widehat{y}$. (

**a**) Near E-field in the xz plane; (

**b**) Near E-field in the yz plane; (

**c**) Near E-field in the xy plane.

**Figure 7.**Near E-field behavior in the xy plane of the graphene disk with $a=50\mathsf{\mu}\mathrm{m}$, $T=300\mathrm{K}$, ${t}_{relax}=1\mathrm{ps}$, for different values of the chemical potential at the resonance frequencies corresponding to the standing waves with two oscillations along the radial direction, when a plane wave orthogonally impinges onto the disk with ${\underset{\_}{E}}_{0}={E}_{0}\widehat{y}$. (

**a**) Near E-field for ${\mu}_{c}=0.25\mathrm{eV}$ and $f=2.536462\mathrm{THz}$; (

**b**) Near E-field for ${\mu}_{c}=0.5\mathrm{eV}$ and $f=3.478723\mathrm{THz}$; (

**c**) Near E-field for ${\mu}_{c}=0.75\mathrm{eV}$ and $f=4.135205\mathrm{THz}$; (

**d**) Near E-field for ${\mu}_{c}=1\mathrm{eV}$ and $f=4.637150\mathrm{THz}$.

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**MDPI and ACS Style**

Lucido, M.
Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances. *Mathematics* **2021**, *9*, 1429.
https://doi.org/10.3390/math9121429

**AMA Style**

Lucido M.
Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances. *Mathematics*. 2021; 9(12):1429.
https://doi.org/10.3390/math9121429

**Chicago/Turabian Style**

Lucido, Mario.
2021. "Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances" *Mathematics* 9, no. 12: 1429.
https://doi.org/10.3390/math9121429