# Green formulation for studying electromagnetic scattering from graphene-coated wires of arbitrary section

## TL;DR

This paper introduces a Green's function-based electromagnetic method to analyze plasmonic responses of graphene-coated wires of arbitrary shapes, validated against Mie theory and extended to elliptical geometries revealing anisotropic plasmonic features.

## Contribution

The paper develops a rigorous Green's function approach for arbitrary-shaped graphene-coated wires, including elliptical geometries, and demonstrates its accuracy and ability to reveal anisotropic plasmonic effects.

## Key findings

- Excellent agreement with Mie theory for circular wires.
- Identification of anisotropic plasmonic resonances in elliptical wires.
- Near-field distributions confirm multipolar resonance orders.

## Abstract

We present a rigorous electromagnetic method based on Green's second identity for studying the plasmonic response of graphene-coated wires of arbitrary shape. The wire is illuminated perpendicular to its axis by a monochromatic electromagnetic wave and the wire substrate is homogeneous and isotropic. The field is expressed everywhere in terms of two unknown source functions evaluated on the graphene coating which can be obtained from the numerical solution of a coupled pair of inhomogeneous integral equations. To assess the validity of the Green formulation, the scattering and absorption efficiencies obtained numerically in the particular case of circular wires are compared with those obtained from the multipolar Mie theory. An excellent agreement is observed in this particular case, both for metallic and dielectric substrates. To explore the effects that the break of the rotational symmetry of the wire section introduces in the plasmonic features of the scattering and absorption response, the Green formulation is applied to the case of graphene-coated wires of elliptical section. As might be expected from symmetry arguments, we find a two-dimensional anisotropy in the angular optical response of the wire, particularly evident in the frequency splitting of multipolar plasmonic resonances. The comparison between the spectral position of the enhancements in the scattering and absorption efficiency spectra for low-eccentricity elliptical and circular wires allows us to guess the multipolar order of each plasmonic resonance. We present calculations of the near field distribution for different frequencies which explicitly reveal the multipolar order of the plasmonic resonances. They also confirm the previous guess and serve as a further test on the validity of the Green formulation.