Scattering of graphene plasmons at abrupt interfaces: an analytic and numeric study

TL;DR

This paper provides an analytical and numerical study of how graphene surface plasmons scatter at interfaces with different doping levels or substrates, including radiation effects, with implications for plasmonic device design.

Contribution

It introduces approximate analytic formulas for scattering coefficients and recasts the problem as a Fredholm equation, advancing understanding of graphene plasmon behavior at interfaces.

Findings

Minimal free radiation emission during scattering

Back-scattered SPPs carry little energy under typical conditions

Analytic solutions closely match numerical results

Abstract

We discuss the scattering of graphene surface plasmon-polaritons (SPPs) at an interface between two semi-infinite graphene sheets with different doping levels and/or different underlying dielectric substrates. We take into account retardation effects and the emission of free radiation in the scattering process. We derive approximate analytic expressions for the reflection and the transmission coefficients of the SPPs as well as the same quantities for the emitted free radiation. We show that the scattering problem can be recast as a Fredholm equation of the second kind. Such equation can then be solved by a series expansion, with the first term of the series correspond to our approximated analytical solution for the reflection and transmission amplitudes. We have found that almost no free radiation is emitted in the scattering process and that under typical experimental conditions the back-scattered SPP transports very little energy. This work provides a theoretical description of graphene plasmon scattering at an interface between distinct Fermi levels which could be relevant for the realization of plasmonic circuitry elements such as plasmonic lenses or reflectors, and for controlling plasmon propagation by modulating the potential landscape of graphene.