Dyadic Green's Functions and Guided Surface Waves for a Surface Conductivity Model of Graphene

TL;DR

This paper derives exact electromagnetic Green's functions for graphene with surface conductivity, analyzing surface wave propagation and showing how tuning chemical potential controls wave characteristics.

Contribution

It provides an exact Green's function solution for graphene's electromagnetic response and characterizes surface wave conditions based on conductivity.

Findings

TE surface wave exists if imaginary conductivity part is positive

TM surface wave exists if imaginary conductivity part is negative

Chemical potential tuning allows control over surface wave properties

Abstract

An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper transverse-electric (TE) surface wave exists if and only if the imaginary part of conductivity is positive (associated with interband conductivity), and a proper transverse-magnetic (TM) surface wave exists when the imaginary part of conductivity is negative (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of the imaginary part of conductivity can be varied, allowing for some control over surface wave properties.