Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene

TLDR

Graphene is modeled as an infinitesimally thin, local, isotropic two‑sided conductivity surface. The study presents plane‑wave reflection and transmission solutions and investigates surface‑wave propagation along graphene via poles of the Sommerfeld integrals. An exact dyadic Green’s‑function solution for the field of a current above graphene is derived, showing that TE surface waves exist only when the conductivity’s imaginary part is positive and TM waves only when it is negative, and that tuning the chemical potential at infrared frequencies can switch the sign of the imaginary part and thus control surface‑wave behavior.

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.