Dyadic Green’s Functions and Guided Surface Waves on Graphene

An exact solution is obtained for the electromagnetic field due to an electric current source near graphene located at the interface between two dielectrics. The field is obtained in terms of dyadic Green’s functions represented as Sommerfeld integrals. The graphene is modeled as an infinitely-thin surface characterized by a surface conductance σ, which could be obtained via microscopic theory or measurement. The solution of plane-wave reflection and transmission is also presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductance σ = σr + jσi, a proper TE surface wave exists if and only if σi > 0, and a proper TM surface wave exists for σi < 0. PACS number(s): 41.20.Jb, 42.82.Et, 73.25.+i, 81.05.Zx, 84.40.-x