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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 σ=σ′+jσ″, a proper transverse-electric surface wave exists if and only if σ″0 (associated with interband conductivity), and a proper transverse-magnetic surface wave exists for σ″0 (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of σ″ can be varied, allowing for some control over surface wave properties.
George W. Hanson (Sat,) studied this question.
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