  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.
