  We derive and interpret solutions of time-harmonic Maxwell's equations with a
vertical and a horizontal electric dipole near a planar, thin conducting film,
e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic
media. Exact expressions for all field components are extracted in terms of
rapidly convergent series of known transcendental functions when the ambient
media have equal permittivities and both the dipole and observation point lie
on the plane of the film. These solutions are simplified for all distances from
the source when the film surface resistivity is large in magnitude compared to
the intrinsic impedance of the ambient space. The formulas reveal the
analytical structure of two types of waves that can possibly be excited by the
dipoles and propagate on the film. One of these waves is intimately related to
the surface plasmon-polariton of transverse-magnetic (TM) polarization of plane
waves.
