  We present a rigorous electromagnetic method based on Green's second identity
for studying the plasmonic response of graphene-coated wires of arbitrary
shape. The wire is illuminated perpendicular to its axis by a monochromatic
electromagnetic wave and the wire substrate is homogeneous and isotropic. The
field is expressed everywhere in terms of two unknown source functions
evaluated on the graphene coating which can be obtained from the numerical
solution of a coupled pair of inhomogeneous integral equations. To assess the
validity of the Green formulation, the scattering and absorption efficiencies
obtained numerically in the particular case of circular wires are compared with
those obtained from the multipolar Mie theory. An excellent agreement is
observed in this particular case, both for metallic and dielectric substrates.
To explore the effects that the break of the rotational symmetry of the wire
section introduces in the plasmonic features of the scattering and absorption
response, the Green formulation is applied to the case of graphene-coated wires
of elliptical section. As might be expected from symmetry arguments, we find a
two-dimensional anisotropy in the angular optical response of the wire,
particularly evident in the frequency splitting of multipolar plasmonic
resonances. The comparison between the spectral position of the enhancements in
the scattering and absorption efficiency spectra for low-eccentricity
elliptical and circular wires allows us to guess the multipolar order of each
plasmonic resonance. We present calculations of the near field distribution for
different frequencies which explicitly reveal the multipolar order of the
plasmonic resonances. They also confirm the previous guess and serve as a
further test on the validity of the Green formulation.
