  A self-consistent theory involving Maxwell equations and a density-matrix
linear-response theory is solved for an electromagnetically-coupled doped
graphene micro-ribbon array and a quantum-well electron gas sitting at an
interface between a half-space of air and another half-space of a doped
semiconductor substrate which supports a surface-plasmon mode in our system.
The coupling between a spatially-modulated total electromagnetic field and the
electron dynamics in a Dirac-cone of a graphene ribbon, as well as the coupling
of the far-field specular and near-field higher-order diffraction modes, are
included in the derived electron optical-response function. Full analytical
expressions are obtained with non-locality for the optical-response functions
of a two-dimensional electron gas and a graphene layer with an induced bandgap,
and are employed in our numerical calculations beyond the long-wavelength limit
(Drude model). Both the near-field transmissivity and reflectivity spectra, as
well as their dependence on different configurations of our system and on the
array period, ribbon width, graphene chemical potential of quantum-well
electron gas and bandgap in graphene, are studied. Moreover, the transmitted
E-field intensity distribution is calculated to demonstrate its connection to
the mixing of specular and diffraction modes of the total electromagnetic
field. An externally-tunable electromagnetic coupling among the surface,
conventional electron-gas and massless graphene intraband plasmon excitations
is discovered and explained. Furthermore, a comparison is made between the
dependence of the graphene-plasmon energy on the ribbon width and chemical
potential in this paper and the recent experimental observation given by Ju, et
al., [Nature Nanotechnology, 6, 630 (2011)] for a graphene micro-ribbon array
in the terahertz-frequency range.
