  Periodic metallic structures are known to support resonant extraordinary
transmission (EOT). When covered with graphene, these structures can be
employed to effectively manipulate the light. In this work, we propose an
analytical circuit model for graphene-covered one-dimensional metallic
gratings. By using the circuit theory, we demonstrate that one-dimensional
periodic array of cut-through slits which are covered by a continuous graphene
sheet exhibit tunable EOT resonance whose amplitude, unlike its spectral
position, can be dynamically tuned by varying the Fermi level of graphene. In
this fashion, it is shown that placing a perfect reflector at the bottom of the
graphene-covered metallic grating results in the realization of a
graphene-based absorber. By utilizing the circuit theory, it is illustrated
that perfect absorption in the structure is not exclusive to the TM
polarization, but also the TE polarized plane waves can be completely absorbed
by duly adjusting the Fermi level of graphene. Criteria for the enhanced
absorption are accordingly presented. Results of this work may provide a useful
tool for designing novel devices based on the graphene-covered metallic
gratings such as filters, modulators and efficient absorbers.
