  We carry out the homogenization of time-harmonic Maxwell's equations in a
periodic, layered structure made of two-dimensional (2D) metallic sheets
immersed in a heterogeneous and in principle anisotropic dielectric medium. In
this setting, the tangential magnetic field exhibits a jump across each sheet.
Our goal is the rigorous derivation of the effective dielectric permittivity of
the system from the solution of a local cell problem via suitable averages.
Each sheet has a fine-scale, inhomogeneous and possibly anisotropic surface
conductivity that scales linearly with the microstructure scale, $d$. Starting
with the weak formulation of the requisite boundary value problem, we prove the
convergence of its solution to a homogenization limit as $d$ approaches zero.
The effective permittivity and cell problem express a bulk average from the
host dielectric and a surface average germane to the 2D material (metallic
layer). We discuss implications of this analysis in the modeling of plasmonic
crystals.
