  We study optical coefficients that characterize wave propagation through
layered structures called plasmonic crystals. These consist of a finite number
of stacked metallic sheets embedded in dielectric hosts with a subwavelength
spacing. By adjustment of the frequency, spacing, number as well as geometry of
the layers, these structures may exhibit appealing transmission properties in a
range of frequencies from the terahertz to the mid-infrared regime. Our
approach uses a blend of analytical and numerical methods for the distinct
geometries with infinite, translation invariant, flat sheets and nanoribbons.
We describe the transmission of plane waves through a plasmonic crystal in
comparison to an effective dielectric slab of equal total thickness that
emerges from homogenization, in the limit of zero interlayer spacing. We
demonstrate numerically that the replacement of the discrete plasmonic crystal
by its homogenized counterpart can accurately capture a transmission
coefficient akin to the extinction spectrum, even for a relatively small number
of layers. We point out the role of a geometry-dependent corrector field, which
expresses the effect of subwavelength surface plasmons. In particular, by use
of the corrector we describe lateral resonances inherent to the nanoribbon
geometry.
