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.
Bibliographical noteFunding Information:
We wish to thank Prof. M. I. Weinstein, Prof. A. Alù, and Prof. P. Cazeaux for engaging discussions on homogenization and metamaterials. D.M. also thanks Prof. T. T. Wu for a discussion which motivated part of this work. The authors acknowledge partial support by the ARO MURI Award No. W911NF-14-1-0247. M.M. also acknowledges partial support by the NSF under Grant No. DMS-1912847. M.L. was also supported by the NSF under Grant No. DMS-1906129. The research of D.M. was also partially supported by a Research and Scholarship award by the Graduate School, University of Maryland. Part of this research was carried out when the authors were visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by NSF under Grant No. DMS-1440415.