%0 Journal Article
%J Proceedings of the Royal Society A
%D 2019
%T Homogenization of plasmonic crystals: Seeking the epsilon-near-zero behavior.
%A M. Maier
%A M.Mattheakis
%A E. Kaxiras
%A M. Luskin
%A D. Margetis
%X By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell{\textquoteright}s equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host.\ This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. By using a Drude model for the surface conductivity of the sheet, we construct a Lorentzian function that describes the effective dielectric permittivity tensor of the plasmonic crystal as a function of frequency.
%B Proceedings of the Royal Society A
%V 475
%G eng
%U https://royalsocietypublishing.org/doi/10.1098/rspa.2019.0220
%N 2230