Homogenization of plasmonic crystals: Seeking the epsilon-near-zero effect

TL;DR

This paper develops a homogenized model for plasmonic crystals with 2D conducting sheets, enabling analysis of epsilon-near-zero effects and guiding the design of advanced optical materials.

Contribution

It introduces a homogenization approach for Maxwell's equations in plasmonic structures with 2D materials, incorporating surface conductivity and edge effects.

Findings

Derived a homogenized Maxwell's system for plasmonic crystals.

Highlighted the importance of vector-valued corrector fields in microscopic modes.

Provided a foundation for computational design of optical responses.

Abstract

By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell'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. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.