Lorentz Resonance in the Homogenization of Plasmonic Crystals

TL;DR

This paper provides an explicit, rigorous formula describing Lorentz resonances in plasmonic crystals, linking material properties and geometric resonances, with applications to designing periodic optical devices.

Contribution

It introduces a decoupled, explicit formula for Lorentz resonances in plasmonic crystals derived from electrostatic corrector fields, advancing analytical understanding.

Findings

Derived a rigorous formula for Lorentz resonances in plasmonic crystals.

Validated the formula with examples of nanotubes and nanoribbons.

Provided a computational tool for frequency response analysis of optical devices.

Abstract

We explain the Lorentz resonances in plasmonic crystals that consist of 2D nano dielectric inclusions as the interaction between resonant material properties and geometric resonances of electrostatic nature. One example of such plasmonic crystals are graphene nanosheets that are periodically arranged within a non-magnetic bulk dielectric. We identify local geometric resonances on the length scale of the small scale period. From a materials perspective, the graphene surface exhibits a dispersive surface conductance captured by the Drude model. Together these phenomena conspire to generate Lorentz resonances at frequencies controlled by the surface geometry and the surface conductance. The Lorentz resonances found in the frequency response of the effective dielectric tensor of the bulk metamaterial is shown to be given by an explicit formula, in which material properties and geometric resonances are decoupled. This formula is rigorous and obtained directly from corrector fields describing local electrostatic fields inside the heterogeneous structure. Our analytical findings can serve as an efficient computational tool to describe the general frequency dependence of periodic optical devices. As a concrete example, we investigate two prototypical geometries composed of nanotubes and nanoribbons.