High-frequency homogenization for periodic dispersive media

TL;DR

This paper develops a high-frequency homogenization method to analyze dispersive periodic media, deriving effective properties near specific dispersion points and validating results with finite element simulations in 1D and 2D.

Contribution

It introduces a novel high-frequency homogenization approach for dispersive media with periodic inclusions, providing accurate asymptotic dispersion diagrams and wavefield approximations.

Findings

Effective properties are accurately derived near dispersion diagram points.

Asymptotic approximations match finite element simulations.

Method applies to media with Lorentz or Drude models with damping.

Abstract

High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective properties are obtained near a given point of the dispersion diagram in frequency-wavenumber space. The asymptotic approximations of the dispersion diagrams, and the wavefields, so obtained are then cross-validated via detailed comparison with finite element method simulations in both one and two dimensions.