Mathematical analysis of transmission properties of electromagnetic meta-materials

TL;DR

This paper analyzes how electromagnetic waves transmit through meta-materials with different geometries and contrasts, using mathematical models and numerical simulations to understand their behavior.

Contribution

It provides a mathematical framework for transmission in high-contrast and perfect conductor meta-materials, including effective equations and numerical validation.

Findings

Transmission depends on geometry and material contrast.

Numerical simulations confirm theoretical predictions.

Multiscale method effectively models heterogeneous media.

Abstract

We study time-harmonic Maxwell's equations in meta-materials that use either perfect conductors or high-contrast materials. Based on known effective equations for perfectly conducting inclusions, we calculate the transmission and reflection coefficients for four different geometries. For high-contrast materials and essentially two-dimensional geometries, we analyze parallel electric and parallel magnetic fields and discuss their potential to exhibit transmission through a sample of meta-material. For a numerical study, one often needs a method that is adapted to heterogeneous media; we consider here a Heterogeneous Multiscale Method for high contrast materials. The qualitative transmission properties, as predicted by the analysis, are confirmed with numerical experiments. The numerical results also underline the applicability of the multiscale method.