Electromagnetic wave propagation in media consisting of dispersive metamaterials

TL;DR

This paper analyzes electromagnetic wave propagation in dispersive metamaterials, establishing mathematical properties like well-posedness and finite speed, and provides numerical simulations to illustrate dispersive effects.

Contribution

It proves well-posedness, finite speed propagation, and regularity for Maxwell's equations in dispersive metamaterials, focusing on causality and passivity assumptions.

Findings

Well-posedness of Maxwell's equations in dispersive media

Finite speed of electromagnetic wave propagation

Numerical demonstration of dispersive behavior using Drude's model

Abstract

We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drude's and Lorentz' models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drude's model to illustrate its dispersive behaviour.