Mathematical models for dispersive electromagnetic waves: an overview

TL;DR

This paper reviews mathematical models of dispersive electromagnetic wave propagation, focusing on physical-mathematical links, non-dissipativity, and passivity, using energy and spectral analysis.

Contribution

It provides a comprehensive overview of models for dispersive media, emphasizing the connection between physical principles and mathematical properties.

Findings

Analysis of local and passive media models

Energy and spectral methods applied to wave dispersion

Clarification of non-dissipativity and passivity concepts

Abstract

In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notion of non-dissipativity and passivity. We consider successively the case of so-called local media and general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.