An Integrodifferential Equation for Electromagnetic Fields in Linear Dispersive Media

TL;DR

This paper derives a novel integrodifferential wave equation for electromagnetic fields in dispersive media, emphasizing a time-domain causal approach, which offers new insights beyond traditional Fourier-based methods.

Contribution

The paper introduces a new integrodifferential wave equation for electromagnetic fields in dispersive media, not previously documented in literature, highlighting its potential usefulness.

Findings

Derivation of a new integrodifferential wave equation

Emphasis on time-domain causal functions

Potential applications in analyzing dispersive media

Abstract

We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in Fourier space. However, it can be rewarding to consider these properties as causal functions of time. Due to temporal non locality, this procedure gives rise to an integrodifferential equation for the electromagnetic fields, which we also call a wave equation. We have not found this equation in the literature and we show in this paper why it can be useful.