Can a single PDE govern well the propagation of the electric wave field in a heterogeneous medium in 3D?

TL;DR

This paper shows that under certain conditions, the complex 3D electric wave propagation in heterogeneous media can be effectively modeled by a single PDE derived from Maxwell's equations, simplifying analysis and applications.

Contribution

It demonstrates that a single PDE can accurately govern 3D electric wave propagation in heterogeneous media, simplifying the modeling process from Maxwell's system.

Findings

A single PDE can approximate electric wave propagation in 3D heterogeneous media.

The dominant electric field component justifies simplified modeling.

Results support previous numerical studies on electromagnetic inverse problems.

Abstract

It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single PDE, which is derived from the Maxwell's equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single PDE rather than with the complete Maxwell's system, then the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.