On the perturbation of the electromagnetic energy due to the presence of inhomogeneities with small diameters

TL;DR

This paper derives asymptotic expansions for electromagnetic solutions in the presence of small inhomogeneities and analyzes how these inhomogeneities affect the electromagnetic energy in three-dimensional space.

Contribution

It provides a rigorous derivation of asymptotic expansions for Maxwell solutions with small inhomogeneities and describes their impact on electromagnetic energy.

Findings

Asymptotic expansions for Maxwell solutions with small inhomogeneities

Quantitative description of energy perturbations due to inhomogeneities

Theoretical framework applicable to multiple small inclusions

Abstract

We consider solutions to the time-harmonic Maxwell problem in $\R^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of small diameter are imbedded in the entire space. Then, we describe the behavior of the electromagnetic energy caused by the presence of these inhomogeneities.