Quantitative estimates for enhancement of the field excited by an emitter due to presence of two closely located spherical inclusions

TL;DR

This paper provides precise quantitative estimates for the amplification of a dipole-excited field caused by two closely spaced spherical inclusions, highlighting differences from background field enhancement.

Contribution

It derives new estimates for field enhancement due to spherical inclusions near an emitter, revealing differences from background field behavior.

Findings

Enhancement factor is approximately $(rac{1}{\sqrt{ ext{epsilon}} ext{| extlog} ext{epsilon}|})$ when enhancement occurs.

The enhancement behavior differs from that of the smooth background field, which is $( ext{epsilon}| extlog} ext{epsilon}|)^{-1}$.

The estimates clarify the impact of inclusion proximity on field amplification.

Abstract

A field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium. In this paper precise quantitative estimates for such enhancement are derived when the given field is the one excited by an emitter of a dipole type and inclusions are spheres of the same radii in three dimensions. Derived estimates reveal the difference, as well as the similarity, between enhancement of the field excited by the emitter and that of the smooth back-ground field. In particular, an estimate shows that when the enhancement occurs, the factor of enhancement is $(\sqrt{\epsilon}|\log \epsilon|)^{-1}$, which is different from that for the smooth background field, which is known to be $(\epsilon|\log \epsilon|)^{-1}$ ($\epsilon$ is the distance between two inclusions).