Electromagnetic wave scattering by many small particles and creating materials with a desired permeability

TL;DR

This paper develops a theoretical framework for manipulating electromagnetic wave scattering by embedding numerous small particles to engineer media with specific, spatially varying permeability properties.

Contribution

It introduces an explicit analytical formula for the effective permeability of a medium created by embedding small particles with prescribed boundary impedances.

Findings

Derived the limiting equation for the effective EM field as particle size approaches zero.

Provided an explicit formula for the inhomogeneous permeability $(x)$ of the engineered medium.

Demonstrated how to control the permeability by adjusting particle distribution and boundary impedances.

Abstract

Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit $a\to 0$, where $a$ is the characteristic size of a particle and the number $M(a)$ of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with an inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability $\mu(x)$ of the limiting medium. While the initial medium has a constant permeability $\mu_0$, the limiting medium, obtained as a result of embedding many small particles with prescribed boundary impedances, has a non-homogeneous permeability which is expressed analytically in terms of the density of the distribution of the small particles and their boundary impedances.