Electromagnetic wave scattering by a thin layer in which many small particles are embedded

TL;DR

This paper investigates how electromagnetic waves scatter when they encounter a thin layer embedded with many small particles, deriving effective boundary conditions as particle size approaches zero.

Contribution

It introduces a new method to derive limiting interface boundary conditions for EM fields in media with densely embedded small particles.

Findings

Derived effective boundary conditions for EM fields in the limit of small particle size.

Showed how the number of particles affects the limiting behavior.

Provided a mathematical framework for modeling wave scattering in complex layered media.

Abstract

Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a thin layer, is studied. Physical properties of the particles are described by their boundary impedances. The thin layer of depth of the order $O(a)$ with many embedded in it small particles of characteristic size $a$, is described by a boundary condition on the surface of the layer. The limiting interface boundary condition is obtained for the effective EM field in the limiting medium, in the limit $a\to 0$, where the number $M(a)$ of the particles tends to infinity at a suitable rate.