Scattering of electromagnetic waves by many nanowires

TL;DR

This paper derives an asymptotic equation for electromagnetic wave scattering by many thin impedance cylinders and provides a formula for the effective refraction coefficient, modeling nanowires embedded in a medium.

Contribution

It introduces a new asymptotic approach to analyze wave scattering by numerous nanowires and derives an explicit formula for the medium's effective refraction coefficient.

Findings

Derived an equation for the self-consistent field as cylinder radius tends to zero.

Established a formula for the effective refraction coefficient influenced by nanowires.

Showed how nanowires modify the electromagnetic properties of the medium.

Abstract

Electromagnetic wave scattering by many parallel to $z-$axis, thin, impedance, circular infinite cylinders is studied asymptotically as $a\to 0$. Let $D_m$ be the crossection of the $m-$th cylinder, $a$ be its radius, and $\hat{x}_m=(x_{m1},x_{m2})$ be its center, $1\le m \le M$, $M=M(a)$. It is assumed that the points $\hat{x}_m$ are distributed so that $$\mathcal{N}(\Delta)=\frac 1{2\pi a}\int_{\Delta}N(\hat{x})d\hat{x}[1+o(1)], $$ where $\mathcal{N}(\Delta)$ is the number of points $\hat{x}_m$ in an arbitrary open subset $\Delta$ of the plane $xoy$. The function $N(\hat{x})\geq 0$ is a given continuous function. An equation for the self-consistent (efficient) field is derived as $a\to 0$. A formula is derived for the effective refraction coefficient in the medium in which many thin impedance cylinders are distributed. These cylinders may model nanowires embedded in the medium. Our result shows how these cylinders influence the refraction coefficient of the medium.