Creating materials with a desired refraction coefficient

TL;DR

This paper presents a method to engineer materials with specific refraction properties by embedding numerous small particles with controlled boundary impedances into a known medium, enabling precise manipulation of wave propagation.

Contribution

It introduces a novel approach for creating materials with desired refraction coefficients through the strategic embedding of small particles with prescribed properties.

Findings

The method allows for the design of materials with tailored refraction coefficients.

The distribution and impedance of particles determine the resulting refraction properties.

The approach provides a systematic way to modify wave behavior in engineered materials.

Abstract

A method is given for creating material with a desired refraction coefficient. The method consists of embedding into a material with known refraction coefficient many small particles of size $a$. The number of particles per unit volume around any point is prescribed, the distance between neighboring particles is $O(a^{\frac{2-\kappa}{3}})$ as $a\to 0$, $0<\kappa<1$ is a fixed parameter. The total number of the embedded particle is $O(a^{\kappa-2})$. The physical properties of the particles are described by the boundary impedance $\zeta_m$ of the $m-th$ particle, $\zeta_m=O(a^{-\kappa})$ as $a\to 0$. The refraction coefficient is the coefficient $n^2(x)$ in the wave equation $[\nabla^2+k^2n^2(x)]u=0$.