A method for 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 balls with calculated densities and refraction coefficients into a domain, enabling precise control over the material's optical characteristics.

Contribution

It introduces a novel approach to design materials with targeted refraction coefficients through the strategic embedding of small, specially characterized balls.

Findings

Calculated density distribution for embedding small balls.

Determined constant refraction coefficients for the balls.

Method enables creation of materials with desired refraction properties.

Abstract

It is proposed to create materials with a desired refraction coefficient in a bounded domain $D\subset \R^3$ by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit volume around every point $x\in D$, i.e., their density distribution, is calculated, as well as the constant refraction coefficients in these balls. Embedding into $D$ small balls with these refraction coefficients according to the calculated density distribution creates in $D$ a material with a desired refraction coefficient.