A method for creating materials with a desired refraction coefficient

Abstract

It is proposed to create materials with a desired refraction coefficient in a bounded domain $D\subset {\mathbb{R}}^3$ 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.