Creating materials with a desired refraction coefficient

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 2−κ 3 ) as a → 0, 0 < κ < 1 is a fixed parameter. The total number of the embedded particle is O(aκ−2). The physical properties of the particles are described by the boundary impedance ζm of the m− th particle, ζm = O(a−κ) as a→ 0. The refraction coefficient is the coefficient n(x) in the wave equation [∇ + kn(x)]u = 0. PACS: 03.40.Kf, 03.50 De, 41.20.Jb, 71.36.+c