Abstract
In this talk a method is described for preparing materials 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(a2−κ3) 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 n2(x) in the wave equation [∇2+κ2n2(x)]u = 0.
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