### Materials with a desired refraction coefficient can be created by embedding small particles into a given material

#### 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*, *ka *1, where *k > *0 is the wave number. 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*2(*x*) in the wave equation [*∇*2+*k*2*n*2(*x*)]*u *= 0. Technological problems, which should be dealt with before the method can be implemented practically, are formulated and discussed. The desired refraction coefficient can be complex-valued. This means that the enrgy absorption in the new material can also be designed as one wishes.