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


  • A G Ramm Department of Mathematics, Kansas State University


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(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+k2n2(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.