  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 $O(a^{\frac{2-\kappa}{3}})$ as $a\to 0$, $0<\kappa<1$
is a fixed parameter. The total number of the embedded particle is
$O(a^{\kappa-2})$. The physical properties of the particles are described by
the boundary impedance $\zeta_m$ of the $m-th$ particle,
$\zeta_m=O(a^{-\kappa})$ as $a\to 0$. The refraction coefficient is the
coefficient $n^2(x)$ in the wave equation $[\nabla^2+k^2n^2(x)]u=0$.
