Creation of media with prescribed permeability using the asymptotic solution of EM field scattering problem

Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedance. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium.