ELECTROMAGNETIC WAVE SCATTERING BY MANY SMALL PARTICLES AND CREATING MATERIALS WITH A DESIRED PERMEABILITY

Scattering of electromagnetic (EM) waves by many small particles (bodies)embedded in a homogeneous medium is studied. Physical properties of theparticles are described by their boundary impedances. The limiting equation isobtained for the effective EM field in the limiting medium, in the limit $a\to0$, where $a$ is the characteristic size of a particle and the number $M(a)$ ofthe particles tends to infinity at a suitable rate. The proposed theory allowsone to create a medium with an inhomogeneous permeability. The main newphysical result is the explicit analytical formula for the permeability$\mu(x)$ of the limiting medium. While the initial medium has a constantpermeability $\mu_0$, the limiting medium, obtained as a result of embeddingmany small particles with prescribed boundary impedances, has a non-homogeneouspermeability which is expressed analytically in terms of the density of thedistribution of the small particles and their boundary impedances.