Electromagnetic wave scattering by many small particles is studied. An integral equation is derived for the self-consistent field E in a medium, obtained by embedding many small particles into a given region D.
The derivation of this integral equation uses a lemma about convergence of certain sums. These sums are similar to Riemannian sums for the integral equation for E.
Convergence of these sums is essentially equivalent to convergence of a collocation method for solving this integral equation.
By choosing the distribution law for embedding the small particles and their physical properties one can create a medium with a desired refraction coefficient. This coefficient can be a tensor. It may have desired absorption properties.
