Wave scattering by many small particles and creating materials with desired refraction coefficients

Many-body wave scattering problems are solved asymptotically, as the size \(a\) of the particles tends to zero and the number of the particles tends to infinity.

Acoustic, quantum-mechanical, and electromagnetic wave scattering by many small particles is studied. This theory allows one to give a recipe for creating materials with a desired refraction coefficient.

One can create material with negative refraction, that is, the group velocity in this material is directed opposite to the phase velocity. One can create material with some desired wave-focusing properties. For example, one can create a new material which scatters plane wave mostly in a fixed given solid angle.