Alexander Ramm
Kansas State University, USA
Title: Creating materials with a desired refraction coecient
Biography
Biography: Alexander Ramm
Abstract
The theory of electromagnetic (EM) wave scattering by one and many small impedance particles of arbitrary shapes is developed. The basic assumptions are: a d , where a is the characteristic size of particles, d is the smallest distance between the neighboring particles, is the wavelength. The impedance boundary condition is: [N; [E;N]]jSm = m[N;H]jSm, where m, Rem 0, is the boundary impedance of the mô€€€th particle Dm, Sm is the smooth surface of Dm, N is the outer unit normal to Sm, [A;B] is the cross product of two vectors, E and H are electric and magnetic elds satisfying the Maxwell's equations, the impedance boundary conditions on Sm, 1 m N; and the radiation condition at in nity. Here N is the total number of particles. An ecient computational method is given for solving the wave scattering problem by one and many, 1 m N, particles under the assumptions a d . The particles are distributed in an arbitrary nite domain in R3. If N is very large and a is very small, then the e ective eld in the medium, where the small particles are distributed, is proved to be a solution of a linear integral equation. This theory allows one to give a recipe for creating materials with a desired refraction coecient. One can create material with negative refraction: the group velocity in this material is directed opposite to the phase velocity. One can create a material with a desired permeability. The theory presented in this talk is developed in monograph and in papers cited.