3 - Wave Scattering and the Effective Medium

Abstract

This chapter provides an overview of wave scattering and the effective medium. In the classical scalar wave case, the single scatterer is taken to be a sphere of radius R with dielectric constant. When there are infinitely many scatterers, the T-matrix and the exact Green's function are impossible to obtain accurately. However, it is determined that in the wave vector representation, the averaged Green's function is given by a particular function. For the three-dimensional (3D) coherent potential approximation (CPA), the evaluation of the Green's function is perhaps the most time-consuming part of the numerical calculation. A useful and efficient approach to the calculation of the 3D Green's function is to compile a numerical table of the density of states for the ordered lattice and store it in computer memory. The diagonal Green's function can then be obtained from an equation, which involves only one integration.