Selection of Material Parameters in a Chaotic Small Particle Embedded Medium for Wave Scattering Design

Abstract

Solution to the problem of electromagnetic (EM) wave scattering on a set of small size impedance particles of arbitrary shape with the chaotic rule of their distribution is sought for by the asymptotic approach. The particles are distributed in a homogeneous volume with the constant material parameters. Solution to the problem is derived under the condition that the characteristic size of particles tends to zero; besides, the quantity of particles approaches to infinity at a specific principle. The solving procedure is reduced to derivation of an explicit form of solution that avoids the need to solve the governing integral equation, which is used to determine the fields in the particle’s surfaces. This allows to keep out of integration of the derivatives of Green function, which are presented in a kernel of the derived integral equation. The practical importance of approach consists of creating the media or materials with the close to desired inhomogeneous value of the effective refractive index or magnetic permeability. The explicit analytical relations are reduced for the above physical parameters, and they are verified by computations. It is substantiated that the chaotic distribution of particles in the initial medium makes possible to obtain more contrast material parameters comparing with the regular distribution of particles.