Asymptotic regularisation of the solution to the problem of electromagnetic field scattering from a set of small impedance particles

Abstract

Abstract The solution to the problem of electromagnetic (EM) wave scattering from a set of small‐size impedance particles of arbitrary shape is derived by the asymptotic approach. Particles are located in a homogeneous domain with constant ɛ0 and μ0. The solution is derived under the condition b → 0, where b is the characteristic size of the particle; further, the number M(b) of particles tends to infinity at a specific rate. The regularising procedure consists of the derivation of the explicit form of a solution that excludes the necessity to solve the respective integral equation for determination of the fields at the surface of particles and thus avoids integrating the Green function derivatives, which are in the kernel of this boundary integral equation. Practical application of this approach yields an ability to create media with the desired inhomogeneous distribution of effective refractive index n and magnetic permeability μ(x). Explicit analytical formulas are derived for these physical parameters and supported by computations.

Keywords

• boundary integral equations
• electromagnetic fields
• electromagnetic wave scattering
• Green‐s function methods
• integral equations
• magnetic permeability