Electromagnetic wave scattering by many small particles

TL;DR

This paper presents a rigorous reduction of electromagnetic wave scattering by numerous small particles to a linear algebraic system, with explicit formulas for polarizability tensors, enabling the design of advanced 'smart' materials.

Contribution

It introduces a novel approach to model wave scattering using linear algebraic systems and provides analytical formulas for polarizability tensors of arbitrary shapes.

Findings

Linear algebraic system effectively models scattering by many particles.

Explicit formulas for polarizability tensors of arbitrary shapes.

Framework for designing 'smart' materials with embedded particles.

Abstract

Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a "smart" material by embedding many small particles in a given region is formulated.