Scattering of electromagnetic waves by many thin cylinders: theory and computational modeling

TL;DR

This paper develops a theoretical and computational framework for analyzing electromagnetic wave scattering by numerous thin, perfectly conducting cylinders, deriving effective medium properties and demonstrating potential for creating materials with negative refraction.

Contribution

It introduces an asymptotic method for modeling EM scattering by many cylinders and derives formulas for the effective refraction coefficient of the resulting medium.

Findings

Derived an equation for the self-consistent scattering field.

Provided formulas for the effective refraction coefficient.

Numerical results confirm the approach's validity and efficiency.

Abstract

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a tends to 0, where a is the radius of the cylinders. It is assumed that the centres of the cylinders are distributed so that their numbers is determined by some positive function N(x). The function N(x) >= 0 is a given continuous function. An equation for the self-consistent (limiting) field is derived as a tends to 0. The cylinders are assumed perfectly conducting. Formula for the effective refraction coefficient of the new medium, obtained by embedding many thin cylinders into a given region, is derived. The numerical results presented demonstrate the validity of the proposed approach and its efficiency for solving the many-body scattering problems, as well as the possibility to create media with negative refraction coefficients.