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

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a→0a→0, where a   is the radius of the cylinders. It is assumed that the centers of the cylinders x^m are distributed so that N(Δ)=ln(1/a)∫ΔN(x)dx[1+o(1)], where N(Δ)N(Δ) is the number of points x^m=(xm1,xm2) in an arbitrary open subset of the plane xOy, the axes of cylinders are parallel to z  -axis. The function N(x)≥0N(x)≥0 is a given continuous function. An equation for the self-consistent (limiting) field is derived as a→0a→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.