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 → 0, where a is the radius of the cylinders. It is assumed that the centers of the cylinders x̂m are distributed so that N (∆) = ln( 1 a ) ∫ ∆ N(x)dx[1 + o(1)], where N (∆) is the number of points x̂m = (xm1, xm2) in an arbitrary open subset of the plane xOy, the axes of cylinders are parallel to z-axis. The function N(x) ≥ 0 is a given continuous function. An equation for the self-consistent (limiting) field is derived as a → 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.