Scattering of Electromagnetic Waves by Many Nano-Wires

Abstract

Electromagnetic wave scattering by many parallel to the z−axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as a → 0. Let Dm be the cross-section of the m−th cylinder, a be its radius and x ^ m = (x m1 , x m2 ) be its center, 1 ≤ m ≤ M , M = M (a). It is assumed that the points, x ^ m , are distributed, so that N(Δ)= 1 2πa ∫ Δ N ( x ^ )d x ^ [1+o(1)] where N (∆) is the number of points, x ^ m , in an arbitrary open subset, ∆, of the plane, xoy. The function, N( x ^ ) ≥0 , is a continuous function, which an experimentalist can choose. An equation for the self-consistent (effective) field is derived as a → 0. A formula is derived for the refraction coefficient in the medium in which many thin impedance cylinders are distributed. These cylinders may model nano-wires embedded in the medium. One can produce a desired refraction coefficient of the new medium by choosing a suitable boundary impedance of the thin cylinders and their distribution law.