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 ^xm = (xm1, xm2) be its center, 1 ≤ m ≤ M, M = M(a). It is assumed that the points, ◯m, are distributed, so that N(Δ) = 1/2πa ∫ Δ N(◯)d◯[1 + o(1)], where N(Δ) is the number of points, ◯m, in an arbitrary open subset, Δ, of the plane, xoy. The function, N(◯) ≥ 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.