Scattering of Electromagnetic Waves by Many Nano-Wires

Electromagnetic wave scattering by many parallel to the z − axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as a → 0. Let D m 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 2 π a ∫ 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.