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 (？) ？= (1 / 2 π a) * ∫？ N ( x？) dx？[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.