%0 Journal Article
%T Scattering of Electromagnetic Waves by Many Nano-Wires
%A Alexander G. Ramm
%J Mathematics
%D 2013
%I MDPI AG
%R 10.3390/math1030089
%X Electromagnetic wave scattering by many parallel to the z £¿axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as a ¡ú 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 ¡Ü m ¡Ü M , M =£¿ £¿ M ( a). It is assumed that the points, x£¿ m, are distributed, so that N (£¿) £¿= (1 / 2 ¦Ð a) * ¡Ò£¿ 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£¿) ¡Ý 0, is a continuous function, which an experimentalist can choose. An equation for the self-consistent (effective) field is derived as a ¡ú 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.
%K metamaterials
%K refraction coefficient
%K EM wave scattering
%U http://www.mdpi.com/2227-7390/1/3/89