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Scattering of Electromagnetic Waves by Many Nano-Wires

Author(s): Alexander G. Ramm

Journal: Mathematics
ISSN 2227-7390

Volume: 1;
Issue: 3;
Start page: 89;
Date: 2013;
Original page

Keywords: metamaterials | refraction coefficient | EM wave scattering

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

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