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Mathematics 2013, 1(3), 89-99; doi:10.3390/math1030089

Scattering of Electromagnetic Waves by Many Nano-Wires

Received: 10 May 2013 / Revised: 11 July 2013 / Accepted: 11 July 2013 / Published: 18 July 2013
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Electromagnetic wave scattering by many parallel to the zaxis, thin, impedance, parallel, infinite cylinders is studied asymptotically as a 0. Let Dm be the cross-section of the mth 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 2πa 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.
Keywords: metamaterials; refraction coefficient; EM wave scattering metamaterials; refraction coefficient; EM wave scattering
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Ramm, A.G. Scattering of Electromagnetic Waves by Many Nano-Wires. Mathematics 2013, 1, 89-99.

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