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

# Scattering of Electromagnetic Waves by Many Nano-Wires

Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA
Received: 10 May 2013 / Revised: 11 July 2013 / Accepted: 11 July 2013 / Published: 18 July 2013

# Abstract

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 ${\text{x ^}}_{\text{m}}{\text{= (x}}_{\text{m1}}{\text{, x}}_{\text{m2}}\text{)}$ be its center, 1 m M , M = M (a). It is assumed that the points, ${\stackrel{^}{x}}_{m}$ , are distributed, so that $N\left(\Delta \right)=\frac{1}{2\pi a}\underset{\Delta }{\int }N\left(\stackrel{^}{x}\right)d\stackrel{^}{x}\left[1+o\left(1\right)\right]$ where N (∆) is the number of points, ${\stackrel{^}{x}}_{m}$ , in an arbitrary open subset, ∆, of the plane, xoy. The function, $N\left(\stackrel{^}{x}\right)\text{}\ge 0$, 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. View Full-Text
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MDPI and ACS Style

Ramm, A.G. Scattering of Electromagnetic Waves by Many Nano-Wires. Mathematics 2013, 1, 89-99.

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