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Mathematics 2013, 1(3), 8999; doi:10.3390/math1030089
Article
Scattering of Electromagnetic Waves by Many NanoWires
Department of Mathematics, Kansas State University, Manhattan, KS 665062602, USA
Received: 10 May 2013 / Revised: 11 July 2013 / Accepted: 11 July 2013 / Published: 18 July 2013
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Abstract
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 crosssection of the m−th 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, ${\hat{x}}_{m}$ , are distributed, so that $N\left(\Delta \right)=\frac{1}{2\pi a}\underset{\Delta}{\int}N\left(\hat{x}\right)d\hat{x}[1+o(1\left)\right]$ where N (∆) is the number of points, ${\hat{x}}_{m}$ , in an arbitrary open subset, ∆, of the plane, xoy. The function, $N\left(\hat{x}\right)\text{}\ge 0$, is a continuous function, which an experimentalist can choose. An equation for the selfconsistent (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 nanowires 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
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