Open AccessThis article is
- freely available
Scattering of Electromagnetic Waves by Many Nano-Wires
Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA
Received: 10 May 2013; in revised form: 11 July 2013 / Accepted: 11 July 2013 / Published: 18 July 2013
Abstract: 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.
Keywords: metamaterials; refraction coefficient; EM wave scattering
Article StatisticsClick here to load and display the download statistics.
Notes: Multiple requests from the same IP address are counted as one view.
Cite This Article
MDPI and ACS Style
Ramm, A.G. Scattering of Electromagnetic Waves by Many Nano-Wires. Mathematics 2013, 1, 89-99.
Ramm AG. Scattering of Electromagnetic Waves by Many Nano-Wires. Mathematics. 2013; 1(3):89-99.
Ramm, Alexander G. 2013. "Scattering of Electromagnetic Waves by Many Nano-Wires." Mathematics 1, no. 3: 89-99.