Scattering of Electromagnetic Waves by Many Nano-Wires

• Main Author: Alexander G. Ramm
• Format: Article
• Language: English
• Published: MDPI AG 2013-07-01
• Series: Mathematics
• Subjects: metamaterials; refraction coefficient; EM wave scattering
• Online Access: http://www.mdpi.com/2227-7390/1/3/89

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.