Scattering of Electromagnetic Waves by Many Nano-Wires
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 poin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-07-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/1/3/89 |
| _version_ | 1818331076188176384 |
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| author | Alexander G. Ramm |
| author_facet | Alexander G. Ramm |
| author_sort | Alexander G. Ramm |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T13:14:06Z |
| format | Article |
| id | doaj.art-3396a11a2b0f4194999850fe6dc27271 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T13:14:06Z |
| publishDate | 2013-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3396a11a2b0f4194999850fe6dc272712022-12-21T23:44:35ZengMDPI AGMathematics2227-73902013-07-0113899910.3390/math1030089Scattering of Electromagnetic Waves by Many Nano-WiresAlexander G. RammElectromagnetic 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.http://www.mdpi.com/2227-7390/1/3/89metamaterialsrefraction coefficientEM wave scattering |
| spellingShingle | Alexander G. Ramm Scattering of Electromagnetic Waves by Many Nano-Wires Mathematics metamaterials refraction coefficient EM wave scattering |
| title | Scattering of Electromagnetic Waves by Many Nano-Wires |
| title_full | Scattering of Electromagnetic Waves by Many Nano-Wires |
| title_fullStr | Scattering of Electromagnetic Waves by Many Nano-Wires |
| title_full_unstemmed | Scattering of Electromagnetic Waves by Many Nano-Wires |
| title_short | Scattering of Electromagnetic Waves by Many Nano-Wires |
| title_sort | scattering of electromagnetic waves by many nano wires |
| topic | metamaterials refraction coefficient EM wave scattering |
| url | http://www.mdpi.com/2227-7390/1/3/89 |
| work_keys_str_mv | AT alexandergramm scatteringofelectromagneticwavesbymanynanowires |