Scattering of electromagnetic waves by many thin cylinders

✍ Scribed by A.G. Ramm

• Publisher: Elsevier
• Year: 2011
• Tongue: English
• Weight: 190 KB
• Volume: 1
• Category: Article
• ISSN: 2211-3797
• DOI: 10.1016/j.rinp.2011.05.002

✦ Synopsis

Electromagnetic wave scattering by many parallel to z-axis, thin, perfectly conducting, circular infinite cylinders is studied asymptotically as a ? 0. Let D m be the cross-section of the mth cylinder, a be its radius, and xm ¼ ðx m1 ; x m2 Þ be its center, 1 6 m 6 M, M = M(a). It is assumed that the points xm are distributed so that

where NðDÞ is the number of points xm in an arbitrary open subset D of the plane xoy. The function N(x) P 0 is a given continuous function. An equation for the self-consistent (efficient) field is derived as a ? 0. The cylinders are assumed perfectly conducting. A formula is derived for the effective refraction coefficient in the medium in which many cylinders are distributed. These cylinders may model nanowires embedded in the medium. Our result shows how these cylinders influence the refraction coefficient of the medium.