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# Scattering of Electromagnetic Waves by Many Nano-Wires

Received: 10 May 2013; in revised form: 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**be the cross-section of the*_{m}*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 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

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**MDPI and ACS Style**

Ramm, A.G. Scattering of Electromagnetic Waves by Many Nano-Wires. *Mathematics* **2013**, *1*, 89-99.

**AMA Style**

Ramm AG. Scattering of Electromagnetic Waves by Many Nano-Wires. *Mathematics*. 2013; 1(3):89-99.

**Chicago/Turabian Style**

Ramm, Alexander G. 2013. "Scattering of Electromagnetic Waves by Many Nano-Wires." *Mathematics* 1, no. 3: 89-99.

*Mathematics*EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert