Electromagnetic wave scattering by many parallel to the *z**−*axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as *a **→ *0. Let *D*_{m}be the cross-section of the *m**−*th cylinder, *a *be its radius and ${\text{x ^}}_{\text{m}}{\text{}}_{}$

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Electromagnetic wave scattering by many parallel to the

*z**−*axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as

*a **→ *0. Let

*D*_{m} be the cross-section of the

*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.

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