Scattering of electromagnetic waves by many thin cylinders

Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as a → 0. Here a is the radius of the cylinders. It is assumed that the points x̂m are distributed so that N (∆) = 1 a R ∆ N(x)dx[1+o(1)], whereN (∆) is the number of points x̂m = (xm1, xm2) in an arbitrary open subset of the plane xoy, the axes of the cylinders are passing through points x̂m, these axes are parallel to the z-axis. The function N(x) ≥ 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. Formula is derived for the effective refraction coefficient in the medium in which many cylinders are distributed. PACS: 03.40.Kf, 03.50 De, 41.20.Jb, 71.36.+c