Effective Permittivity and Permeability of a Fibers Grating

Abstract

ABSTRACT A diffraction problem for a grating consisting of thin parallel cylinders (fibers) is considered in the low frequency approximation. Relative permittivity and permeability are supposed to be constant in each fiber. An electric field vector of an incident plane wave is parallel to the fibers. Results of this approximation are compared with the field scattered by a homogeneous hypothetical layer. Thus, its relative effective permittivity (εe ), permeability (µe), refractive index (ηe), and impedance (z e) are determined. It has been shown that such an equivalent material is sometimes characterized by negative values of either Im(εe ) or Im(µe) (with the time dependence e−iωt), and may be interpreted as a medium with an internal generation.