Wave propagation in metamaterial structures and retrieval of homogenization parameters

Abstract

Electromagnetic wave propagation in metamaterial structures (metamaterial slabs, metamaterial cylinders, metamaterial coated conducting cylinders etc.) are investigated. Scattered and transmitted electromagnetic fields by these structures due to electric line sources or plane wave illuminations are found. A generic formulation of these wave propagation problems is done, enabling any kind of metamaterial or conventional material to be used, having any sign combination of constitutive parameters and having any electric and/or magnetic losses. For one of these propagation problems i.e., metamaterial coated conducting cylinders illuminated normally with plane waves, achieving transparency and maximizing scattering are investigated thoroughly. It is found out that, rigorous derivation of transparency and resonance (scattering maximization) conditions for PEC core cylinder case under the sub-wavelength limitations yields the same conditions of two electrically small concentric layers of conjugately paired cylinders, given in the literature (when the inner core layer is also taken to the PEC limit). These transparency and resonance conditions are found to be heavily dependent on the permittivity of the metamaterial coating (for TE polarization) and the ratio of core-shell radii. The relations between the permittivity of the coating and the ratio of core-shell radii are investigated for achieving transparency and scattering maximization. Numerical results show that these analytical relations are quite successful and work better when the cylindrical scatter is electrically very small. A novel homogenization method for the retrieval of effective constitutive parameters of metamaterials is proposed and implemented. The method is based on the simple idea that the total reflection coefficient from a finite metamaterial structure has to resemble the reflection from an homogeneous equivalent. While implementing the method, 1, 2, . . ., 20 unit cells of the same metamaterial structure are stacked and their reflection coefficients are collected. The homogenization quality of the metamaterial is evaluated in terms of various factors, which showed that the method is very successful to retrieve the effective constitutive parameters of the metamaterial. Finally, another method has been proposed for the retrieval of surface wave propagation constants on any periodic or non-periodic grounded slab medium. As a preliminary, the method is applied to grounded dielectric slabs. The numerical results generally show good agreement with their theoretical counterparts.