Effective dielectric constant and design of sliced Lüneberg lens

Abstract

In this article, a design of Lüneberg lens with slices made from low loss dielectric material with hemispherical air-holes drilled appropriately on the top and bottom surface of each of them is presented. A formula to estimate the values of radial dependent effective dielectric constant of air-holes dielectric composite material is suggested. The estimated values are compared with the ones calculated from finite difference time domain method electromagnetic simulations of a periodic lattice of spherical and cylindrical air-holes embedded in a dielectric slab using Nicolson-Ross method. Calculation of S-parameters and near field of lens with hemispherical air-holes under an incident plane wave, using estimated effective constants by the suggested formula are compared with ones using precise theoretical values of dielectric constants.