Flat bands in metamaterials based on angularly layered metal–dielectric scatterers

In this work, we propose the realization of electromagnetic metamaterials in two and three dimensions by means of highly anisotropic rods and spheres. The two-dimensional case is deeply analyzed, and the realization of an anisotropic rod by means of angularly layered cylinders is proposed. The band structure of a periodic arrangement of angularly layered rods is computed, showing a low frequency band gap and some flat modes within it which increases as a function of the number of sectors in the cylinder. The system is studied by means of an effective medium approach, and it is found that the flat bands correspond to a sharp frequency region where the effective metamaterial is doubly negative. A perfect agreement is found between the dispersion curves obtained by means of the effective medium model and the full band structure computed by the finite element method. It is also found that only four sectors in the angularly layered cylinder are enough to obtain the desired double negativity, which is a promising result in view of the fabrication of the presented structures. Finally, the three-dimensional version of these materials is analyzed by means of anisotropic spheres, showing similar results. (paper)