Reflectance and absorbance of all-dielectric metamaterial composites with fractal boundaries: A numerical investigation

Abstract

Two-dimensional two-phase heterostructures have been the subject of many investigations including computer simulations. An outstanding issue is the shape analysis of the reflectance for dielectric inclusions of arbitrarily complex geometry. We report on finite element numerical calculations to investigate the effects a fractal-shaped object having an intrinsic complex permittivity with a negative real part embedded in a host matrix with real and positive permittivity can have on reflectance and absorbance of a uniform plane wave impinging on it. The simulations were performed at a wavelength much larger than the length scales of the inhomogeneities. The reflectance and absorbance of the structures are shown to be highly sensitive to the details of the fractal metamaterial environment and to its intrinsic loss. We comment on how these results may be used to provide a quantitative framework for the design, selection, and optimization of artificial metamaterial microwave reflectors and other complex systems yet to be explored.