Discontinuous refractive index in metamaterial study

Abstract

This paper proposes a geometrical method to determine ambiguity that arises in metamaterials that displays discontinuity in refractive index in the frequency spectrum. Three cases of such metamaterial designs presented in literatures are investigated using the proposed method. First, numerical simulations of the three metamaterial designs are performed to extract the device parameters across the frequency spectrum and the results are compared with the reported results. Then, we investigate the refractive index discontinuity geometrically using a numerical simulation of a prism consists of the metamaterial unit cell excited by an electromagnetic plane wave. The prism simulation will allow us to confirm the refractive index discontinuity by observing the electromagnetic wave propagation at the output of the prism across the frequency spectrum of interest and determine whether the refractive index become negative at the discontinuity. Finally, the phase of an incident electromagnetic wave across the metamaterial are observed at the frequencies where the refractive index crosses over into the negative region at the discontinuities to investigate the physical behavior of the wave within and outside the boundary of the metamaterial.