Numerical studies of left handed metamaterials

TLDR: In this article, the authors used the three dimensional finite difference time domain (FDTD) technique to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands.

Abstract: We use the three dimensional Finite Difference Time Domain (FDTD) technique to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands. The structure under study is the well-known periodic arrangement of rods and split-ring resonators, previously used in experimental setups. The three parameters we study are the transmission coefficient of a slab, the phase variation of the propagating fields within the metamaterial, and the refraction of a wave through a prism. To our knowledge, this is the first time that the last two parameters are studied rigorously using a numerical method. The results of this work show that fields propagating inside the metamaterial with a forward power direction exhibit a backward phase velocity and negative index of refraction.