Modal Analysis and Wave Propagation in Finite 2D Transmission-Line Metamaterials

In this paper we examine the propagation of plane waves and Gaussian beams in 2D periodic grids constructed with lumped reactive immitances. We demonstrate the equivalence between the Bloch/Floquet modal description and the multiple coupled-line modal analysis of finite-sized periodic grids. This establishes that the Floquet analysis of 2D metamaterial negative-refractive-index grids and the associated exotic wave propagation/refraction/focusing phenomena, can be deduced from traditional analysis of M coupled lines (and hence M eigenmodes), albeit with considerable algebraic complexity. We present simulation results of Gaussian beams through these grids to demonstrate that they can be analyzed using simple geometrical optics along with the index of refraction associated with Bloch/Floquet analysis.