Periodic analysis of a 2-D negative refractive index transmission line structure

The propagation characteristics of a two-dimensional (2-D) negative refractive index (NRI) transmission line (TL) structure are explained using Bloch theory. Bloch analysis of a generalized 2-D periodic electrical network is performed and the results are applied to the NRI TL structure. A 2-D Brillouin diagram of the NRI TL metamaterial is presented and its band structure is intuitively explained. Voltage and current relationships, Bloch impedance expressions and dispersion equations which aid in the design, proper excitation and termination of such structures are derived. Effective material parameters for regions of isotropic and homogeneous operation are also derived, providing a simplified understanding of the NRI TL metamaterial's 2-D band structure. Finally, simulations of negative refraction for a relative refractive index of n=-1 are shown. The simulation results verify the analytic expressions presented in this paper and demonstrate the proper termination and excitation of finite size structures.