A two-dimensional uniplanar transmission-line metamaterial with a negative index of refraction

A uniplanar transmission-line (TL) network has been loaded with lumped elements (chip or printed), enabling one to achieve a two-dimensional (2D) uniplanar negative-refractive-index (NRI) metamaterial. The metamaterial consists of a 2D array of unit cells, composed of TL sections connected in series and loaded in a specified manner. The unit cell dimensions can be designed to be much smaller than the operating wavelength, enabling one to identify the structure as an effective medium, with a negative index of refraction. This NRI metamaterial supports transverse electric (TE) waves, as opposed to related previous work on NRI-TL media that supported transverse magnetic (TM) waves. The dispersion characteristics are calculated using a simple, fast 2D loaded TL model with periodic (Bloch) boundary conditions. Subsequently the dispersion relation is simplified in the homogeneous limit, thus allowing one to identify effective permittivities and permeabilities, which are shown to be simultaneously negative. Simulations demonstrating the negative refraction of a plane wave on an interface between such a NRI uniplanar metamaterial and a commensurate positive-refractive-index (PRI) metamaterial verify the validity of the proposed concept and theory. A fully printed unit cell is presented at microwave frequencies (∼10 GHz) along with a prescription for synthesizing an isotropic 3D transmission line NRI metamaterial based on this unit cell