Design Method for Negative Refractive Index Metasurface Lenses by Using a One-Dimensional Distributed Transmission-Line Model

A design method for negative refractive index (NRI) metasurface lenses whose thickness is thinner than that of conventional NRI metamaterial ones is presented. A one-dimensional distributed transmission-line model is introduced to the design and the design formulas for determining the line length and the characteristic impedance are shown. As an example, a NRI metasurface lens operating at 1.85 GHz is designed based on the proposed method. A circuit simulation is carried out and complex voltage distributions are calculated to confirm the focusing operation of the designed lens whose thickness is sufficiently thinner than the wavelength.

I. Introduction

Negative refractive index (NRI) lenses [1], [2] have been proposed as one of the applications of NRI metamaterials [3]–[13]. To design NRI metamaterials, a composite right/left-handed transmission-line (TL) model by lumped circuit elements has often been used [3], [4], but there is an issue that many calculations to determine the structural parameters are needed since the resonant circuit elements are included in the model. As a result, the adjustment of the refractive index is difficult and the degree of freedom in the design is not very high, and therefore realizing NRI lenses by this method is not very easy. Other design methods of NRI metamaterials [5]–[9] or NRI lenses [10]–[12] also have a similar issue basically.