Equivalent circuit technique for designing split ring resonator based metasurfaces

Abstract

Metasurfaces are essentially two-dimensional equivalents of metamaterials. They are artificially engineered composite structures of constituent resonators embedded on a substrate that exhibit unconventional responses to electromagnetic waves at certain frequencies when the dielectric constant and magnetic permeability are simultaneously negative. These bulk material properties govern the behavior and nature of electromagnetic propagation through the materials. Several computational models have been developed to study the different geometrical configurations of resonators and examine their collective function in metasurfaces. As such, basic equivalent circuit models and numerical solvers are based on the mathematical discretization of surfaces to achieve three-dimensional (3D) full-wave simulations of resonant structures. However, numerical solvers require significant amounts of memory storage and processing power to run simulations, particularly for an array of closely coupled resonators in metasurface designs. The direct graphic manipulation of structures in commercially available numerical solvers is demanding and time-consuming. On the other hand, the existing equivalent circuit for modelling resonators is based on the LC circuit model, which is suitable for estimating the resonance frequency but lacks a structure to describe the magnetic properties and the effects of couplings between rings and unit cells in metasurfaces. The contribution of this study is an analytically scalable lumped element equivalent circuit model of a double-split ring resonator, which is solvable by mesh analysis to simultaneously determine the resonance frequency and induce current. The model not only predicts the resonance frequency with a high degree of accuracy, but also provides a mathematical description of electromagnetic couplings between rings in single and coupled resonators. The induced current, susceptibility, and permeability were used to characterize the magnetic properties of a double-split ring resonator. These results suggest that the electrical properties of the nonmagnetic conducting material significantly affect the susceptibility of the structure. Furthermore, the coupling effects between the rings of a resonator and inter-resonator positioning can significantly alter the resonance frequency of the structure. With this method, magnetic dipoles, polarization, scattered fields, and other current-dependent parameters can be studied analytically.