Equivalent circuit technique for designing split ring resonator based metasurfaces

Metasurfaces are two-dimensional artificially engineered structures capable of manipulating the phase, direction and orientation of electromagnetic waves by exhibiting simultaneously negative values of permittivity and permeability. These unconventional properties have been tailored and explored in many applications such as in bio-sensors, waveguides and antennas. The split ring resonators are the commonly used constituent meta-atoms of metasurfaces whose design and analysis rely on commercially available numerical electromagnetic fields (EM) solvers and experimental analysis. These numerical EM solvers are based on meshing and partitioning of graphical structures into the desire grids or patches to solve Maxwell equations in discrete form. However, graphical rendering and meshing of 3D objects requires significant space-time computational resources to analyze the structure. With the cost of licenses of EM solvers being very expensive, analytical solution were explored. The use of LC resonant frequency analytical formula provides an approximate value of resonant frequency which is less accurate and does not gives information about the current characteristics induced on the constinuent meta-atom of a metasurface. This paper presents an analytical approach to the design and analysis of a doubly split double rings (DSRR) using lumped element equivalent circuit that can be solved by mesh network analysis. The resonant frequency is extracted from the induced current characteristics which agrees with simulations and experimental results. The resonant frequency errors for a single DSRR unit cell ranged from1.05% to 7%, and for two coupled DSRR unit cells, they ranged from 1.4% to 11%.