An approximation for reflection and transmission coefficients of periodic arrays of metal rings and circular slots

Abstract

As long as the wavelength of the incident electromagnetic wave is larger than the unit cell, electromagnetic properties of metamaterials and meta-sheets can be approximated by equivalent circuit models. These models consist of reactances and capacitances with values that can be estimated analytically only for several specific particle shapes. For metal circular rings, which are the focus of our study, the equivalent circuit model has not been developed yet. In this study the complex reactance and capacitance are described by Taylor series in terms of the radius of the ring. The corresponding analytical transmission function is fitted to full-wave simulations to determine the coefficients of the expansion. By using the Babinet principle, the reflection coefficient of the complementary structure (periodic array of circular slots in a metal screen) is obtained from the transmission coefficient of the ring array without recalculation. It is assumed that the influence of the thin dielectric substrate and of the thickness of the planar particle on reflection/transmission can be neglected. The developed approximation is used to describe the bandpass and bandstop behavior of meta-sheets in the microwave frequency range.