Mapping directivity of coupled dimers of meta-atoms

Abstract

Arrays of coupled split ring resonators (SRRs) capable of carrying slow short-wavelength magneto-inductive waves have been shown to support the rapidly varying current distributions required for superdirectivity. However, the superposition of both electric and magnetic dipole resonance modes contributing to radiation of SRRs challenge pure physical intuition in the selection of the optimal dimer configuration reaching the maximum theoretical value of superdirectivity. In this paper a comprehensive analytical model for characterizing the radiation of dimers of coupled meta-atoms with only one element being driven is presented. The model leverage an equivalent circuit description of the coupled resonators in combination with standard radiation formulas. Based on this model, maps of directivity are produced for any orientations of two co-planar split rings resonant at about 2 GHz, leading to identifying the conditions for superdirectivity in terms of orientation and possibly size of the meta-atoms.