Near-field interaction of twisted split-ring resonators

We present experimental, numerical, and analytical results for the study of near-field interaction of twisted split-ring resonators, the basic elements of the so-called stereometamaterials. In contrast to previous results, we observe a crossing point in the dispersion curves where the symmetric and antisymmetric modes become degenerate. We introduce a model to describe the interplay between magnetic and electric near-field interactions and demonstrate how this model describes the crossing of the dispersion curves, initially considering lossless identical resonators. Finally, we apply the theory of Morse critical points to demonstrate the competition between losses and differences between the rings in determining whether or not the symmetric and antisymmetric modes cross.