Miniaturization and control of split ring structures from an analytic solution of their resonance

TL;DR

This paper presents an analytic approach to determine the resonance spectra of split ring structures, enabling precise miniaturization and control of their electromagnetic properties, validated by simulations.

Contribution

It introduces polynomial equations for resonance spectra and demonstrates linear dependence of resonance frequency on ring separation, advancing split ring design.

Findings

Resonance frequency depends linearly on ring separation.

The lowest resonance wavelength can match the ring size.

Simulations confirm the analytic predictions.

Abstract

We derived simple polynomial equations to determine the entire resonance spectra of split ring structures. For double stacking split rings made with flat wires, we showed that the resonance frequency depends linearly on the ring-ring separation. In particular, we found that the wavelength of the lowest resonance mode can be made as large as the geometrical size of the ring for realistic experimental conditions, whereas for current systems this ratio is of the order of 10. Finite-difference-time-domain simulations on realistic structures verified the analytic predictions.