On geometrical scaling of split-ring and double-bar resonators at optical frequencies

TL;DR

This paper investigates how the resonant frequency of split-ring and double-bar resonators scales at optical frequencies, revealing limitations due to metal properties and deriving formulas for small particle shapes.

Contribution

It introduces an approximate formula for the resonant frequency of split rings at visible frequencies, accounting for shape-dependent limitations.

Findings

Resonant frequency scaling breaks down at optical frequencies.

Derived an approximate formula for small split rings.

Showed the impact of particle shape on resonance limits.

Abstract

In this paper we consider the resonant frequency of split-ring resonators and double-bar resonators used to create artificial magnetic response at terahertz and optical frequencies. It is known that geometrical scaling of the resonant frequency of split rings breaks down at high frequencies (in the visible) due to electromagnetic properties of metals at those frequencies. Here we will discuss this phenomenon in terms of equivalent inductance and capacitance of the ring, derive an approximate formula for the resonant frequency of split rings in the visible and show how the limiting value of the resonant frequency of extremely small split rings and double bars depends on particle shape.