On the bandwidth of singular plasmonic resonators in relation to the Chu limit

TL;DR

This paper investigates how singular plasmonic nanostructures, specifically nearly touching cylinders, can exhibit broadband scattering responses that challenge traditional bounds like the Chu limit, revealing complex resonance behaviors.

Contribution

The study derives bounds for radiation Q factors of 2D objects, analyzes plasmonic resonances in cylinder dimers, and explains broadband responses in singular geometries.

Findings

Radiation Q factor always exceeds the minimum Q.

Bandwidth is inversely proportional to Q when peaks are well separated.

Touching cylinders produce broadband spectra due to continuum resonances.

Abstract

Plasmonic nanostructures with singular geometries can exhibit a broadband scattering response that at first glance appears to violate the lower bounds for the radiation quality (Q) factor of small radiators, known as the Chu limit. Here we explore this apparent contradiction, investigating the Q factor of the resonant modes supported by two nearly touching cylinders, and analyze how their fractional bandwidth fares in relation to the Chu limit. We first derive lower bounds for the radiation Q factors of two-dimensional objects of arbitrary cross-section. We then discuss the dissipation and radiation Q factors associated with the plasmonic resonances of a cylinder dimer as a function of its gap size. We show that the radiation Q factor is always larger than the minimum Q and, as long as the peaks in the scattering spectrum are well separated, their bandwidth is equal to the inverse of their Q factor. In the limit of touching cylinders, the resonance spectra transition from discrete to a continuum around an accumulation point, yielding a broadband response for any finite level of material loss. Within any given frequency interval, the response is the result of a multitude of plasmon resonances, each individually obeying the Chu limit. Nevertheless, the connection between the Q factor and the overall bandwidth of the scattering response is lost. Our study sheds light onto the exotic resonant phenomena emerging when plasmonic materials are shaped in singular geometries, and outlines their opportunities and limitations for nanophotonics.