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Plasmonic nanostructures with singular geometries can exhibit a broadbandscattering response that at first glance appears to violate the lower boundsfor the radiation quality (Q) factor of small radiators, known as the Chulimit. Here we explore this apparent contradiction, investigating the Q factorof the resonant modes supported by two nearly touching cylinders, and analyzehow their fractional bandwidth fares in relation to the Chu limit. We firstderive lower bounds for the radiation Q factors of two-dimensional objects ofarbitrary cross-section. We then discuss the dissipation and radiation Qfactors associated with the plasmonic resonances of a cylinder dimer as afunction of its gap size. We show that the radiation Q factor is always largerthan the minimum Q and, as long as the peaks in the scattering spectrum arewell separated, their bandwidth is equal to the inverse of their Q factor. Inthe limit of touching cylinders, the resonance spectra transition from discreteto a continuum around an accumulation point, yielding a broadband response forany finite level of material loss. Within any given frequency interval, theresponse is the result of a multitude of plasmon resonances, each individuallyobeying the Chu limit. Nevertheless, the connection between the Q factor andthe overall bandwidth of the scattering response is lost. Our study sheds lightonto the exotic resonant phenomena emerging when plasmonic materials are shapedin singular geometries, and outlines their opportunities and limitations fornanophotonics.

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