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We develop an approximate quasi-static theory describing the low-frequencyplasmonic resonances of slender nanometallic rings and configurations thereof.First, we use asymptotic arguments to reduce the plasmonic eigenvalue problemgoverning the geometric (material- and frequency-independent) modes of a givenring structure to a 1D-periodic integro-differential problem in which theeigenfunctions are represented by azimuthal voltage and polarization-chargeprofiles associated with each ring. Second, we obtain closed-form solutions tothe reduced eigenvalue problem for azimuthally invariant rings (includingtorus-shaped rings but also allowing for non-circular cross-sectional shapes),as well as coaxial dimers and chains of such rings. For more generalgeometries, involving azimuthally non-uniform rings and non-coaxial structures,we solve the reduced eigenvalue problem using a semi-analytical scheme based onFourier expansions of the reduced eigenfunctions. Third, we used theasymptotically approximated modes, in conjunction with the quasi-staticspectral theory of plasmonic resonance, to study and interpret the frequencyresponse of a wide range of nanometallic slender-ring structures underplane-wave illumination.

Plasmonic resonances of slender nanometallic rings