Line position and quality factor of plasmonic resonances beyond the quasi-static limit: A full-wave eigenmode analysis route

In this study, we introduce a rigorous full-wave eigenmode analysis technique based on a volumetric method of moments to the optical spectrum. We first apply this technique to a nanorod as an example to illustrate how the real part of the eigenfrequency and the modal quality factor (defined as the ratio of the real part of the eigenfrequency to the imaginary part) together with the eigenmode determine the line position and quality factor of a resonance and the corresponding resonant mode. Then, the eigenfrequencies and eigenmodes of a composite plasmonic nanostructure, a Dolmen, and its two individual constituents, a dimer and a monomer, are extracted. The line position of the Fano dip in Dolmen's spectrum is discussed by examining the relative positions of the eigenfrequencies of the dimer and the monomer in the complex plane. Further, the formation of the Fano dip is reinterpreted as the destructive interference between the nonorthogonal eigenmodes of the whole Dolmen structure. The proposed full-wave modal analysis brings a new perspective on understanding and designing the plasmonic response of nanoantennae beyond the quasi-static limit.