Subwavelength hexahedral plasmonic scatterers: History, symmetries, and resonant characteristics

In this work, we investigate the resonant characteristics of hexahedral (cubical) inclusions at the plasmonic domain. After an introduction to the notion of superquadric surfaces, i.e., surfaces that model various versions of a rounded cube, we present the main resonant spectrum and the surface distributions for two particular cases of a smooth and a sharp cube in the plasmonic domain. We present a historical comparative overview of the main contributions available since the 1970s. A new categorization scheme of the resonances of a cube is introduced, based on symmetry considerations. The obtained results are compared against several recent works, exposing that the higher-order modes are extremely susceptible to both the choice of sharpness of the cube and the modeling mesh. This work can be readily used as a reference for both historical and contemporary studies of the plasmonic aspects of a cube.