On the Use of Group Theory in Understanding the Optical Response of a Nanoantenna

Symmetry holds a prominent position in defining the optical response of a nanoantenna. In this work, we harness a mathematical tool, group representation theory, combine it with the eigenmode analysis for a nanoantenna, and illustrate how the symmetry allows or forbids the energetic coupling (i.e., interference) between a nanoantenna's eigenmodes. We do this especially using a nanobar structure and a symmetric cross structure. Further, the consequence of symmetry-breaking is illustrated by an asymmetric cross-shaped nanostructure, i.e., a strong asymmetric Fano-type resonance line shape due to mode interference is observed with the physics behind elaborated. Both numerical and experimental evidences are provided.