General Rules for Optical Activity in Light Scattering of Plasmonic Nanostructures

We study the general properties of optical activity of plasmonic nanostructures in theory using the eigenmode technique for light-scattering problem. Explicit formulas for the optical rotational strengths associated with the resonance modes and their sum rule are derived for plasmonic nanostructures. Moreover, relations between symmetry and optical activity are discussed. How optical activity arises from symmetry breaking is investigated by introducing dissymmetric parts to a symmetric achiral nanostructure, and a linear dependence of the optical rotational strength on the volume of dissymmetric parts is revealed. This work not only establishes a theoretical framework for studying chiral plasmonic nanostructures but also provides guidelines for tailoring their optical activities.