Conservation of optical chirality in nanoscale light-matter interactions: A study of the Born-Kuhn model system

Optical chirality density is a measure of the local handedness of electromagnetic fields. Like energy density, it may be absorbed or scattered through the interaction between light and matter. Here we utilize the conservation of optical chirality to connect the parity and time-reversal symmetries of the intrinsic excitational eigenmodes of a material to those of their associated electromagnetic eigenfields as dictated by Maxwell's equations. To make this connection explicit, we theoretically examine the Born-Kuhn (BK) system, composed of a pair of plasmonic nanorods of variable separation, as a prototypical material model that is both geometrically chiral in its static structure and truly excitationally chiral in its eigenexcitations and eigenfields. By relaying optical chirality metrics of the BK eigenfields back to their underlying sourcing material degrees of freedom, we derive a unique mechanical chirality measure that is related to, but distinct from, other pseudoscalar metrics recently discussed in the literature. Beyond analysis in the absence of sources, we further derive optical chiral extinction, scattering, and absorption cross sections under external drive and discuss their rigorous connection to more common circular dichroism measurements as well as their limitations in comparison to eigenfield chirality metrics. Finally, we investigate the conversion of achiral linearly polarized light into chiral elliptically polarized light through interaction with the BK system, illustrating the conservation of optical chirality in the interaction between light and matter through an analytically tractable example.