Interplay between Dynamic Phase and Geometric Phase Determines the Circular Dichroism and Helical Dichroism.

Understanding the interaction between light and chiral nanostructures is of fundamental importance, yet the principles governing chiral interactions have remained largely phenomenological. In this work, we present a chiral field-mode (FM) matching model to quantify the circular dichroism (CD) and helical dichroism (HD) of chiral plasmonic nanostructures interacting with beams of different spin-orbit states. The chiral FM matching model posits that among the inherent resonance modes within the nanostructure, the most efficiently excited mode is the one that matches the external field structure by possessing one more node along the vibration direction, with the field structure itself being determined by the interaction between the geometric phase and dynamic phase through a Doppler-like effect. The geometric phase in this model is well-defined by the product of the winding angle of the nanohelix and the angular momenta of light, including both its spin and orbital components. Thus, the beams of different spin-orbit states excite the specific resonance mode possessing one more node compared with the field structure, resulting in the spin-related CD and orbit-related HD. This model is extended to various chiral nanocomplexes, demonstrating how the field structure determines mode excitation and offering a comprehensive explanation for the CD and HD observed in various experimental setups. This model offers insights into the CD and HD microscopy in chiral nanostructures, contributing to the advancement of the fundamental theory of chiral nanophotonics.