Interplay between\nDynamic Phase and Geometric Phase\nDetermines the Circular Dichroism and Helical Dichroism

Understanding the interaction between light and chiral\nnanostructures\nis of fundamental importance, yet the principles governing chiral\ninteractions have remained largely phenomenological. In this work,\nwe present a chiral field-mode (FM) matching model to quantify the\ncircular dichroism (CD) and helical dichroism (HD) of chiral plasmonic\nnanostructures interacting with beams of different spin–orbit\nstates. The chiral FM matching model posits that among the inherent\nresonance modes within the nanostructure, the most efficiently excited\nmode is the one that matches the external field structure by possessing\none more node along the vibration direction, with the field structure\nitself being determined by the interaction between the geometric phase\nand dynamic phase through a Doppler-like effect. The geometric phase\nin this model is well-defined by the product of the winding angle\nof the nanohelix and the angular momenta of light, including both\nits spin and orbital components. Thus, the beams of different spin–orbit\nstates excite the specific resonance mode possessing one more node\ncompared with the field structure, resulting in the spin-related CD\nand orbit-related HD. This model is extended to various chiral nanocomplexes,\ndemonstrating how the field structure determines mode excitation and\noffering a comprehensive explanation for the CD and HD observed in\nvarious experimental setups. This model offers insights into the CD\nand HD microscopy in chiral nanostructures, contributing to the advancement\nof the fundamental theory of chiral nanophotonics.