Unified description of Fano resonances in excitonic nanostructures across multiple geometries

The optical properties of excitonic materials can be described by an excitonic dielectric function consisting of a background dielectric constant and a Lorentzian term associated with the exciton transition. In excitonic nanostructures, the background dielectric constant is expected to produce a nonresonant response, whereas the excitonic term is expected to yield a resonant response; interference between these contributions has been proposed as the origin of Fano line shapes across different geometries. To test this scenario and establish a unified description, we develop a general theoretical formalism and apply it to light-scattering spectra of excitonic spheres and cylinders, as well as the reflection spectra of excitonic slabs. Calculations for a sphere and a cylinder with radii of 40 nm and for a 40 nm-thick slab show that all these nanostructures show similar asymmetric line shapes superposed on monotonically increasing background spectra. When the spectra are normalized to the background spectra, they exhibit Fano profiles arising from interference between a constant background component and a resonant excitonic component described by a complex Lorentzian function. These results demonstrate that the general formalism provides a unified framework for identifying the common origin of the Fano resonances in excitonic nanostructures of different geometries.