Light-Matter Interaction at the Nanoscale: From Rayleigh Scattering to Mie Resonance

Abstract

Light–matter interaction at the nanoscale underpins many emerging technologies such as nanosensors, photovoltaic devices, and nanophotonics. At subwavelength scales, traditional scattering models transition from simple Rayleigh scattering to complex Mie resonances, dramatically altering optical responses. This research systematically explores this transition, establishing unified analytical models, numerical simulations, and experimental validations. Beginning with Rayleigh's r⁶‑scaling with particle radius in the dipole limit, we expand into Mie theory for spherical nanoparticles of varying sizes and refractive indices. By deriving resonance conditions for electric and magnetic multipole modes, we reveal size-dependent optical cross-sections and resonance tunability. Simulated field distributions using finite‑difference time‑domain (FDTD) and discrete dipole approximation (DDA) methods reveal plasmonic hot spots in metallic particles and high‑Q dielectric resonances sensitive to shape perturbations. Experimental measurements on colloidal gold and silicon nanoparticles validated the predicted scattering spectra and near‑field enhancements. Our findings indicate that carefully engineered nanospheres can transition from Rayleigh‑like broadband scatterers to Mie‑resonant elements with narrowband, directionally selective responses. These insights enable optimization strategies for enhanced light harvesting, sensing, and nanoscale energy conversion. This work offers a comprehensive understanding of the fundamental optical behavior of subwavelength particles, guiding design principles for next-generation nanophotonic devices.