Description
The size-dependent optical properties of plasmonic Au spherical nanoparticles have been extensively studied using Mie’s scattering theory.1 When the particle diameter is much smaller than the wavelength of incident light (2r << λ), dipole oscillations dominate the extinction process, comprising both absorption and scattering, while higher-order multipoles are negligible. Under the dipole approximation, the extinction cross-section is determined by the nanoparticle’s polarizability, which depends on its radius, dielectric constant, and the surrounding medium. For small homogeneous Au spheres, absorption dominates over scattering, and the spectral peak corresponds to the surface plasmon resonance condition. Theoretical calculations using the dipole approximation provide accurate predictions of absorption spectra as a function of particle size, enabling the estimation of nanoparticle morphology. Deviations between theory and experiment may arise from surface defects, size-dependent energy levels, and chemical interactions with the surrounding matrix or capping agents. Overall, the dipole approximation offers a simple and effective approach for analyzing the linear optical response and size characterization of plasmonic Au nanoparticles.