Departure from the electric dipole approximation in small gold nanoparticles revealed by hyper-Rayleigh scattering

Polarization-resolved hyper-Rayleigh scattering is employed to uncover the far-field response in small spherical gold nanoparticles (about 15 nm). A comprehensive theoretical framework, validated against well-characterized benchmark molecules, enables the extraction of a dipolar response factor, f, from measurements under linearly, elliptically, and circularly polarized laser excitation. For these reference molecules, a factor close to unity confirms purely dipolar far-field emission, validating the method. When applied to an aqueous suspension of citrate-stabilized spherical gold nanoparticles across 800-1300 nm fundamental excitation, the analysis reveals pronounced wavelength-dependent departures from dipolar behaviour. Moreover, depolarization ratios reach values that are forbidden within the dipole approximation when the second harmonic frequency matches the plasmonic frequency. These results demonstrate a substantial multipolar contribution in small spherical gold nanoparticles, challenging the common assumption of their purely dipolar nature. Importantly, the proposed interpretation does not invoke shape anisotropy or multiple plasmonic resonances. The presented method, along with its theoretical framework, provides a broadly applicable tool for monitoring deviations from the dipolar response in both plasmonic and dielectric nanostructures in solution.