Second harmonic generation from small gold metallic particles: from the dipolar to the quadrupolar response

Hyper Raleigh scattering, a common technique to investigate the second harmonic light scattered from a liquid suspension of molecular compounds and to determine their quadratic hyperpolarizability, has been used for aqueous suspensions of gold nanoparticles, the diameter of which ranges from 20 up to 150 nm. The hyper Rayleigh signal intensity was recorded as a function of the angle of polarization of the incident fundamental wave. For the particles with a diameter smaller than 50 nm, the response is dominated by the dipolar contribution arising from the deviation of the particle shape from that of a perfect sphere. For larger diameter particles, retardation effects in the interaction of the electromagnetic fields with the particles cannot be neglected any longer and the response deviates from the pure dipolar response, exhibiting a strong quadrupolar contribution. It is then shown that in order to quantify the relative magnitude of these two dipolar and quadrupolar contributions, a weighting parameter zeta(V) which equals unity for a pure quadrupolar contribution and vanishes for a pure dipolar response, can be introduced.