Symmetry Cancellations in the Quadratic Hyperpolarizability of Non-Centrosymmetric Gold Decahedra

We report the second harmonic response of non-centrosymmetric gold decahedra with four different sizes, (side length between 17 and 150 nm). We show that, for small sizes, symmetry cancellations occur, leading to quadratic hyperpolarizabilities similar to that of gold spherical nanoparticles despite the non-centrosymmetric shape of the particles. For larger sizes, the quadratic hyperpolarizabilities scale with the volume of the particles, as expected from the multipolar contribution arising from the field retardation effects.