Multipolar analysis of second-harmonic generation in (111) Gallium Arsenide nanoparticles

We perform multipolar analysis of second-harmonic generation (SHG) from (111)-grown gallium arsenide (GaAs) nanoantennas and discuss its specifics. It was experimentally demonstrated that the conversion efficiency in axially-symmetric (111) GaAs nanoparticles remains constant under the polarization rotation of normally incident radiation in a wide range of particle sizes, while the SHG radiation pattern changes. We apply the analytical method based on the Lorentz lemma to explain this behaviour. The induced nonlinear current is decomposed into two rotating contributions, which are shown to generate multipoles of different parities. Thus, the total SHG intensity in the far-field is proved to be independent of the in-plane rotation of the pump polarization. Nevertheless, due to the threefold symmetry of the crystal with regard to the (111) direction, the SHG radiation pattern rotates around the polar axis repeating its shape every 60°.