Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry

The discrete rotational symmetry of nanostructures provides a powerful and simple guiding principle for designing the second-harmonic generation process in nonlinear metamaterials. We demonstrate that, in achiral nanostructures with threefold rotational symmetries, a circularly polarized fundamental beam produces a countercircularly polarized second-harmonic beam. In this case, the polarization state of the second harmonic is determined in a very simple manner. We also demonstrate how rotational symmetries in nonlinear metamaterials manifest themselves in SHG selection rules.