  Nonlinear processes are often governed by selection rules imposed by the
symmetries of the molecular configurations. The most well-known examples
include the role of mirror symmetry breaking for the generation of even
harmonics, and the selection rule related to the rotation symmetry in harmonic
generation for fundamental beams with circular polarizations. While the role of
mirror symmetry breaking in second harmonic generation has been extensively
studied in plasmonic systems, the investigation on selection rules pertaining
to circular polarization states of harmonic generation has been limited to
crystals, i.e. symmetries at the atomic level. Here we demonstrate the
rotational symmetry dependent third harmonic generation from nonlinear
plasmonic metacrystals. We show that the selection rule can be imposed by the
rotational symmetry of meta-crystals embedded into an isotropic organic
nonlinear thin film. The results presented here may open new avenues for
designing symmetry-dependent nonlinear optical responses with tailored
plasmonic nanostructures.
