  Metasurface, a kind of two-dimensional structured medium, represents a novel
platform to manipulate the propagation of light at subwavelength scale. In
linear optical regime, many interesting topics such as planar metalens,
metasurface optical holography and so on have been widely investigated.
Recently, metasurfaces go into nonlinear optical regime. While it is recognized
that the local symmetry of the meta-atoms plays vital roles, its relationship
with global symmetry of the nonlinear metasurfaces remains elusive. According
to the Penrose tiling and the newly proposed hexagonal quasicrystalline tiling,
here we designed and fabricated the nonlinear optical quasicrystal metasurfaces
based on the geometric phase controlled plasmonic meta-atoms with local
rotational symmetry. The second harmonic waves will be determined by both the
tiling schemes of quasicrystal metasurfaces and the local symmetry of
meta-atoms they consist of. The proposed concept opens new routes for designing
nonlinear metasurface crystals with desired optical functionalities.
