  Optical materials with centrosymmetry, such as silicon and germanium, are
unfortunately absent of second-order nonlinear optical responses, hindering
their developments in efficient nonlinear optical devices. Here, a design with
an array of slotted nanocubes is proposed to realize remarkable second harmonic
generation (SHG) from the centrosymmetric silicon, which takes advantage of
enlarged surface second-order nonlinearity, strengthened electric field over
the surface of the air-slot, as well as the resonance enhancement by the bound
states in the continuum. Compared with that from the array of silicon nanocubes
without air-slots, SHG from the slotted nanocube array is improved by more than
two orders of magnitude. The experimentally measured SHG efficiency of the
silicon slotted nanocube array is high as 1.8*10^-4 W^-1, which is expected to
be further engineered by modifying the air-slot geometries. Our result could
provide a new strategy to expand nonlinear optical effects and devices of
centrosymmetric materials.
