  Second harmonic generation (SHG) is prohibited in centrosymmetric crystals
such as silicon or germanium due to the presence of inversion symmetry.
However, the structuring of such materials makes it possible to break the
inversion symmetry, thus achieving generation of second-harmonic. Moreover,
various symmetry properties of the resulting structure, such as chirality, also
influence the SHG. In this work we investigate second harmonic generation from
an array of nanohelices made of germanium. The intensity of the second harmonic
displayed a remarkable enhancement of over 100 times compared to a
non-structured Ge thin film, revealing the influence of interaction between
nanohelices. In particular, nonlinear circular dichroism, characterized through
the SHG anisotropy factor g, changed its sign not only with the helix
handedness, but with its density as well. We believe that our discoveries will
open up new paths for the development of nonlinear photonics based on
metamaterials and metasurfaces made of centrosymmetric materials.
