Second-Order Nonlinear Circular Dichroism in Square Lattice Array of Germanium Nanohelices

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 nonstructured Ge thin film, revealing
the influence of interaction between nanohelices. In particular, nonlinear
circular dichroism, characterized through the SHG anisotropy factor gSHG–CD, changed its sign not only with
the helix handedness but also 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.